Elementary Differential Equations with Boundary / Edition 3

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Overview

Anticipates and addresses the questions and difficulties that students typicallyencounter when they study standard elementary techniques of solution of differential equations and the mathematical modeling of real-world situations. Features computer-generated artwork to illustrate geometric aspects of differential equations; revised discussion of numerical methods; simple BASIC programs; and over 1800 computational drill problems and diverse applications to help explain first order differential equations, linear equations of higher order, nonlinear differential equations and systems, fourier series and separation of variables, Eigenvalues and boundary value problems. and more. For sophomore/junior-level professors of differential equations.
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Editorial Reviews

Booknews
First edition published in 1985. Textbook for undergraduate science, engineering, and mathematics students focuses on matters of definition, classification, and logical structure. Acidic paper. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780132534109
  • Publisher: Prentice Hall Professional Technical Reference
  • Publication date: 1/28/1993
  • Edition description: Older Edition
  • Edition number: 3
  • Pages: 800
  • Product dimensions: 8.35 (w) x 9.52 (h) x 1.35 (d)

Table of Contents

Preface
1 First Order Differential Equations 1
1.2 Solution by Direct Integration 11
1.3 Existence and Uniqueness of Solutions 19
1.4 Separable Equations and Applications 32
1.5 Linear First Order Equations 46
1.6 Substitution Methods 57
1.7 Exact Equations and Integrating Factors 67
1.8 Population Models 76
1.9 Motion with Variable Acceleration 84
2 Linear Equations of Higher Order 102
2.2 General Solutions of Linear Equations 115
2.3 Homogeneous Equations with Constant Coefficients 126
2.4 Mechanical Vibrations 136
2.5 Nonhomogeneous Equations and the Method of Undetermined Coefficients 149
2.6 Reduction of Order and Euler-Cauchy Equations 159
2.7 Variation of Parameters 171
2.8 Forced Oscillations and Resonance 179
2.9 Electrical Circuits 192
2.10 Endpoint Problems and Eigenvalues 200
3 Power Series Solutions of Linear Equations 215
3.1 Introduction and Review of Power Series 216
3.2 Series Solutions Near Ordinary Points 230
3.3 Regular Singular Points 240
3.4 Method of Frobenius: The Exceptional Cases 254
3.5 Bessel's Equation 267
3.6 Applications of Bessel Functions 277
3.7 Appendix on Infinite Series and the Atom 284
4 The Laplace Transform 290
4.1 Laplace Transforms and Inverse Transforms 291
4.2 Transformation of Initial Value Problems 302
4.3 Translation and Partial Fractions 312
4.4 Derivatives, Integrals, and Products of Transforms 320
4.5 Periodic and Piecewise Continuous Forcing Functions 328
4.6 Impulses and Delta Functions 341
Table of Laplace Transforms 353
5 Linear Systems of Differential Equations 354
5.1 Introduction to Systems 355
5.2 The Method of Elimination 366
5.3 Linear Systems and Matrices 375
5.4 The Eigenvalue Method for Homogeneous Systems 396
5.5 Second Order Systems and Mechanical Applications 410
5.6 Multiple Eigenvalue Solutions 425
5.7 Nonhomogeneous Linear Systems 441
5.8 Matrix Exponentials and Linear Systems 451
6 Numerical Methods 459
6.1 Introduction: Euler's Method 460
6.2 A Closer Look at the Euler Method, and Improvements 468
6.3 The Runge-Kutta Method 479
6.4 Systems of Differential Equations 488
7 Nonlinear Differential Equations and Systems 504
7.1 Introduction to Stability 505
7.2 Stability and the Phase Plane 511
7.3 Linear and Almost Linear Systems 522
7.4 Ecological Applications: Predators and Competitors 535
7.5 Nonlinear Mechanical Systems 550
7.6 Chaos and Bifurcation 564
8 Fourier Series and Separation of Variables 582
8.1 Periodic Functions and Trigonometric Series 583
8.2 General Fourier Series and Convergence 593
8.3 Even-Odd Functions and Termwise Differentiation 601
8.4 Applications of Fourier Series 612
8.5 Heat Conduction and Separation of Variables 619
8.6 Vibrating Strings and the One-Dimensional Wave Equation 631
8.7 Steady-State Temperature and Laplace's Equation 644
9 Eigenvalues and Boundary Value Problems 658
9.1 Sturm-Liouville Problems and Eigenfunction Expansions 659
9.2 Applications of Eigenfunction Series 670
9.3 Steady Periodic Solutions and Natural Frequencies 681
9.4 Applications of Bessel Functions 689
9.5 Nuclear Reactors and Other Applications 704
References for Further Study 719
Appendix 722
Answers 738
Index 765
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