Abell / Braselton Differential Equations with Maple V®

1. Auflage 2014
ISBN: 978-1-4832-6657-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 698 Seiten, Web PDF

Differential Equations with Maple V provides an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Maple V is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Maple V can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Autoren/Hrsg.

Abell, Martha L

Braselton, James P.

Inhaltsverzeichnis

1;Front Cover;1
2;Differential Equations with Maple V®;4
3;Copyright Page;5
4;Table of
Contents;6
5;Preface;14
6;CHAPTER 1. INTRODUCTION TO DIFFERENTIAL EQUATIONS;16
6.1;1.1 PURPOSE;16
6.2;1.2 Definitions and Concepts;17
6.3;1.3 Solutions of Differential Equations;20
6.4;1.4 Initial-and Boundary-Value Problems;25
6.5;1.5 Direction Fields;26
7;CHAPTER 2. FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS;32
7.1;2.1 Separation of Variables;32
7.2;2.2 Homogeneous Equations;38
7.3;2.3 Exact Equations;45
7.4;2.4 Linear Equations;53
7.5;2.5 Some Special Differential Equations;64
7.6;2.6 Theory of First-Order Equations;79
7.7;2.7 Numerical Approximation of First-Order Equations;81
8;CHAPTER 3. APPLICATIONS OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS;100
8.1;3.1 Orthogonal Trajectories;100
8.2;3.2 Population Growth and Decay;108
8.3;3.3 Newton's Law of Cooling;116
8.4;3.4 Free-Falling Bodies;122
9;CHAPTER 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS;132
9.1;4.1 Preliminary Definitions and Notation;132
9.2;4.2 Solutions of Homogeneous Equations with Constant Coefficients;141
9.3;4.3 Nonhomogeneous Equations with Constant Coefficients: The Annihilator Method;162
9.4;4.4 Nonhomogeneous Equations with Constant Coefficients: The Method of Undeternined Coefficients;178
9.5;4.5 Nonhomogeneous Equations with Constant Coefficients:Variation of Parameters;188
10;CHAPTER 5. APPLICATIONS OF HIGHER-ORDER DIFFERENTIAL EQUATIONS;206
10.1;5.1 Simple Harmonic Motion;206
10.2;5.2 Damped Motion;214
10.3;5.3 Forced Motion;226
10.4;5.4 Other Applications;241
10.5;5.5 The Pendulum Problem;247
11;CHAPTER 6. ORDINARY DIFFERENTIAL EQUATIONS WITH NONCONSTANT COEFFICIENTS;260
11.1;6.1 Cauchy-Euler Equations;260
11.2;6.2
Power Series Review;272
11.3;6.3
Power Series Solutions about Ordinary Points;280
11.4;6.4
Power Series Solutions about Regular Singular Points;291
11.5;6.5 Some Special Equations;307
12;CHAPTER 7. INTRODUCTION TO THE LAPLACE TRANSFORM;316
12.1;7.1 The Laplace Transform: Preliminary Definitions and Notation;317
12.2;7.2 The Inverse Laplace Transform;328
12.3;7.3 Solving Initial-Value Problems with the Laplace Transform;337
12.4;7.4 Laplace Transforms of Several Important Functions;346
12.5;7.5 The Convolution Theorem;370
13;CHAPTER 8. APPLICATIONS OF LAPLACE TRANSFORMS;376
13.1;8.1 Spring-Mass Systems Revisited;376
13.2;8.2 L-R-C Circuits Revisited;385
13.3;8.3 Population Problems Revisited;393
14;CHAPTER 9. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS;396
14.1;9.1 Systems of Equations: The Operator Method;396
14.2;9.2 Review of Matrix Algebra and Calculus;406
14.3;9.3 Preliminary Definitions and Notation;424
14.4;9.4 Homogeneous Linear Systems with Constant Coefficients;433
14.5;9.5 Variation of Parameters;455
14.6;9.6 Laplace Transforms;464
14.7;9.7 Nonlinear Systems, Linearization, and Classification of Equilibrium Points;469
14.8;9.8 Numerical Methods;484
15;CHAPTER 10. APPLICATIONS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS;502
15.1;10.1 L-R-C Circuits with Loops;502
15.2;10.2 Diffusion Problems;514
15.3;10.3 Spring-Mass Systems;523
15.4;10.4 Population Problems;529
15.5;10.5 Applications Using Laplace Transforms;535
15.6;10.6 Special Nonlinear Equations and Systems of Equations;548
16;CHAPTER 11. EIGENVALUE PROBLEMS AND FOURIER SERIES;560
16.1;11.1 Boundary-Value, Eigenvalue, and Sturm-Liouville Problems;560
16.2;11.2 Fourier Sine Series and Cosine Series;568
16.3;11.3 Fourier Series;582
16.4;11.4 Generalized Fourier Series: Bessel-Fourier Series;592
17;CHAPTER 12. PARTIAL DIFFERENTIAL EQUATIONS;604
17.1;12.1 Introduction to Partial Differential Equations and Separation of Variables;604
17.2;12.2 The One-Dimensional Heat Equation;606
17.3;12.3 The One-Dimensional Wave Equation;616
17.4;12.4 Problems in Two Dimensions: Laplace's Equation;625
17.5;12.5 Two-Dimensional Problems in a Circular Region;631
18;APPENDIX: GETTING HELP FROM MAPLE V;650
18.1;A Note Regarding Different Versions of Maple;650
18.2;Getting Started with Maple V;650
18.3;Getting Help from Maple V;654
18.4;The Maple V Tutorial;659
18.5;Loading Miscellaneous Library Functions;662
18.6;Loading Packages;663
19;GLOSSARY;668
20;SELECTED REFERENCES;692
21;INDEX;694