Differential Equations with Maple V(R) (eBook)

Martha L Abell, James P. Braselton (Autoren)

eBook Download: PDF

2014 | 1. Auflage
698 Seiten
Elsevier Science (Verlag)
978-1-4832-6657-2 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 9.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• ISBN-10: 1-4832-6657-5 / 1483266575
• ISBN-13: 978-1-4832-6657-2 / 9781483266572