Elementary Differential Equations with Boundary Value Problems

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9780132540612: Elementary Differential Equations with Boundary Value Problems

This accessible, attractive, and interesting book enables readers to first solve those differential equations that have the most frequent and interesting applications. This approach illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques. The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications. Topics covered include first-order differential equations, linear equations of higher order, power series methods, Laplace transform methods, linear systems of differential equations, numerical methods, nonlinear systems and phenomena, Fourier series methods, and Eigenvalues and boundary value problems. For those involved in the fields of science, engineering, and mathematics.

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From the Publisher:

Focused on the standard elementary techniques of solution of differential equations and the mathematical modeling of real-world situations, this book anticipates and addresses the questions and difficulties typically encountered by those studying the subject for the first time.

From the Back Cover:

Maintaining a contemporary perspective, this strongly algebraic-oriented text provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics readers take following calculus. Matters of definition, classification, and logical structure deserve (and receive here) careful attention for the first time in the mathematical experience of many of the readers. While it is neither feasible nor desirable to include proofs of the fundamental existence and uniqueness theorems along the way in an elementary course, readers need to see precise and clear-cut statements of these theorems, and understand their role in the subject. Appropriate existence and uniqueness proofs in the Appendix are included, and referred to where appropriate in the main body of the text. Applications are highlighted throughout the text. These include: What explains the commonly observed lag time between indoor and outdoor daily temperature oscillations?; What makes the difference between doomsday and extinction in alligator populations?; How do a unicycle and a two-axle car react differently to road bumps?; Why are flagpoles hollow instead of solid?; Why might an earthquake demolish one building and leave standing the one next door?; How can you predict the time of next perihelion passage of a newly observed comet?; Why and when does non-linearity lead to chaos in biological and mechanical systems?; What explains the difference in the sounds of a guitar, a xylophone, and a drum? Includes almost 300 computer-generated graphics throughout the text. This text, with enough material for 2 terms, provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics readers take following calculus.

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