The Maple Book

by ;
Edition: 1st
Format: Paperback
Pub. Date: 2001-11-28
Publisher(s): Chapman & Hall/
List Price: $85.95

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Summary

Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author's MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPLE 7.0The MAPLE Book serves both as an introduction to Maple and as a reference. Organized according to level and subject area of mathematics, it first covers the basics of high school algebra and graphing, continues with calculus and differential equations then moves on to more advanced topics, such as linear algebra, vector calculus, complex analysis, special functions, group theory, number theory and combinatorics. The MAPLE Book includes a tutorial for learning the Maple programming language. Once readers have learned how to program, they will appreciate the real power of Maple.The convenient format and straightforward style of The MAPLE Book let users proceed at their own pace, practice with the examples, experiment with graphics, and learn new functions as they need them. All of the Maple commands used in the book are available on the Internet, as are links to various other files referred to in the book. Whatever your level of expertise, you'll want to keep The MAPLE Book next to your computer.

Table of Contents

Getting Started
1(14)
Starting a MAPLE session
1(2)
Different versions of MAPLE
3(1)
Basic syntax
3(2)
Editing mistakes
5(1)
Help
5(2)
A sample session and context menus
7(3)
Palettes
10(2)
Spreadsheets
12(2)
Quitting MAPLE
14(1)
MAPLE as a Calculator
15(4)
Exact arithmetic and basic functions
15(1)
Floating-point arithmetic
16(3)
High School Algebra
19(22)
Polynomials and rational functions
19(10)
Factoring a polynomial
19(1)
Expanding an expression
19(1)
Collecting like terms
20(1)
Simplifying an expression
21(1)
Simplifying radicals
22(1)
Working in the real domain
23(2)
Simplifying rational functions
25(2)
Degree and coefficients of a polynomial
27(1)
Substituting into an expression
28(1)
Restoring variable status
28(1)
Evaluations
29(2)
Left- and right hand sides
29(1)
Finding exact solutions
30(1)
Finding approximate solutions
30(1)
Assigning solutions
31(1)
Fun with integers
31(3)
Complete integer factorization
31(1)
Quotient and remainder
32(1)
Gcd and lcm
32(1)
Primes
33(1)
Integer solutions
33(1)
Reduction mod p
34(1)
Unit conversion
34(2)
Trigonometry
36(5)
Degree and radians
36(1)
Trigonometric functions
37(1)
Simplifying trigonometric functions
38(3)
Data Types
41(6)
Sequences
41(1)
Sets
42(1)
Lists
43(1)
Tables
44(1)
Arrays
44(1)
Data conversions
45(1)
Other data types
46(1)
Calculus
47(20)
Defining functions
47(1)
Composition of functions
48(1)
Summation and product
48(2)
Limits
50(1)
Differentiation
51(1)
Extrema
52(2)
Integration
54(4)
Techniques of integration
56(1)
Substitution
56(1)
Integration by parts
57(1)
Partial fractions
57(1)
Taylor and series expansions
58(1)
The student package
58(9)
Graphics
67(34)
Two-dimensional plotting
67(18)
Restricting domain and range
69(1)
Parametric plots
69(1)
Multiple plots
70(1)
Polar plots
71(1)
Plotting implicit functions
72(1)
Plotting points
73(1)
Title and text in a plot
74(2)
Plotting options
76(3)
Saving and printing a plot
79(1)
Other plot functions
79(6)
Three-dimensional plotting
85(14)
Parametric plots
88(1)
Multiple plots
88(1)
Space curves
89(1)
Contour plots
90(1)
Plotting surfaces defined implicitly
91(1)
Title and text in a plot
92(1)
Three-dimensional plotting options
92(3)
Other three-dimensional plot functions
95(4)
Animation
99(2)
MAPLE Programming
101(46)
The MAPLE procedure
101(2)
Local and global variables
102(1)
Conditional statements
103(4)
Boolean expressions
105(2)
The ``for'' loop
107(4)
Type declaration
