Trivial Questions From Newbies

Topics: General
Dec 5, 2011 at 11:30 AM

Best Wishes for all the Orchard Community. At the moment following two trivial questions tickle me, the replies to which may improve my competence:

1. There are three recipies Blog, Default and Core in Orchard. When there is a separate Recipie for BLOG. What is the logic for having "Blog Options" EVEN  in Core and Default Recipies. What is the difference between the both rather three choices for creating Blogs.

2.The words Data and Content ( in CMS and Database) seem to be synonymous in meaning. What is the  difference between a CMS and Database?

Any member of the Community is requested to oblige me.

Dec 5, 2011 at 3:35 PM

1. I'm not really sure I get the question. The recipes decide what modules, features and content types are enabled by default when you install Orchard. If you select Core then you only get a bare minimum, although you can always enable the blog module later on, for instance. You can also create your own recipes to add to the list. They're in Orchard.Setup\Recipes if you want to see what's in them.

2. They're not at all synonymous. Data can mean really any type of information, and usually specifically in the context of an SQL database, which is a storage mechanism. Content is just one of the types of data Orchard (and all CMSs) store in their database. Although in Orchard, "content" has a very wide meaning, and a lot of unexpected types of data are actually stored as content behind the scenes (e.g. User and Site). However, content has a much broader meaning than that - when Orchard refers to Content Items it is specifically talking about database content, but it can also mean content files, e.g. media. So, a CMS is a tool for interacting with all those kinds of content.

Dec 7, 2011 at 6:55 AM

Thank you very much Randompete! for a quick reply.

Since then, another trivial question has propped up:

1. When creating  buttons  for my pages in a horizontal line at the top of my Orchafrd Web Site.  second line of button is initiated when first line finishes. But I want the buttons to be aligned vertically. I tried to enroce my will by manipulating order in Navigation thru Dashboard by inserting order like 1.2, 1.2 & 1.3 but it did not work. The question is how to create  a vertical order instead of a horizontal order in button of pages?

2. What I understad for enabling Blogging function in Non-Blog Recipies is (a speculation!)  that after opting for Core or Detault Recipes and going ahead, when one feels the need to revert to Blog Recipe, it may be waste of time and labour to discard current project to resurme the project anew by Bog Recipe. But the question remains the same: What is the difference between the (1) using the Blog Recipes at the very outset and (2) and Enabling Blog in a Default OR Core Recipe.     Is the difference Qualitative or Quantitative in nature. I presume the difference is  only Quantitaive. This raises another question. What is the ratio between these two quantities  e.g. (1) a tea spoonful ( or a pot)  of blog by enabling it   and (2)  Bringing in a Full Qualdron of Blogging Functionality in the Shpae of BLOG RECIPIE?

 

 

Dec 7, 2011 at 10:41 AM

Hi Randompete!  thank you again. I have got a couple of other trivial questions:

1. I use tags as links within a text page. If we are to use more than one tag, how can we separate them? Because otherwise they are selected all at once.

2.How can we give different color to the text of different pages? Can it be done through Site.css? What about changing the color of buttons on the home page.

Dec 7, 2011 at 1:10 PM

1. Use CSS styling to make the button list vertical (hint - float:none)

2. Everything the Blog recipe does can be done manually from the admin. Additionally, you can always run the recipe later on. Just open up the Orchard command line and type "recipes execute Setup Blog". All the recipe does is add a few extra Parts to the BlogPost content type, set some default settings, and create some default layers and widgets as example content. This can all be done by hand in the admin. If you enable the "Content Types" feature then you get a new tab on the "Content" menu which allows you to edit all the content types and add/remove parts from them and configure settings.

P.S. You get bonus points for use of the word "qualdron"! ;)

3. Tags should be comma-separated: tag1, tag2, tag3

4. There are various ways to apply different styles around the site, which one is best depends on how much you want to change. You can create separate version of your Theme (in Theme.txt there is a BasedOn property so you can inherit everything from another theme) and then use Vandelay Industries Theme Switcher feature to change to different themes on different Urls. Or for smaller, simpler changes, you could use the Url Alternates so you can define different override templates on different urls. Another way is to apply a CSS class to the root of the page depending on the url or content, then use that CSS class to apply whatever styles in Site.css. There are loads of other ways to do it as well, so it depends on exactly what you need to change.

