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by C. Henry Edwards and David E. Penney

ISBN13: 978-0139737510

ISBN10: 0139737510

Cover type:

Edition: 01

Copyright: 2001

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

ISBN10: 0139737510

Cover type:

Edition: 01

Copyright: 2001

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

**1. First-Order Differential Equations. **

Differential Equations and Mathematical Model. Integrals as General and Particular Solutions. Direction Fields and Solution Curves. Separable Equations and Applications. Linear First-Order Equations. Substitution Methods and Exact Equations.

**2. Mathematical Models and Numerical Methods. **

Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method. The Runge-Kutta Method.

**3. Linear Systems and Matrices. **

Introduction to Linear Systems. Matrices and Gaussian Elimination. Reduced Row-Echelon Matrices. Matrix Operations. Inverses of Matrices. Determinants. Linear Equations and Curve Fitting.

**4. Vector Spaces. **

The Vector Space **R^3**. The Vector Space **R**** n** and Subspaces. Linear Combinations and Independence of Vectors. Bases and Dimension for Vector Spaces. General Vector Spaces.

**5. Linear Equations of Higher Order. **

Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Undetermined Coefficients and Variation of Parameters. Forced Oscillations and Resonance.

**6. Eigenvalues and Eigenvectors. **

Introduction to Eigenvalues. Diagonalization of Matrices. Applications Involving Powers of Matrices.

**7. Linear Systems of Differential Equations. **

First-Order Systems and Applications. Matrices and Linear Systems. The Eigenvalue Method for Linear Systems. Second-Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Numerical Methods for Systems.

**8. Matrix Exponential Methods. **

Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems. Spectral Decomposition Methods.

**9. Nonlinear Systems and Phenomena. **

Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems.

**10. Laplace Transform 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 Forcing Functions.

**11. Power Series Methods. **

Introduction and Review of Power Series. Power Series Solutions. Frobenius Series Solutions. Bessel's Equation.

References for Further Study.

Appendix A: The Existence and Uniqueness of Solutions.

Appendix B: Theory of Determinants.

Answers to Selected Problems.

Index.

C. Henry Edwards and David E. Penney

ISBN13: 978-0139737510ISBN10: 0139737510

Cover type:

Edition: 01

Copyright: 2001

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

Table of Contents

**1. First-Order Differential Equations. **

**2. Mathematical Models and Numerical Methods. **

**3. Linear Systems and Matrices. **

**4. Vector Spaces. **

**R^3**. The Vector Space **R**** n** and Subspaces. Linear Combinations and Independence of Vectors. Bases and Dimension for Vector Spaces. General Vector Spaces.

**5. Linear Equations of Higher Order. **

**6. Eigenvalues and Eigenvectors. **

Introduction to Eigenvalues. Diagonalization of Matrices. Applications Involving Powers of Matrices.

**7. Linear Systems of Differential Equations. **

**8. Matrix Exponential Methods. **

**9. Nonlinear Systems and Phenomena. **

**10. Laplace Transform Methods. **

**11. Power Series Methods. **

References for Further Study.

Appendix A: The Existence and Uniqueness of Solutions.

Appendix B: Theory of Determinants.

Answers to Selected Problems.

Index.

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