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 Variables. Linear
Equations. Exact Equations and Integrating Factors. 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 Differential Equations. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory-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. Solving Systems of Linear Differential
Equations 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. 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 FIRST-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous
Linear Systems. Matrix Exponential. Chapter 8 in Review.
9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order
Equations and Systems. Second-Order Boundary-Value Problems.
Chapter 9 in Review.
Appendix I: Gamma Function.
Appendix II: Matrices.
Appendix III: Laplace Transforms.
Answers for Selected Odd-Numbered Problems.
Dennis Zill, Ph.D., received a doctorate in applied mathematics from Iowa State University and is a former professor of mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa and California Polytechnic State University. He is also the former chair of the mathematics department at Loyola Marymount University, where he currently holds the title of Professor Emeritus of Mathematics. Zill has interests in astronomy, modern literature, music, golf and good wine, while his research interests include special functions, differential equations, integral transformations and complex analysis.
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