111(1)
The ``while'' loop
112(3)
Recursive procedures
115(2)
Explicit return
117(1)
Error statement
118(4)
args and nargs
122(1)
Input and output
123(8)
Formatted output
123(2)
Interactive input
125(2)
Reading commands from a file
127(1)
Reading data from a file
127(2)
Writing data to a file
129(1)
Writing and saving to a file
129(2)
Generating C and Fortran code
131(1)
Viewing built-in MAPLE code
132(1)
The MAPLE interactive debugger
132(3)
Writing your own packages
135(6)
Packages as tables
135(2)
Modules for packages
137(4)
Answers to programming exercises
141(6)
Differential Equations
147(26)
Solving ordinary differential equations
147(4)
Implicit solutions
149(1)
Initial conditions
149(2)
Systems of differential equations
151(1)
First-order differential equations
151(6)
odeadvisor
151(3)
Integrating factors
154(1)
Direction fields
155(2)
Numerical solutions
157(2)
Second- and higher order linear DEs
159(2)
Constant coefficients
159(1)
Variation of parameters
159(1)
Reduction of order
160(1)
Series solutions
161(3)
The method of Frobenius
162(2)
The Laplace transform
164(5)
The Heaviside function
165(3)
The Dirac delta function
168(1)
The DEtools package
169(4)
DE plotting functions
169(1)
Dynamical systems
170(1)
DE manipulation
170(1)
Lie symmetry methods
171(1)
Differential operators
171(1)
Closed form solutions
172(1)
Simplifying DEs and rifsimp
172(1)
Linear Algebra
173(64)
Vectors, Arrays, and Matrices
173(11)
Matrix and Vector entry assignment
175(2)
The Matrix and Vector palettes
177(1)
Matrix operations
178(2)
Matrix and vector construction shortcuts
180(2)
Viewing large Matrices and Vectors
182(2)
Matrix context menu
184(5)
The Export As submenu
185(1)
The Norm submenu
186(1)
The Select Element submenu
186(1)
The Solvers submenu
186(1)
The Conversions submenu
187(1)
The In-place Options submenu
188(1)
Elementary row and column operations
189(2)
Gaussian elimination
191(1)
Inverses, determinants, minors, and the adjoint
192(1)
Special matrices and vectors
193(8)
Band matrix
193(1)
Constant matrices and vectors
193(1)
Diagonal matrices
194(1)
Givens rotation matrices
195(1)
Hankel matrices
195(1)
Hilbert matrices
195(1)
Householder matrices
196(1)
Identity matrix
196(1)
Jordan block matrices
197(1)
Random matrices and vectors
197(3)
Toeplitz matrices
200(1)
Vandermonde matrices
200(1)
Zero matrices and vectors
201(1)
Systems of linear equations
201(4)
Row space, column space, and nullspace
205(2)
Eigenvectors and diagonalization
207(1)
Jordan form
208(1)
Inner products, and Vector and matrix norms
209(3)
The dot product and bilinear forms
209(1)
Vector norms
210(1)
Matrix norms
211(1)
Least squares problems
212(2)
QR-factorization and the Gram-Schmidt process
214(2)
LU-factorization
216(2)
Other Linear Algebra functions
218(11)
The linalg package
229(8)
Matrices and vectors
230(1)
Conversion between linalg and Linear Algebra
231(2)
Matrix operations in linalg
233(1)
The functions in the linalg package
234(3)
Multivariable and Vector Calculus
237(34)
Vectors
237(4)
Vector operations
237(1)
Length, dot product, and cross product
238(1)
Plotting vectors
239(2)
Lines and planes
241(3)
Lines
241(1)
Planes
242(2)
Vector-valued functions
244(7)
Differentiation and integration of vector functions
244(1)
Space curves
245(2)
Tangents and normals to curves
247(3)
Curvature
250(1)
The gradient and directional derivatives
251(1)
Extrema
252(4)
Local extrema and saddle points
252(2)
Lagrange multipliers
254(2)
Multiple integrals
256(3)
Double integrals
256(1)
Triple integrals
257(1)
The Jacobian
258(1)
Vector field
259(2)
Plotting a vector field
259(1)
Divergence and curl
259(1)
Potential functions
260(1)
Line integrals
261(1)
Green's theorem
262(1)
Surface integrals
263(8)
Flux of a vector field
