| Preface | p. xiii |
| Plan of this Book | p. xv |
| A Tour of Maple V | |
| Introduction | p. 1 |
| Maple's User Interface | p. 3 |
| Just a Maple Session | p. 4 |
| Numerical Calculations | p. 5 |
| Symbolic Calculations | p. 9 |
| Worksheets and Assignments | p. 15 |
| Worksheet 1a. Numbers | p. 15 |
| Assignments 1a. Numbers | p. 21 |
| Worksheet 1b. Variables and Names | p. 21 |
| Assignments 1b. Variables and Names | p. 29 |
| Exercises | p. 30 |
| Survey of Used Maple Expressions | p. 32 |
| Functions and Sequences | |
| Introduction | p. 35 |
| Selected Concepts from Analysis | p. 36 |
| A Tricky Probability Function | p. 38 |
| Mathematical Functions | p. 38 |
| Investigating a Probability Function | p. 40 |
| Investigating a Strange Sequence | p. 45 |
| Worksheets and Assignments | p. 47 |
| Exercises | p. 60 |
| Survey of Used Maple Expressions | p. 62 |
| Matrices and Vectors | |
| Introduction | p. 63 |
| Selected Concepts from Linear Algebra | p. 64 |
| A Least Squares Filter | p. 66 |
| Matrices and Vectors | p. 66 |
| Removing Noise from a Data Set | p. 68 |
| Worksheets and Assignments | p. 72 |
| Exercises | p. 85 |
| Survey of Used Maple Expressions | p. 86 |
| Counting and Summation | |
| Introduction | p. 89 |
| Selected Concepts from Discrete Mathematics | p. 90 |
| Binomial Coefficients | p. 92 |
| Maple's binomial Function | p. 93 |
| Two Binomial Identities | p. 95 |
| The Binomial Series | p. 96 |
| The De Moivre-Laplace Limit Theorem | p. 97 |
| Worksheets and Assignments | p. 102 |
| Worksheet 4a. Symbolic Summation | p. 102 |
| Assignments 4a. Symbolic Summation | p. 106 |
| Worksheet 4b. Counting and Random Numbers | p. 108 |
| Assignments 4b. Counting and Random Numbers | p. 113 |
| Exercises | p. 114 |
| Survey of Used Maple Expressions | p. 116 |
| Derivative and Integral | |
| Introduction | p. 119 |
| Further Concepts from Analysis | p. 120 |
| Riemann's Non-differentiable Function | p. 122 |
| Investigating the Riemann Function | p. 122 |
| Finding a Primitive Function | p. 130 |
| Worksheets and Assignments | p. 134 |
| Exercises | p. 147 |
| Survey of Used Maple Expressions | p. 150 |
| Vector Spaces and Linear Mappings | |
| Introduction | p. 151 |
| Further Concepts from Linear Algebra | p. 152 |
| Diagonalization and the SVD | p. 155 |
| A Simple Orthogonal Projection | p. 155 |
| Singular Value Decomposition | p. 159 |
| Worksheets and Assignments | p. 166 |
| Worksheet 6a. Linear Mappings | p. 167 |
| Assignments 6a. Linear Mappings | p. 170 |
| Worksheet 6b. Eigenvectors and Eigenspaces | p. 171 |
| Assignments 6b. Eigenvectors and Eigenspaces | p. 176 |
| Exercises | p. 177 |
| Survey of Used Maple Expressions | p. 180 |
| Exercises in Experimentation | |
| Upper Bound for a Parameterized Function | p. 181 |
| Matrix Differentiation | p. 183 |
| Chaotic Sequences | p. 185 |
| Hints and Answers | |
| Exercises 1.5 | |
| Exercises 2.5 | |
| Exercises 3.5 | |
| Exercises 4.5 | |
| Exercises 5.5 | |
| Exercises 6.5 | |
| Quick Guide to Selected Maple Commands | |
| Linear Algebra | p. 204 |
| Elementary Matrix Algebra | p. 204 |
| Elementary Vector Algebra | p. 205 |
| Solving a System of Linear Equations Ax = b | p. 206 |
| Eigenvalues and Eigenvectors | p. 207 |
| Mathematical Analysis | p. 207 |
| Writing Your Own Procedures | p. 208 |
| Plotting the Graph of a Function | p. 208 |
| Computing Limits | p. 208 |
| Differential Calculus | p. 209 |
| Integration | p. 209 |
| Solving Equations | p. 210 |
| Solving Differential/Difference Equations | p. 211 |
| Statistics | p. 211 |
| Probabilities | p. 212 |
| Generating Random Numbers | p. 212 |
| Analysis of Statistical Data | p. 213 |
| Linear Programming | p. 213 |
| Mathematical Finance | p. 214 |
| Bibliography | p. 217 |
| Index | p. 219 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
