Author | Cornil, Jack-Michel. author |
---|---|
Title | An Introduction to Maple V [electronic resource] / by Jack-Michel Cornil, Philippe Testud |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-642-56729-2 |
Descript | XX, 470p. 105 illus. online resource |
1. What MAPLE Can Do for You -- 1.1 Arithmetic -- 1.2 Numerical Computations -- 1.3 Polynomials and Rational Functions -- 1.4 Trigonometry -- 1.5 Differentiation -- 1.6 Truncated Series Expansions -- 1.7 Differential Equations and Systems -- 1.8 Integration -- 1.9 Plot of Curves -- 1.10 Plot of Surfaces -- 1.11 Linear Algebra -- 2. Introduction -- 2.1 First Steps -- 2.2 Assignment and Evaluation -- 2.3.1 Fundamental Operations -- 2.4 First Approach to Functions -- 2.5 Simplification of Power Functions -- 3. Arithmetic -- 3.1 Divisibility -- 3.2 Diophantian Equations -- 4. Real Numbers, Complex Numbers -- 4.1 The Real Numbers -- 4.2 The Complex Numbers -- 5.1 Curves Defined by an Equation y = f (x) -- 5.2 The Environment of plot -- 5.3 Parametrized Curves in Cartesian Coordinates -- 5.4 Curves in Polar Coordinates -- 5.5 Curves Defined Implicitly -- 5.6 Polygonal Plots -- 5.7 Mixing Drawings -- 5.8 Animation -- 5.9 Using Logarithmic Scales -- 6. Equations and Inequations -- 6.1 Symbolic Solution: solve -- 6.2 Approximate Solution of Equations: fsolve -- 6.3 Solution of Recurrences: rsolve -- 7. Limits and Derivatives -- 7.1 Limits -- 7.2 Derivatives -- 8. Truncated Series Expansions -- 8.1 The Function series -- 8.2 Operations on Truncated Series Expansions -- 8.3 Series Expansion of an Implicit Function -- 9. Differential Equations -- 9.1 Methods for Solving Exactly -- 9.2 Methods for Approximate Solutions -- 9.3 Methods to Solve Graphically -- 10. Integration and Summation -- 10.1 Integration -- 10.2 Operations on Unevaluated Integrals -- 10.3 Discrete Summation -- 11. Three-Dimensional Graphics -- 11.1 Surfaces Defined by an Equation z = f (x, y) -- 11.2 The Environment of plot3d -- 11.3 Surface Patches Parametrized in Cartesian Coordinates -- 11.4 Surfaces Patches Parametrized in Cylindrical Coordinates -- 11.5 Surface Patches Parametrized in Spherical Coordinates -- 11.6 Parametrized Space Curves -- 11.7 Surfaces Defined Implicitly -- 11.8 Mixing Plots from Different Origins -- 12. Polynomials with Rational Coefficients -- 12.1 Writing Polynomials -- 12.2 Coefficients of a Polynomial -- 12.3 Divisibility -- 12.4 Computation of the g.c.d. and the I.c.m -- 12.5 Factorization -- 13. Polynomials with Irrational Coefficients -- 13.1 Algebraic Extensions of ? -- 13.2 Computation Over an Algebraic Extension -- 13.3 Polynomials with Coefficients in ?/p? -- 14. Rational Functions -- 14.1 Writing of the Rational Functions -- 14.2 Factorization of the Rational Functions -- 14.3 Partial Fraction Decomposition -- 14.4 Continued Fraction Series Expansions -- 15. Construction of Vectors and of Matrices -- 15.1 The linalg Library -- 15.2 Vectors -- 15.3 Matrices -- 15.4 Problems of Evaluation -- 15.5 Special Matrices -- 15.6 Random Vectors and Matrices -- 15.7 Functions to Extract Matrices -- 15.8 Constructors of Matrices -- 16. Vector Analysis and Matrix Calculus -- 16.1 Operations upon Vectors and Matrices -- 16.2 Basis of a Vector Subspace -- 17. Systems of Linear Equations -- 17.1 Solution of a Linear System -- 17.2 The Pivotโs Method -- 18. Normalization of Matrices -- 18.1 Determinant, Characteristic Polynomial -- 18.2 Eigenvalues and Eigenvectors of a Matrix -- 19. Orthogonality -- 19.1 Euclidean and Hermitean Vector Spaces -- 19.2 Orthogonal Polynomials -- 20. Vector Analysis -- 20.1 Jacobian Matrix, Divergence -- 20.2 Gradient, Laplacian, Curl -- 20.3 Scalar Potential, Vector Potential -- 21. The MAPLE Objects -- 21.1 Basic Expressions -- 21.2 Real and Complex Numerical Values -- 21.3 Expression Sequences -- 21.4 Ranges -- 21.5 Sets and Lists -- 21.6 Unevaluated Integrals -- 21.7 Polynomials -- 21.8 Truncated Series Expansions -- 21.9 Boolean Relations -- 21.10 Tables and Arrays -- 22. Working More Cleverly with the Subexpressions -- 22.1 The Substitution Functions -- 22.2 The Function map -- 23. Programming: Loops and Branches -- 23.1 Loops -- 23.2 Branches -- 24. Programming: Functions and Procedures -- 24.1 Functions -- 24.2 Procedures -- 24.3 About Passing Parameters -- 24.4 Follow-up of the Execution of a Procedure -- 24.5 Save and Reread a Procedure -- 25. The Mathematical Functions -- 25.1 Catalogue of Mathematical Functions -- 25.2 How Does a MAPLE Function Work? -- 26. Maple Environment in Windows -- 26.1 The MAPLE Worksheet -- 26.2 The File Menu -- 26.3 The Edit Menu -- 26.4 The View Menu -- 26.5 The Insert Menu -- 26.6 The Format Menu -- 26.7 The Options Menu -- 26.8 The Window Menu -- 26.9 On-line Help