微分方程及其應用

內(nèi)容概要

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.

書籍目錄

Chapter 1 First-order differential equations   1.1 Introduction   1.2 First-order linear differential equations   1.3 The Van Meegeren art forgeries   1.4 Separable equations   1.5 Population models   1.6 The spread of technological innovations   1.7 An atomic waste disposal problem   1.8 The dynamics of tumor growth， mixing problems， and orthogonal trajectories   1.9 Exact equations， and why we cannot solve very many differential equations   1.10 The existence-uniqueness theorem； Picard iteration   1.11 Finding roots of equations by iteration     1.11.1 Newton‘s method   1.12 Difference equations， and how to compute the interest due on your student loans   1.13 Numerical approximations； Euler‘s method     1.13.1 Error analysis for Euler‘s method   1.14 The three term Taylor series method  1.15 An impwoved Euler method  1.16 The Runge-Kutta method  1.17 What to do in practiceChapter 2 Second-order linear differential equations  2.1 Algebraic properties of solutions  2.2 Linear equations with constant coefficients  2.3 The nonhomogeneous equation  2.4 The method of variation of parameters  2.5 the method of judicious guessing……Chapter 3 Systems of differential equationsChapter 4 Qualitative theory of differential equationsChapter 5 Separation of varibles and Fourier seriesChapter 6 Sturm-Liouville boundary value problemsAppendix A Some simple facts concerning functions of several variablesAppendix B Sequences and seriesAppendix C C ProgramsAnswers to odd-numbered dexercisesIndex

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