Differential Equations Computing and Modeling and Differential Equations and Boundary Value Problems Computing and Modeling 5th Edition Edwards Solutions Manual

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

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