# lecture4 - (* Content-type: application/mathematica *) (...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (* Content-type: application/mathematica *) ( (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) ( (* CreatedBy='Mathematica 6.0' *) ( (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 137016, 3974] NotebookOptionsPosition[ 82944, 2753] NotebookOutlinePosition[ 128230, 3730] CellTagsIndexPosition[ 128156, 3725] WindowFrame-&gt;Normal*) W (* Beginning of Notebook Content *) Notebook[{ Cell[&quot;\&lt;\ Introduction to Mathematical Software 21-126 2 Lecture 4: Calculus\ \&gt;&quot;, &quot;Subtitle&quot;, CellChangeTimes-&gt;{3.41117300640625*^9, 3.411173189*^9}, TextAlignment-&gt;Center, TextJustification-&gt;0], Cell[CellGroupData[{ C Cell[&quot;Differentiation&quot;, &quot;Section&quot;, CellChangeTimes-&gt;{3.41117300640625*^9, 3.411173189*^9}], Cell[CellGroupData[{ C Cell[&quot;Derivatives and Partial derivatives&quot;, &quot;Subsection&quot;, CellChangeTimes-&gt;{3.41117300640625*^9, 3.411173189*^9}], Cell[TextData[{ &quot;Partial derivatives are produced by the function &quot;, ButtonBox[&quot;D&quot;, BaseStyle-&gt;&quot;RefGuideLink&quot;], StyleBox[&quot;[&quot;, FontWeight-&gt;&quot;Bold&quot;], StyleBox[&quot;f,x&quot;, FontSlant-&gt;&quot;Italic&quot;], StyleBox[&quot;]&quot;, FontWeight-&gt;&quot;Bold&quot;], &quot;, where the expression &quot;, StyleBox[&quot;f&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; should be either an implicit or explicit function of the variable &quot;, StyleBox[&quot;x&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; for which the derivative is sought. Partial derivatives with respect to \ several variables simultaneously are obtained by using a sequence of \ variables in the argument list. Multiple derivatives with respect to the \ same variable are specified by arguments of the form &quot;, StyleBox[&quot;{x,n}&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; where &quot;, StyleBox[&quot;n&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; is the degree of differentiation or by including &quot;, StyleBox[&quot;n&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; instances of &quot;, StyleBox[&quot;x&quot;, FontSlant-&gt;&quot;Italic&quot;], &quot; in the sequence of differentiation variables. &quot; }], &quot;Text&quot;, CellChangeTimes-&gt;{3.41117300640625*^9, 3.411173189*^9}], Cell[TextData[{ &quot;There are many equivalent input forms for this function to reflect common \ usages. The prime notation is convenient for writing ordinary differential \ equations and can be entered directly from the keyboard; a slightly more \ appealing form is obtained by entering \[EscapeKey]'\[EscapeKey] in a \ superscript box. The &quot;, Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox[&quot;\[PartialD]&quot;, RowBox[{ RowBox[{&quot;{&quot;, RowBox[{&quot;x&quot;, &quot;,&quot;, &quot;n&quot;}], &quot;}&quot;}], &quot;,&quot;, RowBox[{&quot;{&quot;, RowBox[{&quot;y&quot;, &quot;,&quot;, &quot;m&quot;}], &quot;}&quot;}]}]], RowBox[{&quot;f&quot;, &quot;[&quot;, RowBox[{&quot;x&quot;, &quot;,&quot;, &quot;y&quot;}], &quot;]&quot;}]}], TraditionalForm]]], &quot; notation is more flexible and more rigorous, superseding the traditional &quot;, Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ SuperscriptBox[&quot;\[PartialD]&quot;, RowBox[{&quot;n&quot;, &quot;+&quot;, &quot;m&quot;}]], RowBox[{&quot;f&quot;, &quot;[&quot;, RowBox[{&quot;x&quot;, &quot;,&quot;, &quot;y&quot;}], &quot;]&quot;}]}], RowBox[{ RowBox[{ SuperscriptBox[&quot;\[PartialD]&quot;, &quot;n&quot;], &quot;x&quot;}], RowBox[{ SuperscriptBox[&quot;\[PartialD]&quot;, &quot;m&quot;], &quot;y&quot;}]}]], TraditionalForm]]], &quot; notation with its cumbersome fractions which do not divide out. That \ traditional notation cannot be used without constructing special notation \...
View Full Document

## lecture4 - (* Content-type: application/mathematica *) (...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online