A first course in differential equation : with boundary-value problems

Title:

Personal Author:

Zill, Dennis G., 1940-

Edition:

6th ed.

Publication Information:

Belmont, CA : Thomson Brooks/Cole, 2005

Physical Description:

1 CD-ROM; 12cm.

ISBN:

9780534418878

General Note:

Accompanied text of the same title : QA371 Z55 2005

Subject Term:

Differential equations

Boundary value problems

Added Author:

Cullen, Michael R.

Available:*

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Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the how behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

Gilbert N. LewisGilbert N. LewisGilbert N. Lewis

Preface	p. xi
Acknowledgments	p. xv
1 Introduction to Differential Equations	p. 1
1.1 Definitions and Terminology	p. 2
1.2 Initial-Value Problems	p. 15
1.3 Differential Equations as Mathematical Models	p. 22
Chapter 1 in Review	p. 37
2 First-Order Differential Equations	p. 39
2.1 Solution Curves Without the Solution	p. 40
2.2 Separable Variables	p. 51
2.3 Linear Equations	p. 60
2.4 Exact Equations	p. 72
2.5 Solutions by Substitutions	p. 80
2.6 A Numerical Solution	p. 86
Chapter 2 in Review	p. 92
3 Modeling with First-Order Differential Equations	p. 95
3.1 Linear Equations	p. 96
3.2 Nonlinear Equations	p. 109
3.3 Systems of Linear and Nonlinear Differential Equations	p. 121
Chapter 3 in Review	p. 130
Project Module: Harvesting of Renewable Natural Resources	p. 133
4 Higher-Order Differential Equations	p. 138
4.1 Preliminary Theory: Linear Equations	p. 139
4.1.1 Initial-Value and Boundary-Value Problems	p. 139
4.1.2 Homogeneous Equations	p. 142
4.1.3 Nonhomogeneous Equations	p. 148
4.2 Reduction of Order	p. 154
4.3 Homogeneous Linear Equations with Constant Coefficients	p. 158
4.4 Undetermined Coefficients--Superposition Approach	p. 167
4.5 Undetermined Coefficients--Annihilator Approach	p. 178
4.6 Variation of Parameters	p. 188
4.7 Cauchy-Euler Equation	p. 193
4.8 Solving Systems of Linear Equations by Elimination	p. 201
4.9 Nonlinear Equations	p. 207
Chapter 4 in Review	p. 212
5 Modeling with Higher-Order Differential Equations	p. 215
5.1 Linear Equations: Initial-Value Problems	p. 216
5.1.1 Spring/Mass Systems: Free Undamped Motion	p. 216
5.1.2 Spring/Mass Systems: Free Damped Motion	p. 220
5.1.3 Spring/Mass Systems: Driven Motion	p. 224
5.1.4 Series Circuit Analogue	p. 227
5.2 Linear Equations: Boundary-Value Problems	p. 237
5.3 Nonlinear Equations	p. 247
Chapter 5 in Review	p. 259
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge	p. 263
6 Series Solutions of Linear Equations	p. 267
6.1 Solutions About Ordinary Points	p. 268
6.1.1 Review of Power Series	p. 268
6.1.2 Power Series Solutions	p. 271
6.2 Solutions About Singular Points	p. 280
6.3 Two Special Equations	p. 292
Chapter 6 in Review	p. 304
7 The Laplace Transform	p. 306
7.1 Definition of the Laplace Transform	p. 307
7.2 Inverse Transform and Transforms of Derivatives	p. 314
7.3 Translation Theorems	p. 324
7.3.1 Translation on the s-Axis	p. 324
7.3.2 Translation on the t-Axis	p. 328
7.4 Additional Operational Properties	p. 338
7.5 Dirac Delta Function	p. 351
7.6 Systems of Linear Equations	p. 354
Chapter 7 in Review	p. 361
8 Systems of Linear First-Order Differential Equations	p. 364
8.1 Preliminary Theory	p. 365
8.2 Homogeneous Linear Systems with Constant Coefficients	p. 375
8.2.1 Distinct Real Eigenvalues	p. 376
8.2.2 Repeated Eigenvalues	p. 380
8.2.3 Complex Eigenvalues	p. 384
8.3 Variation of Parameters	p. 393
8.4 Matrix Exponential	p. 399
Chapter 8 in Review	p. 404
Project Module: Earthquake Shaking of Multistory Buildings	p. 406
9 Numerical Solutions of Ordinary Differential Equations	p. 410
9.1 Euler Methods and Error Analysis	p. 411
9.2 Runge-Kutta Methods	p. 417
9.3 Multistep Methods	p. 424
9.4 Higher-Order Equations and Systems	p. 427
9.5 Second-Order Boundary-Value Problems	p. 433
Chapter 9 in Review	p. 438
10 Plane Autonomous Systems and Stability	p. 439
10.1 Autonomous Systems, Critical Points, and Periodic Solutions	p. 440
10.2 Stability of Linear Systems	p. 448
10.3 Linearization and Local Stability	p. 458
10.4 Modeling Using Autonomous Systems	p. 470
Chapter 10 in Review	p. 480
11 Orthogonal Functions and Fourier Series	p. 483
11.1 Orthogonal Functions	p. 484
11.2 Fourier Series	p. 489
11.3 Fourier Cosine and Sine Series	p. 495
11.4 Sturm-Liouville Problem	p. 504
11.5 Bessel and Legendre Series	p. 511
11.5.1 Fourier-Bessel Series	p. 512
11.5.2 Fourier-Legendre Series	p. 515
Chapter 11 in Review	p. 519
12 Partial Differential Equations and Boundary-Value Problems in Rectangular Coordinates	p. 521
12.1 Separable Partial Differential Equations	p. 522
12.2 Classical Equations and Boundary-Value Problems	p. 527
12.3 Heat Equation	p. 533
12.4 Wave Equation	p. 536
12.5 Laplace's Equation	p. 542
12.6 Nonhomogeneous Equations and Boundary Conditions	p. 547
12.7 Orthogonal Series Expansions	p. 551
12.8 Boundary-Value Problems Involving Fourier Series in Two Variables	p. 555
Chapter 12 in Review	p. 559
13 Boundary-Value Problems in other Coordinate Systems	p. 561
13.1 Problems Involving Laplace's Equation in Polar Coordinates	p. 562
13.2 Problems in Polar and Cylindrical Coordinates: Bessel Functions	p. 567
13.3 Problems in Spherical Coordinates: Legendre Polynomials	p. 575
Chapter 13 in Review	p. 578
14 Integral Transform Method	p. 581
14.1 Error Function	p. 582
14.2 Applications of the Laplace Transform	p. 584
14.3 Fourier Integral	p. 595
14.4 Fourier Transforms	p. 601
Chapter 14 in Review	p. 607
15 Numerical Solutions of Partial Differential Equations	p. 610
15.1 Elliptic Equations	p. 611
15.2 Parabolic Equations	p. 617
15.3 Hyperbolic Equations	p. 625
Chapter 15 in Review	p. 630
Appendixes	p. 1
I Gamma Function	p. 1
II Introduction to Matrices	p. 3
III Laplace Transforms	p. 25
Selected Answers for Odd-Numbered Problems	p. 1
Index	p. 1

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