Introduction to Ordinary Differential Equations

This text's integrated applications and models, along with graphical and numerical procedures, motivate and explain mathematical techniques. Applied exercises are drawn from a variety of fields, including engineering and life sciences. Numerical methods are covered early and woven throughout the text. The author uses a spiraling approach to develop more abstract concepts so students aren't overwhelmed with definitions and theorems at first.

Table of Contents

1. INTRODUCTION
Examples of ODEs / Solutions of ODEs / Separable Equations / The Geometry of Fir st-Order ODEs / Numerical Estimation of Solutions / Modeling with ODEs
2. FIRST-ORDER ODEs
Linear Equations / Reducible Equations / Exact Equations and Implicit Solutions / Integrating Factors / Reduction of Order
3. GEOMETRY AND APPROXIMATION OF SOLUTIONS
Solutions--Theoretical Matters / Graphical Analysis / Numerical Estimation of So lutions
4. LINEAR SECOND-ORDER ODEs
Introduction / Homogeneous Equations with Constant Coefficients / Free Motion / The Method of Undetermined Coefficients / The Method of Variation of Parameters / Green's Function / Forced Motion
5. ADDITIONAL TOPICS IN LINEAR SECOND-ORDER ODEs
Geometry of Second-Order ODEs / Numerical Estimation of Solutions / Solutions to Linear Second-Order Equations: Theoretical Matters / Higher-Order Equations
6. LAPLACE TRANSFORMS
Definition and Illustration / Operational Properties / Discontinuous and Periodi c Forcing Functions / Solving Initial Value Problems / Convolution / The Delta F unction
7. SERIES SOLUTIONS OF LINEAR SECOND-ORDER ODEs
Power-Series Methods / Solutions at an Ordinary Point / The Cauchy-Euler Equatio n / Solutions at a Regular Singular Point, I. Solutions at a Regular Singular Po int, II
8. LINEAR TWO-DIMENSIONAL SYSTEMS OF ODEs
Introduction / Homogeneous Linear Systems / A Catalog of Phase Portraits / Nonho mogeneous Linear Systems / Higher-Dimensional Systems
9. NONLINEAR TWO-DIMENSIONAL SYSTEMS OF ODEs
Numerical Approximation of Solutions / Linearization / Stability of Equilibrium Solutions / APPENDIX A: THE FUNDAMENTAL THEOREM OF CALCULUS AND OTHER TOPICS / A PPENDIX B: PARTIAL FRACTIONS / APPENDIX C: MATRICES AND VECTORS / APPENDIX D: PO WER SERIES / ANSWERS TO ODD-NUMBERED EXERCISES