 

Dec 7, 2011 at 4:08 PM

Hi Randompete!

Thank you very much for A Very Revealing & Magnanimous Response to my queries. First of all I applied what you told about Tags. I succeeded in that NOW ONLY required tag is selected. But when I click it “Contents tagged with - - - “ is shown at the top but the tagged text is not pulled up. This is a completely text file (30 pages) and I tag the Headings in the page and expect that the relevant text becomes visible for the users. Is not it that some Html links have to created in the back end OR I’m missing some simple action.


 

Dec 7, 2011 at 4:24 PM

The tag routes should work automatically. I'm wondering if this is a localization issue. What culture are your tags in?

Dec 8, 2011 at 3:16 AM

English.

Dec 8, 2011 at 3:16 AM

English.

Dec 8, 2011 at 3:28 AM

Have you changed any files, using a custom theme, using any modules? You might have changed something by accident.

If not, can you maybe post a screenshot, in case I'm not clear on what's wrong.

Dec 8, 2011 at 4:50 AM

On my own I did the following:

1. The headings were in caps and underlined. I removed there underlinging and converted the Tags to Caps.

2. Also there were empty brackets before the headings which I deleted.

3. SPECIAL INDICATION: When I changed the smalls to caps in Tag Slot, only one tag changed  to caps but when i tried to correct its order  -  IT JUST WON'T inspite of repeated efforts. Besides , also the other tags (3) just defy a chnage from  smalls to caps no matter how far you go to change them.

4.  No, I did nothing. Steering clear of deep waters(themes+modules), I plan to have 8 or 10 buttons on my home page, 4 for text files and 4 or 5 for blogs. Nex I would like to seek your advise how far to cut the tail to get rid of "messiness" or "heavy-ness" to make  the WS lightweight and user-friendly.

Thank you very much for continued cooperation.

Dec 8, 2011 at 4:53 AM

Well I'm pretty stumped to be honest ... can you post a screenshot so I can see the problem, along with the source code that you changed?

Dec 8, 2011 at 7:10 AM

I did not change any code. I tried my level best to send the Updated Html of the text file. Isn't the same thing that you say "Source Code". Perhaps the file is too long to be sent at one stroke. I  tried to send the file in two parts. But failed. I may e-mail it to you as an attachment. How you suggest to manage it then.

Thank you.

Dec 8, 2011 at 7:34 AM

If you click the source code button which looks like </> then you can paste the HTML into the left pane.

Dec 8, 2011 at 12:58 PM

I did what you bid but had :"Codeplex is not responding due to a long-running script" from the browser.

Dec 8, 2011 at 1:50 PM

Which browser are you using? Try a different one...

Dec 8, 2011 at 4:21 PM
Edited Dec 16, 2011 at 10:59 AM

I was using 1E-9 but  few days back I started using  Chrome. It seems better because now the complaint :"Codeplex is not responding due to a long-running script" is not returned. Below is given the Updated Html for a page entitled: " Books Recommended". I have inserted many tags. All are shown but none pulls the text up. Please suggest some further remedy:  

 

