A First Course in Differential Equations with Modeling Applications, International Metric Edition

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.