Preface |
|
xv | |
Why Mathematica? |
|
xvi | |
How to Use this Book |
|
xvi | |
Acknowledgments |
|
xvii | |
|
|
1 | (21) |
|
|
1 | (1) |
|
The Basic Technique for Using Mathematica |
|
|
1 | (1) |
|
The First Computation Is Slow |
|
|
2 | (1) |
|
Commands for Basic Arithmetic |
|
|
2 | (1) |
|
|
3 | (1) |
|
The BasicInput Palette and Two-Dimensional Input |
|
|
4 | (2) |
|
|
6 | (1) |
|
Use Parentheses to Group Terms |
|
|
7 | (2) |
|
Three Well-Known Constants |
|
|
9 | (1) |
|
Typing Commands in Mathematica |
|
|
9 | (7) |
|
Numerical Approximation and Scientific Notation |
|
|
10 | (1) |
|
|
11 | (1) |
|
|
12 | (1) |
|
|
13 | (1) |
|
Factoring and Expanding Polynomials |
|
|
13 | (1) |
|
|
14 | (1) |
|
|
15 | (1) |
|
Real and Imaginary Parts of Complex Numbers |
|
|
16 | (1) |
|
|
16 | (2) |
|
Saving Your Work and Quitting Mathematica |
|
|
18 | (1) |
|
Some Frequently Asked Questions Regarding Mathematica's Syntax |
|
|
19 | (3) |
|
Why Do All Built-In Mathematica Objects Begin with Capital Letters? |
|
|
19 | (1) |
|
Why Are Some Command Names so Long? |
|
|
19 | (1) |
|
Why Are the Arguments of Commands Enclosed in Square Brackets? |
|
|
20 | (1) |
|
What Happens If I Use Incorrect Syntax? |
|
|
20 | (2) |
|
|
22 | (23) |
|
|
22 | (1) |
|
Adding Text to Notebooks - An Introduction to Mathematica's Cell Structure |
|
|
22 | (2) |
|
|
24 | (1) |
|
|
25 | (1) |
|
|
25 | (2) |
|
Numbering Input and Output |
|
|
25 | (1) |
|
Reevaluating Previously Saved Notebooks |
|
|
26 | (1) |
|
Tips for Working Effectively |
|
|
27 | (6) |
|
Referring to Previous Output |
|
|
27 | (1) |
|
Referring to Previous Input |
|
|
28 | (1) |
|
Postfix Command Structure |
|
|
28 | (1) |
|
|
29 | (1) |
|
|
30 | (1) |
|
Typesetting Input-More Shortcuts |
|
|
30 | (2) |
|
Suppressing Output and Entering Sequences of Commands |
|
|
32 | (1) |
|
Getting Help from Mathematica |
|
|
33 | (3) |
|
Information on Known Commands |
|
|
33 | (1) |
|
|
34 | (1) |
|
|
34 | (1) |
|
|
34 | (2) |
|
|
36 | (3) |
|
Problems: Dealing with Them and Preventing Them |
|
|
39 | (6) |
|
|
41 | (1) |
|
Aborting Calculations and/or Recovering from a Crash |
|
|
41 | (2) |
|
Running Efficiently: Preventing Crashes |
|
|
43 | (1) |
|
Memory Gauges for the Mac OS |
|
|
44 | (1) |
|
Functions and Their Graphs |
|
|
45 | (49) |
|
|
45 | (2) |
|
|
47 | (1) |
|
Producing a Table of Values |
|
|
48 | (3) |
|
|
51 | (4) |
|
Using Mathematica's Plot Options |
|
|
55 | (11) |
|
How to Get the Same Scaling on Both Axes |
|
|
56 | (1) |
|
How to Get the Axes to Intersect at the Origin |
|
|
57 | (1) |
|
How to Add Color, and Other Style Changes |
|
|
57 | (2) |
|
How to Remove the Axes or Add a Frame |
|
|
59 | (1) |
|
How to Add Grid Lines and Adjust Tick Marks |
|
|
60 | (1) |
|
|
61 | (1) |
|
How to Give Your Plot a Title |
|
|
62 | (1) |
|
|
63 | (2) |
|
How to Find Out About Other Options |
|
|
65 | (1) |
|
Working with Piecewise Defined Functions |
|
|
66 | (2) |
|
Plotting Implicitly Defined Functions |
|
|
68 | (3) |
|
|
71 | (6) |
|
|
77 | (1) |
|
|
77 | (5) |
|
Manipulating Data - An Introduction to Lists |
|
|
82 | (6) |
|
Importing Data into Mathematica |
|
|
88 | (2) |
|
On a Machine Running the Mac OS |
|
|
89 | (1) |
|
|
90 | (1) |
|
Extracting Columns from the Data (All Platforms) |
|
|
90 | (1) |
|
Working with Difference Equations |
|
|
90 | (4) |
|
|
94 | (36) |
|
