Introduction to Ordinary Differential Equations
Edition: 1st 1998
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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.
Copyright year: 1998
Size: 8.50" wide x 10.25" long x 1.00" tall
1. INTRODUCTION Examples of ODEs / Solutions of ODEs / Separable Equations / The Geometry of First-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 Solutions 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 Periodic Forcing Functions / Solving Initial Value Problems / Convolution / The Delta Function 7. SERIES SOLUTIONS OF LINEAR SECOND-ORDER ODEs Power-Series Methods / Solutions at an Ordinary Point / The Cauchy-Euler Equation / Solutions at a Regular Singular Point, I. Solutions at a Regular Singular Point, II 8. LINEAR TWO-DIMENSIONAL SYSTEMS OF ODEs Introduction / Homogeneous Linear Systems / A Catalog of Phase Portraits / Nonhomogeneous 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 / APPENDIX B: PARTIAL FRACTIONS / APPENDIX C: MATRICES AND VECTORS / APPENDIX D: POWER SERIES / ANSWERS TO ODD-NUMBERED EXERCISES