265(2)
Stoke's theorem
267(1)
The divergence theorem
268(3)
Complex Analysis
271(18)
Arithmetic of complex numbers
271(2)
Polar form
273(1)
nth roots
274(1)
The Cauchy-Riemann equations and harmonic functions
275(2)
Elementary functions
277(2)
Conformal mapping
279(3)
Taylor series and Laurent series
282(4)
Contour integrals
286(1)
Residues and poles
287(2)
Opening, Saving, and Exporting Worksheets
289(6)
Opening an existing worksheet
289(1)
Saving a worksheet
290(1)
Opening a MAPLE text file
291(1)
Exporting worksheets and LaTeX
292(3)
Document Preparation
295(6)
Adding text
295(1)
Inserting math into text
296(1)
Adding titles and headings
296(1)
Creating a subsection
297(1)
Cutting and pasting
297(1)
Bookmarks and hypertext
298(3)
More Graphics
301(28)
The plottools package
301(17)
Two-dimensional plot objects
301(4)
Three-dimensional plot objects
305(6)
Transformation of plots
311(7)
The geometric package
318(2)
The geom3d package
320(9)
Regular polyhedra
320(3)
Quasi-regular polyhedra
323(1)
The Archimedean solids
324(5)
Special Functions
329(26)
Overview of mathematical functions
329(3)
Bessel functions
332(1)
The Gamma function
333(4)
Hypergeometric functions
337(2)
Elliptic integrals
339(2)
The AGM
341(1)
Jacobi's theta functions
342(1)
Elliptic functions
343(2)
The Riemann zeta-function
345(1)
Orthogonal polynomials
346(1)
Integral transforms
347(4)
Fourier transforms
347(2)
Hilbert transform
349(1)
Mellin transform
350(1)
Fast Fourier transform
351(2)
Asymptotic expansion
353(2)
Statistics
355(34)
Introduction
355(1)
Data sets
356(1)
Numerical methods for describing data
357(11)
Describing the center of a data set
357(2)
Describing the dispersion of a data set
359(4)
Describing characteristics of a data set
363(5)
Transforming data
368(4)
Graphical methods for describing data
372(12)
Histogram
374(2)
Box plot
376(2)
Scatter plot
378(6)
Linear regression
384(1)
ANOVA
384(1)
Distributions
385(4)
Evaluating distributions
385(2)
Generating random distributions
387(2)
Overview of Other Packages
389(56)
Finite fields
390(3)
Polynomials
393(3)
Group theory
396(5)
Combinatorics
401(10)
The combinat package
401(6)
The networks package
407(3)
The combstruct package
410(1)
Number theory
411(11)
The numtheory package
411(8)
The GaussInt package
419(1)
p-adic numbers
419(3)
Numerical approximation
422(1)
Miscellaneous packages
423(14)
The algcurves package
423(1)
The codegen package
423(1)
The diffalg package
424(1)
The difforms package
425(1)
The Domains package
425(1)
The finance package
425(1)
The genfunc package
426(1)
The geometry package
426(3)
The geom3d package
429(1)
The Groebner package
430(1)
The liesymm package
431(1)
The LREtools package
431(1)
The Ore_algebra package
432(1)
The PDEtools package
433(1)
The powseries package
433(1)
The process package
434(1)
The simple package
434(1)
The Slode package
434(1)
The Spread package
435(1)
The sumtools package
435(1)
The tensor package
435(2)
New packages
437(8)
The CurveFitting Package
437(1)
The ExternalCalling package
437(1)
The LinearFunctionalSystems package
437(1)
The LinearOperators package
438(1)
The ListTools package
438(1)
The MathML package
439(1)
The OrthogonalSeries package
439(1)
The RandomTools package
439(1)
The Rational Normal Forms package
440(1)
The ReadDomain package
440(1)
The Sockets package
440(1)
The SolveTools package
441(1)
The StringTools package
441(1)
The Units package
442(1)
The XMLTools package
443(2)
Appendix A MAPLE Resources 445(6)
The MAPLE Application Center
445(3)
The MAPLE Student Center
448(1)
The MAPLE Share Library
448(1)
Interesting URLs
448(3)
Appendix B Glossary of Commands 451(10)
Appendix C Further Reading 461(2)
References 463(2)
Index 465

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