<p></p>
<p style="margin: 6pt 0in; line-height: normal; mso-add-space: auto;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; mso-bidi-font-size: 12.0pt; mso-ansi-language: EN-GB;" lang="EN-GB">Books Recommended:<o:p></o:p></span></b></p>
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<p style="margin: 0in 1.3pt 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l0 level1 lfo1;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">1.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Swokowski. E. W., &lsquo;<i>Fundamentals of Algebra and Trigonometry</i>&rsquo;, Latest Edition.<o:p></o:p></span></p>
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<p style="margin: 0in 19.3pt 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l0 level1 lfo1;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">2.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Kaufmann. J. E., &lsquo;<i>College Algebra and Trigonometry</i>&rsquo;, PWS-Kent Company, <st1:city w:st="on"><st1:place w:st="on">Boston</st1:place></st1:city>, Latest Edition.<o:p></o:p></span></p>
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<p style="margin: 0in 19.3pt 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l0 level1 lfo1;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">3.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Walpole, R. E., &lsquo;<i>Introduction of <span style="color: black;">Statistics</span></i><span style="color: black;">&rsquo;, </span>Prentice Hall, Latest Edition.<o:p></o:p></span></p>
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<p style="margin: 0in 19.3pt 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l0 level1 lfo1;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">4.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Wilcox, R. R., &lsquo;<i><span style="color: black;">Statistics for The Social Sciences&rsquo;</span></i><span style="color: black;">, </span><o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></b></p>
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<p style="margin: 0in 0in 0pt;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></b></p>
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<p style="margin: 0in 0in 0pt;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">5.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; mso-bidi-font-size: 10.0pt;">MATHEMATICS FOR CHEMISTRY</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p></o:p></span></b></p>
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<p style="margin: 0in 0in 0pt; text-align: center;" align="center"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Credit Hours:</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; mso-bidi-font-size: 12.0pt;"><span style="mso-tab-count: 2;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">3<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Prerequisites:</span></b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><span style="mso-tab-count: 2;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Mathematics at Secondary level<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 14pt; mso-bidi-font-size: 10.0pt;">Specific Objectives of Course:<o:p></o:p></span></b></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">To prepare the students not majoring in mathematics with the essential tools of Calculus to apply the concepts and the techniques in their respective disciplines. <o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; mso-bidi-font-size: 12.0pt;">Course Outline:<o:p></o:p></span></b></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><i style="mso-bidi-font-style: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Preliminaries:</span></i><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"> Real Numbers and the Real Line, <i style="mso-bidi-font-style: normal;">Functions and their graphs</i>: Polynomial Functions, Rational Functions, Trigonometric Functions, and Transcendental Functions. Slope of a Line, Equation of a Line, Solution of equations involving absolute values, Inequalities. <i style="mso-bidi-font-style: normal;">Limits and Continuity:</i> Limit of a Function, Left Hand and Right Hand Limits, Continuity, Continuous Functions. <i style="mso-bidi-font-style: normal;">Derivatives and its Applications:</i> Differentiation of Polynomial, Rational and Transcendental Functions, Extreme Values of Functions. <i style="mso-bidi-font-style: normal;">Integration and Indefinite Integrals:</i> Integration by Substitution, Integration by Parts, Change of Variables in Indefinite Integrals. Least-Squares Line.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 6pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; mso-bidi-font-size: 12.0pt;">Recommended Books:<o:p></o:p></span></b></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">1.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Thomas, Calculus, 11<sup>th</sup> Edition. Addison Wesley publishing company, 2005.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">2.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">H. Anton, I. Bevens, <st1:place w:st="on">S. Davis</st1:place>, Calculus, 8<sup>th</sup> edition, Jhon Willey &amp; Sons, Inc. 2005.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">3.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Hughes-Hallett, Gleason, McCallum, et al, Calculus Single and Multivariable, 3<sup>rd</sup> Edition. John Wiley &amp; Sons, Inc. 2002.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">4.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Frank A.Jr, Elliott Mendelson, Calculus, Schaum&rsquo;s<span style="mso-spacerun: yes;">&nbsp; </span>Outline Series, 4<sup>th</sup> edition, 1999.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">5.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">E. W. Swokowski, Calculus and Analytic Geometry PWS Publishers, <st1:city w:st="on"><st1:place w:st="on">Boston</st1:place></st1:city>, 1983.<span style="mso-spacerun: yes;">&nbsp; </span><o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.25in; text-align: justify; text-indent: -0.25in; mso-list: l9 level1 lfo2;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">6.<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">John H. Mathews, Numerical Methods for Mathematics Science and Engineering, Prentice-Hall, Second Edition 1992.<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: left;" align="left"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; font-weight: normal; mso-bidi-font-weight: bold; mso-bidi-font-size: 12.0pt; mso-ansi-language: EN-GB;" lang="EN-GB"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: left;" align="left"><strong><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 12.0pt; mso-ansi-language: EN-GB;" lang="EN-GB">6.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style="font-size: large;" size="5"><span style="font-family: 'Arial','sans-serif'; mso-ansi-language: EN-GB;" lang="EN-GB">MATHEMATICS</span><span style="font-family: 'Arial','sans-serif';"> FOR PHYSICS<o:p></o:p></span></span></strong></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt;"><span style="font-family: 'Arial','sans-serif'; font-size: 15pt; font-weight: normal; mso-bidi-font-weight: bold; mso-bidi-font-size: 12.0pt;">Contents<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">1.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Preliminary calculus.</span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l3 level1 lfo3;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Differentiation<o:p></o:p></span></p>
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<p style="margin: 0in 0in 6pt 0.25in;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Differentiation from first principles; products; the chain rule; quotients; implicit differentiation; logarithmic differentiation; Leibnitz&rsquo; theorem; special points of a function; theorems of differentiation.<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l3 level1 lfo3;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Integration<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 6pt 0.25in;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Integration from first principles; the inverse of differentiation; integration by inspection; sinusoidal function; logarithmic integration; integration using partial fractions; substitution method; integration by parts; reduction formulae; infinite and improper integrals; plane polar coordinates; integral inequalities; applications of integration.<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">2.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Complex numbers and hyperbolic functions<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l3 level1 lfo3;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The need for complex numbers<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l3 level1 lfo3;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Manipulation of complex numbers<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Additions and subtraction; modulus and argument; multiplication; complex conjugate; division<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l13 level1 lfo4;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Polar representation of complex numbers<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Multiplication and division in polar form<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l13 level1 lfo4;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">de Moivre&rsquo;s theorem<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Trigonometrical identities; finding the nth roots of unity; solving polynomial equations<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l13 level1 lfo4;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Complex logarithms and complex powers<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.5in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l13 level1 lfo4;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Applications to differentiation and integration<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l13 level1 lfo4;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Hyperbolic functions<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 3pt 0.25in;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Definitions; hyperbolic-trigonometric analogies; identities of hyperbolic functions; solving hyperbolic equations; inverses of hyperbolic functions; calculus of hyperbolic functions<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">3.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Series and limits<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l1 level1 lfo5;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l1 level1 lfo5;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Summation of series<o:p></o:p></span></p>
