Solution Manual for Elementary Differential Equations with Boundary Value Problems 6th Edition

1. First-Order Differential Equations
   • 1.1 Differential Equations and Mathematical Models
   • 1.2 Integrals as General and Particular Solutions
   • 1.3 Slope Fields and Solution Curves
   • 1.4 Separable Equations and Applications
   • 1.5 Linear First-Order Equations
   • 1.6 Substitution Methods and Exact Equations
   • 1.7 Population Models
   • 1.8 Acceleration-Velocity Models
2. Linear Equations of Higher Order
   • 2.1 Introduction: Second-Order Linear Equations
   • 2.2 General Solutions of Linear Equations
   • 2.3 Homogeneous Equations with Constant Coefficients
   • 2.4 Mechanical Vibrations
   • 2.5 Nonhomogeneous Equations and Undetermined Coefficients
   • 2.6 Forced Oscillations and Resonance
   • 2.7 Electrical Circuits
   • 2.8 Endpoint Problems and Eigenvalues
3. Power Series Methods
   • 3.1 Introduction and Review of Power Series
   • 3.2 Series Solutions Near Ordinary Points
   • 3.3 Regular Singular Points
   • 3.4 Method of Frobenius: The Exceptional Cases
   • 3.5 Bessel’s Equation
   • 3.6 Applications of Bessel Functions
4. Laplace Transform Methods
   • 4.1 Laplace Transforms and Inverse Transforms
   • 4.2 Transformation of Initial Value Problems
   • 4.3 Translation and Partial Fractions
   • 4.4 Derivatives, Integrals, and Products of Transforms
   • 4.5 Periodic and Piecewise Continuous Input Functions
   • 4.6 Impulses and Delta Functions
5. Linear Systems of Differential Equations
   • 5.1 First-Order Systems and Applications
   • 5.2 The Method of Elimination
   • 5.3 Matrices and Linear Systems
   • 5.4 The Eigenvalue Method for Homogeneous Systems
   • 5.5 Second-Order Systems and Mechanical Applications
   • 5.6 Multiple Eigenvalue Solutions
   • 5.7 Matrix Exponentials and Linear Systems
   • 5.8 Nonhomogeneous Linear Systems
6. Numerical Methods
   • 6.1 Numerical Approximation: Euler’s Method
   • 6.2 A Closer Look at the Euler Method
   • 6.3 The Runge-Kutta Method
   • 6.4 Numerical Methods for Systems
7. Nonlinear Systems and Phenomena
   • 7.1 Equilibrium Solutions and Stability
   • 7.2 Stability and the Phase Plane
   • 7.3 Linear and Almost Linear Systems
   • 7.4 Ecological Models: Predators and Competitors
   • 7.5 Nonlinear Mechanical Systems
   • 7.6 Chaos in Dynamical Systems
8. Fourier Series Methods
   • 8.1 Periodic Functions and Trigonometric Series
   • 8.2 General Fourier Series and Convergence
   • 8.3 Fourier Sine and Cosine Series
   • 8.4 Applications of Fourier Series
   • 8.5 Heat Conduction and Separation of Variables
   • 8.6 Vibrating Strings and the One-Dimensional Wave Equation
   • 8.7 Steady-State Temperature and Laplace’s Equation
9. Eigenvalues and Boundary Value Problems
   • 9.1 Sturm-Liouville Problems and Eigenfunction Expansions
   • 9.2 Applications of Eigenfunction Series
   • 9.3 Steady Periodic Solutions and Natural Frequencies
   • 9.4 Cylindrical Coordinate Problems
   • 9.5 Higher-Dimensional Phenomena

References for Further Study

Appendix: Existence and Uniqueness of Solutions

Answers to Selected Problems

Index