Elementary Differential Equations with Boundary Value Problems

International Edition

Edwards, C. Henry , Penney, David E. 저자(글)

Pearson Prentice Hall · 2008년 04월 01일

책 소개

작가정보

저자(글) Edwards, C. Henry

저자(글) Penney, David E.

목차

• Preface
  First-Order Differential Equations
  Differential Equations and Mathematical Models
  Integrals as General and Particular Solutions
  Slope Fields and Solution Curves
  Separable Equations and Applications
  Linear First-Order Equations
  Substitution Methods and Exact Equations
  Population Models
  Acceleration-Velocity Models
  Linear Equations of Higher Order
  Introduction: Second-Order Linear Equations
  General Solutions of Linear Equations
  Homogeneous Equations with Constant Coefficients
  Mechanical Vibrations
  Nonhomogeneous Equations and Undetermined Coefficients
  Forced Oscillations and Resonance
  Electrical Circuits
  Endpoint Problems and Eigenvalues
  Power Series Methods
  Introduction and Review of Power Series
  Series Solutions Near Ordinary Points
  Regular Singular Points
  Method of Frobenius: The Exceptional Cases
  Bessel's Equation
  Applications of Bessel Functions
  LaplaceTransform Methods
  Laplace Transforms and Inverse Transforms
  Transformation of Initial Value Problems
  Translation and Partial Fractions
  Derivatives, Integrals, and Products of Transforms
  Periodic and Piecewise Continuous Input Functions
  Impulses and Delta Functions
  Linear Systems of Differential Equations
  First-Order Systems and Applications
  The Method of Elimination
  Matrices and Linear Systems
  The Eigenvalue Method for Homogeneous Systems
  Second-Order Systems and Mechanical Applications
  Multiple Eigenvalue Solutions
  Matrix Exponentials and Linear Systems
  Nonhomogeneous Linear Systems
  Numerical Methods
  Numerical Approximation: Euler's Method
  A Closer Look at the Euler Method
  The Runge-Kutta Method
  Numerical Methods for Systems
  Nonlinear Systems and Phenomena
  Equilibrium Solutions and Stability
  Stability and the Phase Plane
  Linear and Almost Linear Systems
  Ecological Models: Predators and Competitors
  Nonlinear Mechanical Systems
  Chaos in Dynamical Systems
  Fourier Series Methods
  Periodic Functions and Trigonometric Series
  General Fourier Series and Convergence
  Fourier Sine and Cosine Series
  Applications of Fourier Series
  Heat Conduction and Separation of Variables
  Vibrating Strings and the One-Dimensional Wave Equation
  Steady-State Temperature and Laplace's Equation
  Eigenvalues and Boundary Value Problems
  Sturm-Liouville Problems and Eigenfunction Expansions
  Applications of Eigenfunction Series
  Steady Periodic Solutions and Natural Frequencies
  Cylindrical Coordinate Problems
  Higher-Dimensional Phenomena
  References for Further Study
  Appendix: Existence and Uniqueness of Solutions
  Answers to Selected Problems
  Index I-1
  Table of Contents provided by Publisher. All Rights Reserved.

기본정보

ISBN	9780132358811 ( 0132358816 )
발행(출시)일자	2008년 04월 01일
쪽수	792쪽
총권수	1권
언어	영어