INDICE: Preface III 1 Introduction 1 1.1 Guiding Philosophy 1 1.2 Student'sGuide 3 1.3 Instructor's Guide 4 1.3.1 Maple 4 1.3.2 ODE Chapters 5 1.3.3 Computer Problem Sets 5 1.4 A Word about Software Versions 6 2 Getting Started with Maple 7 2.1 Platforms and Versions 7 2.2 Instrallation 7 2.3 Starting Maple8 2.4 Maple Input 8 2.5 Online Help 9 2.6 Ending a Session 9 3 Doing Mathematics with Maple 11 3.1 Arithmetic 11 3.2 Symbolic Computation 12 3.3 Assignments 13 3.4 Working with Output 14 3.5 Recovering from Problems 15 3.5.1 Errors in Input 15 3.5.2 Aborting Calculations 15 3.6 Suppressing Output 16 3.7 The Restart Command 16 3.8 Equations 16 3.9 Solving Equations 17 3.10 Functions and Expressions 19 3.10.1 Built-in Functions 19 3.10.2 User-defined Functions 20 3.10.3 Expressions 21 3.11 Substitution 22 3.12 Sequences, Sets, and Lists 23 3.13 Packages 24 3.14 Graphics 25 3.14.1 Plotting Functions and Expressions 25 3.14.2 Plotting Multiple Curves 26 3.14.3 Plotting Points 27 3.14.4 Adding Text to a Plot 27 3.14.5 Parametric Plots 29 3.14.6 Implicit Plots 30 3.14.7 Contour Plots 30 3.15 Calculus 31 3.16 More on Sequences, Lists, and Sets 34 4.17 Procedures 37 3.18 Some Tips and Reminders 39 4 Using Maple Documents 41 4.1 The Maple Window 41 4.2 Organization of a Document 42 4.3 Document Blocks 42 4.4 Graphics 43 4.5 Preparing Homework Solutions 44 Problem Set A: Practice withMaple 47 5 Solutions of Differential Equations 51 5.1 Finding Symbolic Solutions 51 5.2 Existence and Uniqueness 53 5.3 Stability of Differential Equations55 5.4 Different Types of Symbolic Solutions 59 6 A Qualitative Approach to Differential Equations 65 6.1 Direction Field for a First Order Linear Equation65 6.2 Direction Filed for a Non-Linear Equation 67 6.3 Autonomous Equations 68 6.3.1 Examples of Autonomous Equations 70 Problem Set B: First Order Equations 73 7 Numerical Methods 83 7.1 Numerical Solutions Using Maple 84 7.2 Some Numerical Methods 86 7.2.1 The Euler Method 86 7.2.2 The Improved Euler Method89 7.2.3 The Rung-Kutta Method 90 7.2.4 Inside dsolve( ,numeric) 91 7.2.5 Round-off Error 91 7.3 Controlling the Error in dsolve( ,numeric) 92 7.4 Reliability of Numerical Methods 92 8 Features of Maple 97 8.1 Names and Values 97 8.2Clearing Values 98 8.3 Vectors and Matrices 98 8.3.1 Solving Linear Systems 100 8.3.2 Calculating Eigenvalues and Eigenvectors 101 8.4 Plots for ODEs 102 8.4.1 Commands for Plotting Direction Fields 102 8.4.2 Plotting Families of Numerical Solutions of ODEs 102 8.4.3 More about D Eplot 103 8.5 Stopping Conditions 105 8.6 Numerical Solutions of Higher Order Differential Equations 106 8.7Troubleshooting 107 8.7.1 The Common Mistakes 108 8.7.2 Error and Warning Messages 108 Problem Set C: Numerical Solutions 111 9 Solving and Analyzing Second Order Linear Equations 119 9.1 Second Order Equations with Maple 121 9.2 Comparison Methods 124 9.2.1 The Interlacing of Zeros 126 9.2.2 Proof of the Sturm Comparison Theorem 127 9.3 A Geometric Method 127 9.3.1 The Constant Coefficient Case 128 9.3.2 The Variable Coefficient Case 130 9.3.3 Airy's Equation 130 9.3.4 Bessel's Equation 131 9.3.5 Other Equations 132 Problem Set D: Second Order Equations 135 10 Series Solutions 149 10.1 Series Solutions 150 10.2 Singular Points 152 11 Laplace Transforms 155 11.1 Differential Equations and Laplace Transforms 157 11.2 Discontinuous Functions 160 11.3 Differential Equations with Discontinuous Forcing 162 Problem Set E: Series Solutions and Laplace Transforms 165 12 Higher Order Equations and Systems of First Order Equations 177 12.1 Higher Order Linear Equations 178 12.2 Systems of First Order Equations 179 12.2.1 Linear First Order Systems 179 12.2.2. Using Maple to Find Eigenpairs 182 12.3 Phase Portraits 186 12.3.1 Plotting a Single Trajectory 187 12.3.2 Plotting Several Trajectories 187 12.3.3 Numerical Solutions of First Order Systems 189 13 Qualitative Theory for Systems of Differential Equations 201 Problem Set F: Systems of Differential Equations 215 Glossary 215 Sample Solutions 233 Index 243
- ISBN: 978-0-471-77317-7
- Editorial: John Wiley & Sons
- Encuadernacion: Rústica
- Páginas: 264
- Fecha Publicación: 13/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés