A First Course in Differential Equations with Modeling Applications, 12th Edition Dennis G. Zill

A First Course in Differential Equations with Modeling Applications, 12th Edition Dennis G. Zill

Table of Content

1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.
Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review.
2. FIRST-ORDER DIFFERENTIAL EQUATIONS.
Solution Curves Without a Solution. Separable Equations. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review.
3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS.
Linear Models. Nonlinear Models. Modeling with Systems of First-Order DEs. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Theory of Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Green’s Functions. Solving Systems of Linear DEs by Elimination. Nonlinear Differential Equations. Chapter 4 in Review.
5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review.
6. SERIES SOLUTIONS OF LINEAR EQUATIONS.
Review of Power Series. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review.
7. THE LAPLACE TRANSFORM.
Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review.
8. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS.
Theory of Linear Systems. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.
9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review.
Appendix A: Integral-Defined Functions.
Appendix B: Matrices.
Appendix C: Table of Laplace Transforms.
Answers to Selected Odd-Numbered Problems.
Index.