Factoring and Expanding Polynomials |
|
|
94 | (3) |
|
Finding Roots of Polynomials with Solve and NSolve |
|
|
97 | (7) |
|
Suppressing Complex Output |
|
|
104 | (3) |
|
Simplifying and Manipulating Rational Functions |
|
|
107 | (4) |
|
|
107 | (1) |
|
Simplifying Rational Expressions |
|
|
107 | (2) |
|
|
109 | (1) |
|
|
109 | (1) |
|
|
110 | (1) |
|
Simplifying and Manipulating Other Expressions |
|
|
111 | (6) |
|
|
111 | (3) |
|
Manipulating Trigonometric Expressions |
|
|
114 | (3) |
|
Solving General Equations |
|
|
117 | (7) |
|
Solving Difference Equations |
|
|
124 | (2) |
|
Solving Systems of Equations |
|
|
126 | (4) |
|
|
130 | (41) |
|
|
130 | (3) |
|
Working with Difference Quotients |
|
|
133 | (2) |
|
Producing and Simplifying Difference Quotients |
|
|
133 | (1) |
|
|
134 | (1) |
|
Instantaneous Rate of Change |
|
|
135 | (1) |
|
|
135 | (3) |
|
|
138 | (1) |
|
|
139 | (5) |
|
|
144 | (2) |
|
|
146 | (1) |
|
|
147 | (3) |
|
|
150 | (3) |
|
Definite and Improper Integrals |
|
|
153 | (9) |
|
Computing Definite Integrals |
|
|
153 | (1) |
|
|
154 | (2) |
|
|
156 | (3) |
|
Computing Improper Integrals |
|
|
159 | (1) |
|
Defining Functions with Integrals |
|
|
159 | (1) |
|
Integrands with Discontinuities |
|
|
160 | (2) |
|
|
162 | (1) |
|
|
162 | (4) |
|
|
166 | (5) |
|
|
171 | (61) |
|
|
171 | (5) |
|
Vectors and the Dot Product |
|
|
171 | (2) |
|
Rendering Vectors in the Plane |
|
|
173 | (2) |
|
|
175 | (1) |
|
Real-Valued Functions of Two or More Variables |
|
|
176 | (25) |
|
Defining a Real-Valued Function of Two or More Variables |
|
|
176 | (1) |
|
Plotting Functions of Two Variables |
|
|
177 | (1) |
|
Three-Dimensional Plotting Tips |
|
|
178 | (16) |
|
Differentiation of Functions of Two or More Variables |
|
|
194 | (6) |
|
Integrating Functions of Two or More Variables |
|
|
200 | (1) |
|
Parametric Curves and Surfaces |
|
|
201 | (7) |
|
Parametric Curves in the Plane |
|
|
201 | (3) |
|
Parametric Curves in Space |
|
|
204 | (2) |
|
Parametric Surfaces in Space |
|
|
206 | (2) |
|
|
208 | (12) |
|
|
208 | (5) |
|
Cylindrical and Spherical Coordinates |
|
|
213 | (6) |
|
Integrating in Other Coordinate Systems |
|
|
219 | (1) |
|
|
220 | (7) |
|
|
220 | (1) |
|
Plotting a Two-Dimensional Vector Field |
|
|
221 | (2) |
|
Plotting a Three-Dimensional Vector Field |
|
|
223 | (2) |
|
Divergence and Curl of a Three-Dimensional Vector Field |
|
|
225 | (2) |
|
Line Integrals and Surface Integrals |
|
|
227 | (5) |
|
|
227 | (2) |
|
|
229 | (3) |
|
|
232 | (43) |
|
|
232 | (9) |
|
|
232 | (6) |
|
|
238 | (3) |
|
Performing Gaussian Elimination |
|
|
241 | (3) |
|
Referring to Parts of Matrices |
|
|
241 | (1) |
|
|
242 | (2) |
|
|
244 | (4) |
|
Solving Systems of Linear Equations |
|
|
248 | (5) |
|
Nonhomogeneous Systems of Linear Equations |
|
|
248 | (3) |
|
Homogeneous Systems of Equations |
|
|
251 | (1) |
|
Using LinearSolve and NullSpace to Solve Nonhomogeneous Systems |
|
|
252 | (1) |
|
|
253 | (6) |
|
Span and Linear Independence |
|
|
253 | (1) |
|
|
254 | (2) |
|
|
256 | (1) |
|
Orthonormal Bases and the Gram-Schmidt Process |
|
|
256 | (3) |
|
Eigenvalues and Eigenvectors |
|
|
259 | (5) |
|
Finding Eigenvalues and Eigenvectors Automatically |
|
|
259 | (3) |
|
Finding Eigenvalues and Eigenvectors Manually |
|
|
262 | (1) |
|
|
263 | (1) |
|
Visualizing Linear Transformations |
|
|
264 | (11) |
Index |
|
275 | |