Differential Equations

Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall9780495012658, 0495012653

Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.

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Table of contents :
Front cover……Page 1
About the authors……Page 6
Preface……Page 8
Note to the student……Page 14
Table of contents……Page 16
1 – First-order differential equations……Page 20
2 – First-order systems……Page 170
3 – Linear systems……Page 252
4 – Forcing and resonance……Page 400
5 – Nonlinear systems……Page 470
6 – Laplace transforms……Page 578
7 – Numerical methods……Page 646
8 – Discrete dynamical systems……Page 688
Appendices……Page 742
Hints and answers……Page 768
Index……Page 838