Elementary Differential Equations with Boundary Value Problems, 2nd edition

  • Lee W. Johnson, 
  • Werner E. Kohler

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Overview

Elementary Differential Equations with Boundary Value Problems presents the underlying theory, solution procedures, and numerical/computational aspects of differential equations in a seamless way. Using this useful framework, you'll be able to understand and solve differential equations.

Published by Pearson (July 14th 2021) - Copyright © 2006

ISBN-13: 9780137546398

Subject: Advanced Math

Category: Differential Equations

Table of contents

Table of Contents

  1. INTRODUCTION TO DIFFERENTIAL EQUATIONS
    • 1.1 Examples of Differential Equations
    • 1.2 Direction Fields
  2. FIRST ORDER DIFFERENTIAL EQUATIONS
    • 2.1 Introduction
    • 2.2 First Order Linear Differential Equations
    • 2.3 Introduction to Mathematical Models
    • 2.4 Population Dynamics and Radioactive Decay
    • 2.5 First Order Nonlinear Differential Equations
    • 2.6 Separable First Order Equations
    • 2.7 Exact Differential Equations
    • 2.8 The Logistic Population Model
    • 2.9 Applications to Mechanics
    • 2.10 Euler’s Method
    • 2.11 Review Exercises
  3. SECOND AND HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
    • 3.1 Introduction
    • 3.2 The General Solution of Homogeneous Equations
    • 3.3 Constant Coefficient Homogeneous Equations
    • 3.4 Real Repeated Roots; Reduction of Order
    • 3.5 Complex Roots
    • 3.6 Unforced Mechanical Vibrations
    • 3.7 The General Solution of a Linear Nonhomogeneous Equation
    • 3.8 The Method of Undetermined Coefficients
    • 3.9 The Method of Variation of Parameters
    • 3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance
    • 3.11 Higher Order Linear Homogeneous Differential Equations
    • 3.12 Higher Order Homogeneous Constant Coefficient Differential Equations
    • 3.13 Higher Order Linear Nonhomogeneous Differential Equations
    • 3.14 Review Exercises
  4. FIRST ORDER LINEAR SYSTEMS
    • 4.1 Introduction
    • 4.2 Existence and Uniqueness
    • 4.3 Homogeneous Linear Systems
    • 4.4 Constant Coefficient Homogeneous Systems and the Eigenvalue Problem
    • 4.5 Real Eigenvalues and the Phase Plane
    • 4.6 Complex Eigenvalues
    • 4.7 Repeated Eigenvalues
    • 4.8 Nonhomogeneous Linear Systems
    • 4.9 Numerical Methods for Systems of Differential Equations
    • 4.10 The Exponential Matrix and Diagonalization
    • 4.11 Review Exercises
  5. LAPLACE TRANSFORMS
    • 5.1 Introduction
    • 5.2 Laplace Transform Pairs
    • 5.3 The Method of Partial Fractions
    • 5.4 Laplace Transforms of Periodic Functions and System Transfer Functions
    • 5.5 Solving Systems of Differential Equations
    • 5.6 Convolution
    • 5.7 The Delta Function and Impulse Response
  6. NONLINEAR SYSTEMS
    • 6.1 Introduction
    • 6.2 Equilibrium Solutions and Direction Fields
    • 6.3 Conservative Systems
    • 6.4 Stability
    • 6.5 Linearization and the Local Picture
    • 6.6 Two-Dimensional Linear Systems
    • 6.7 Predator-Prey Population Models
  7. NUMERICAL METHODS
    • 7.1 Euler’s Method, Heun’s Method, the Modified Euler’s Method
    • 7.2 Taylor Series Methods
    • 7.3 Runge-Kutta Methods
  8. SERIES SOLUTION OF DIFFERENTIAL EQUATIONS
    • 8.1 Introduction
    • 8.2 Series Solutions near an Ordinary Point
    • 8.3 The Euler Equation
    • 8.4 Solutions Near a Regular Singular Point and the Method of Frobenius
    • 8.5 The Method of Frobenius Continued; Special Cases and a Summary
  9. SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES
    • 9.1 Heat Flow in a Thin Bar. Separation of Variables
    • 9.2 Series Solutions
    • 9.3 Calculating the Solution
    • 9.4 Fourier Series
    • 9.5 The Wave Equation
    • 9.6 Laplace’s Equation
    • 9.7 Higher-Dimensional Problems; Nonhomogeneous Equations
  10. FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD OF CHARACTERISTICS
    • 10.1 The Cauchy Problem
    • 10.2 Existence and Uniqueness
    • 10.3 The Method of Characteristics
  11. LINEAR TWO-POINT BOUNDARY VALUE PROBLEMS
    • 11.1 Existence and Uniqueness
    • 11.2 Two-Point Boundary Value Problems for Linear Systems
    • 11.3 Sturm-Liouville Boundary Value Problems

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