The Student's Introduction to MATHEMATICA ®: A Handbook for Precalculus, Calculus, and Linear AlgebraCambridge University Press, 1999 M05 13 - 280 pages Increasingly, educators are turning to Mathematica for instructing students in science and mathematics. The growing popularity of this exciting software package creates a need for undergraduate students to be familiar with its many functions and uses. The Student's Introduction to Mathematica® neatly follows a standard mathematics curriculum, allowing students to practice what they learn. The text lucidly presents those aspects of the software that are the most useful to students. Mathematica commands are introduced as a means of solving problems and illuminating the underlying mathematical principles. Following a brief introduction to the program, Bruce and Eve Torrence discuss functions and graphs, algebra, calculus, and multivariate calculus, and finish with a chapter on linear algebra. No prerequisites other than high school level mathematics are assumed. This work can be used in a variety of courses, from precalculus, through single and multi-variable calculus, to linear algebra. In addition to its course use, this book is an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time. The volume is compatible with Mathematica version 3 and higher. |
Contents
Getting Started | 1 |
13 The First Computation Is Slow | 2 |
15 Input and Output | 3 |
16 The BasicInput Palette and TwoDimensional Input | 4 |
17 Decimal In Decimal Out | 6 |
18 Use Parentheses to Group Terms | 7 |
19 Three WellKnown Constants | 9 |
111 Naming Things | 16 |
44 Simplifying and Manipulating Rational Functions | 107 |
45 Simplifying and Manipulating Other Expressions | 111 |
46 Solving General Equations | 117 |
47 Solving Difference Equations | 124 |
48 Solving Systems of Equations | 126 |
Calculus | 130 |
52 Working with Difference Quotients | 133 |
53 The Derivative | 135 |
112 Saving Your Work and Quitting Mathematica | 18 |
113 Some Frequently Asked Questions Regarding Mathematicas Syntax | 19 |
Working with Mathematica | 22 |
23 Printing | 24 |
24 Creating Web Pages | 25 |
26 Tips for Working Effectively | 27 |
27 Getting Help from Mathematica | 33 |
28 Loading Packages | 36 |
Dealing with Them and Preventing Them | 39 |
Functions and Their Graphs | 45 |
32 Clearing a Function | 47 |
33 Producing a Table of Values | 48 |
34 Plotting a Function | 51 |
35 Using Mathematicas Plot Options | 55 |
36 Working with Piecewise Defined Functions | 66 |
37 Plotting Implicitly Defined Functions | 68 |
38 Superimposing Plots | 71 |
39 Animating Plots | 77 |
311 Manipulating Data An Introduction to Lists | 82 |
312 Importing Data into Mathematica | 88 |
313 Working with Difference Equations | 90 |
Algebra | 94 |
42 Finding Roots of Polynomials with Solve and NSolve | 97 |
43 Suppressing Complex Output | 104 |
54 Higher Derivatives | 138 |
55 Maxima and Minima | 139 |
56 Inflection Points | 144 |
57 Implicit Differentiation | 146 |
58 Differential Equations | 147 |
59 Integration | 150 |
510 Definite and Improper Integrals | 153 |
511 Numerical Integration | 162 |
512 Series | 166 |
Multivariable Calculus | 171 |
62 RealValued Functions of Two or More Variables | 176 |
63 Parametric Curves and Surfaces | 201 |
64 Other Coordinate Systems | 208 |
65 Vector Fields | 220 |
66 Line Integrals and Surface Integrals | 227 |
Linear Algebra | 232 |
72 Performing Gaussian Elimination | 241 |
73 Matrix Operations | 244 |
74 Solving Systems of Linear Equations | 248 |
75 Vector Spaces | 253 |
76 Eigenvalues and Eigenvectors | 259 |
77 Visualizing Linear Transformations | 264 |
275 | |
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Common terms and phrases
algebraic approximate ArcTan AspectRatio Automatic Axes BasicInput palette built-in calculation Clear f column complex numbers contour contour lines ContourPlot cube cursor curve default difference equation Difference Quotients DisplayFunction domain dot product eigenvalues eigenvectors Evaluate example expression f[x_ Factor File menu FilledPlot FindRoot font formula graph GrayLevel Help Browser Here's highlight ImplicitPlot input cell instance integral Inverse iterator keyboard linear transformation LinearSolve ListPlot load the package Mathematica Mathematica command mathematical matrix MatrixForm mouse Needs Graphics NSolve NullSpace option output cell palette button parametric Parametric Curves ParametricPlot placeholder plot command Plot f[x Plot3D PlotPoints PlotRange PlotStyle Polygon polynomial produce a plot rational function real number Riemann sum roots second argument Section sequence Simplify solution Solve command specified square surface TAB key Table TableForm three-dimensional values variable vector field vector space zero