Introduction to Ordinary Differential Equations
Stephen H. Saperstone
- 出版商: brooks/cole
- 出版日期: 1998-02-05
- 售價: $1,000
- 貴賓價: 9.5 折 $950
- 語言: 英文
- 頁數: 634
- 裝訂: Hardcover
- ISBN: 0314058192
- ISBN-13: 9780314058195
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商品描述
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