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<p style="margin: 0in 0in 6pt 0.25in;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Arithmetic series; geometric series; arithmetico-geometric series; the difference method; series involving natural numbers; transformation of series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l7 level1 lfo6;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Convergence of infinite series<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Absolute and conditional convergence; convergence of a series containing only real positive terms; alternating series test<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 6pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l7 level1 lfo6;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Operations with series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l7 level1 lfo6;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Power series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Convergence of power series; operations with power series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><st1:city w:st="on"><st1:place w:st="on"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Taylor</span></st1:place></st1:city><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;"> series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><st1:city w:st="on"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Taylor</span></st1:city><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">&rsquo;s theorem; approximation errors in <st1:city w:st="on"><st1:place w:st="on">Taylor</st1:place></st1:city> series; standard Maclaurin series<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Evaluation of limits<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">4.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Partial differentiation<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Definition of the partial derivative<o:p></o:p></span></p>
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<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The total differential and total derivative<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Exact and inexact differentials<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Useful theorems of partial differentiation<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The chain rule<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Change of variables<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><st1:city w:st="on"><st1:place w:st="on"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Taylor</span></st1:place></st1:city><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">&rsquo;s theorem for many-variable functions<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Stationary values of many-variable functions<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l5 level1 lfo7;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Stationary values under constraints<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.5in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">5.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Multiple integrals<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l10 level1 lfo8;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Double integrals<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l10 level1 lfo8;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Triple integrals<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l10 level1 lfo8;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Applications of multiple integrals</span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Areas and volumes; masses, centers of mass and centroids; Pappus&rsquo; theorems; moments of inertia; mean values of functions<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Change of variables in multiple integrals<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Change of variables in double integrals;<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">6.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Vector algebra<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Scalars and vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Addition and subtraction of vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Multiplication by a scalar<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Basis vectors and components<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Magnitude of a vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l11 level1 lfo9;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Multiplication of vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Scalar product; vector product; scalar triple product; vector triple product<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Equations of lines and planes<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Equation of a line; equation of a plane<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Using vectors to find distances<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Point to line; point to plane; line to line; line to plane<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Reciprocal vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">7.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Matrices and vector spaces<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Vectors spaces<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Basic vectors; the inner product; some useful inequalities<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Matrices<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The complex and Hermitian conjugates of a matrix<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l12 level1 lfo10;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The determinant of a matrix<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Properties of determinants<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l2 level1 lfo11;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The inverse of a matrix<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l2 level1 lfo11;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">The rank of a matrix<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l2 level1 lfo11;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Simultaneous linear equations<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">N<span style="mso-spacerun: yes;">&nbsp; </span>simultaneous linear equations in<span style="mso-spacerun: yes;">&nbsp; </span>N<span style="mso-spacerun: yes;">&nbsp; </span>unknowns<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Special square matrices<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Diagonal; symmetric and antisymmetric; orthogonal; Hermitian; unitary normal<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Eigen vectors and eigen values<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Of<span style="mso-spacerun: yes;">&nbsp; </span>a normal matrix; of Hermitian and anti-Hermitian matrices; of a unitary matrix; of a general square matrix<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 8pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 5.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Determination of eigen values and eigen vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Degenerate eigen values<o:p></o:p></span></p>
<p></p>
<p style="margin: 6pt 0in; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></b></p>
<p></p>
<p style="margin: 6pt 0in; text-align: justify;"><b><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">8.<span style="mso-tab-count: 1;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Vector calculus<o:p></o:p></span></b></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Differentiation of vectors</span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Composite vector expressions; differential of a vector<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Integration of vectors<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Space curves<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Vector functions of several arguments<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Surfaces<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Scalar and vector fields<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l8 level1 lfo12;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Vector operators</span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Gradient of a scalar field; divergence of a vector field; curl of a vector field<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l6 level1 lfo14;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Vector operator formulae<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 6pt 0.75in;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Vector operators acting on sums and products; combinations of grad, div and curl<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify; text-indent: -0.25in; mso-list: l4 level1 lfo13;"><span style="font-family: Symbol; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol;"><span style="mso-list: Ignore;">&middot;<span style="font: 7pt/normal 'Times New Roman'; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 10.0pt;">Cylindrical and spherical polar coordinates<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;">Cylindrical polar coordinates; spherical polar coordinates<o:p></o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt 0.75in; text-align: justify;"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: right;" align="right"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: right;" align="right"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p>&nbsp;</o:p></span></p>
<p></p>
<p style="margin: 0in 0in 0pt; text-align: right;" align="right"><span style="font-family: 'Arial','sans-serif'; font-size: 13pt; mso-bidi-font-size: 10.0pt;"><o:p

