Elementary Differential Equations with Boundary / Edition 3

Elementary Differential Equations with Boundary / Edition 3

by Henry H. Edwards, David E. Penney
     
 

ISBN-10: 013253410X

ISBN-13: 9780132534109

Pub. Date: 01/28/1993

Publisher: Prentice Hall Professional Technical Reference

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;…  See more details below

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.

Product Details

ISBN-13:
9780132534109
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
01/28/1993
Edition description:
Older Edition
Pages:
800
Product dimensions:
8.35(w) x 9.52(h) x 1.35(d)

Table of Contents

Preface
1First Order Differential Equations1
1.2Solution by Direct Integration11
1.3Existence and Uniqueness of Solutions19
1.4Separable Equations and Applications32
1.5Linear First Order Equations46
1.6Substitution Methods57
1.7Exact Equations and Integrating Factors67
1.8Population Models76
1.9Motion with Variable Acceleration84
2Linear Equations of Higher Order102
2.2General Solutions of Linear Equations115
2.3Homogeneous Equations with Constant Coefficients126
2.4Mechanical Vibrations136
2.5Nonhomogeneous Equations and the Method of Undetermined Coefficients149
2.6Reduction of Order and Euler-Cauchy Equations159
2.7Variation of Parameters171
2.8Forced Oscillations and Resonance179
2.9Electrical Circuits192
2.10Endpoint Problems and Eigenvalues200
3Power Series Solutions of Linear Equations215
3.1Introduction and Review of Power Series216
3.2Series Solutions Near Ordinary Points230
3.3Regular Singular Points240
3.4Method of Frobenius: The Exceptional Cases254
3.5Bessel's Equation267
3.6Applications of Bessel Functions277
3.7Appendix on Infinite Series and the Atom284
4The Laplace Transform290
4.1Laplace Transforms and Inverse Transforms291
4.2Transformation of Initial Value Problems302
4.3Translation and Partial Fractions312
4.4Derivatives, Integrals, and Products of Transforms320
4.5Periodic and Piecewise Continuous Forcing Functions328
4.6Impulses and Delta Functions341
Table of Laplace Transforms353
5Linear Systems of Differential Equations354
5.1Introduction to Systems355
5.2The Method of Elimination366
5.3Linear Systems and Matrices375
5.4The Eigenvalue Method for Homogeneous Systems396
5.5Second Order Systems and Mechanical Applications410
5.6Multiple Eigenvalue Solutions425
5.7Nonhomogeneous Linear Systems441
5.8Matrix Exponentials and Linear Systems451
6Numerical Methods459
6.1Introduction: Euler's Method460
6.2A Closer Look at the Euler Method, and Improvements468
6.3The Runge-Kutta Method479
6.4Systems of Differential Equations488
7Nonlinear Differential Equations and Systems504
7.1Introduction to Stability505
7.2Stability and the Phase Plane511
7.3Linear and Almost Linear Systems522
7.4Ecological Applications: Predators and Competitors535
7.5Nonlinear Mechanical Systems550
7.6Chaos and Bifurcation564
8Fourier Series and Separation of Variables582
8.1Periodic Functions and Trigonometric Series583
8.2General Fourier Series and Convergence593
8.3Even-Odd Functions and Termwise Differentiation601
8.4Applications of Fourier Series612
8.5Heat Conduction and Separation of Variables619
8.6Vibrating Strings and the One-Dimensional Wave Equation631
8.7Steady-State Temperature and Laplace's Equation644
9Eigenvalues and Boundary Value Problems658
9.1Sturm-Liouville Problems and Eigenfunction Expansions659
9.2Applications of Eigenfunction Series670
9.3Steady Periodic Solutions and Natural Frequencies681
9.4Applications of Bessel Functions689
9.5Nuclear Reactors and Other Applications704
References for Further Study719
Appendix722
Answers738
Index765

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