Dec 8, 2011 at 5:31 PM

ANOTHER ISSUE:  Most of the times following error is displayed on the Web Matrix when I launch a Website. Kindly analyse it for me: 

HTTP Error 404.20 - Not Found

No default document.

<fieldset>

Most likely causes:

  • A default document is not configured for the site.
  • The URL contains a typographical error.
  • Directory browsing is not enabled.
</fieldset>
<fieldset>

Things you can try:

  • Configure a default document for this site. This is commonly default.aspx for ASP.NET and index.php for PHP.
  • Review the browser URL.
  • Enable directory browsing to allow listing the contents of the directory.
</fieldset>
<fieldset>

Detailed Error Information:

Module DefaultDocumentModule
Notification ExecuteRequestHandler
Handler StaticFile
Error Code 0x80070002
Requested URL http://localhost:13619/
Physical Path C:\Users\munim\Desktop\New-O\CMS » orchardsamplesite » C# - Open Source_files
Logon Method Anonymous
Logon User Anonymous
Request Tracing Directory C:\Users\munim\Documents\IISExpress\TraceLogFiles\CMS » ORCHARDSAMPLESITE » C# - OPEN SOURCE_FILES
</fieldset>
<fieldset>

More Information:

A default document is not configured for the site.

View more information »

</fieldset>