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一山

铁杆木虫 (正式写手)

应助: 17 (小学生)
金币: 5709
散金: 15
红花: 3
帖子: 988
在线: 287.6小时
虫号: 92730
注册: 2005-09-10
专业: 光学

[交流] 发：Boundary Value Problems and Partial Differential Equations

好书，共享之！

the back of the book. An Instructor’s Manual is available both online and in
print (ISBN: 0-12-369435-3), with the answers to the even-numbered problems.
A Student Solutions Manual is available both online and in print (ISBN:
0-12-088586-7), that contains detailed solutions of odd-numbered problems.
There are many ways of choosing and arranging topics from the book to
provide an interesting and meaningful course. The following sections form
the core, requiring at least 14 hours of lecture: Sections 1.1–1.3, 2.1–2.5, 3.1–3.3, 4.1–4.3, and 4.5. These cover the basics of Fourier series and the solutions of heat, wave, and potential equations in finite regions. My choice for the next most important block of material is the Fourier integral and the solution of problems on unbounded regions: Sections 1.9, 2.10–2.12, 3.6, and 4.4. These require at least six more lectures.
The tastes of the instructor and the needs of the audience will govern the choice of further material. A rather theoretical flavor results from including: Sections 1.4–1.7 on convergence of Fourier series; Sections 2.7–2.9 on Sturm–Liouville problems, and the sequel, Section 3.4; and the more difficult parts of Chapter 5, Sections 5.5–5.10 on Bessel functions and Legendre polynomials.
On the other hand, inclusion of numerical methods in Sections 1.8 and 3.5 and Chapter 7 gives a very applied flavor.
Chapter 0 reviews solution techniques and theory of ordinary differential
equations and boundary value problems. Equilibrium forms of the heat and
wave equations are derived also. This material belongs in an elementary differential equations course and is strictly optional. However, many students have either forgotten it or never seen it.
For this fifth edition, I have revised in response to students’ changing needs and abilities. Many sections have been rewritten to improve clarity, provide extra detail, and make solution processes more explicit. In the optional Chapter 0, free and forced vibrations are major examples for solution of differential equations with constant coefficients. In Chapter 1, I have returned to deriving the Fourier integral as a “limit” of Fourier series. New exercises are included for applications of Fourier series and integrals. Solving potential problems on a rectangle seems to causemore difficulty than expected. A new section 4.3 gives more guidance and examples as well as some information about the Poisson equation. New exercises have been added and old ones revised throughout.
In particular I have included exercises based on engineering research publications.
These provide genuine problems with real data.
A new feature of this edition is a CD with auxiliary materials: animations
of convergence of Fourier series; animations of solutions of the heat and wave equations as well as ordinary initial value problems; color graphics of solutions of potential problems; additional exercises in a workbook style; review questions for each chapter; text material on using a spreadsheet for numerical methods. All files are readable with just a browser and Adobe Reader, available without cost.
http://www.namipan.com/d/28ccb8ba507c786de3203af617b24cbe753c804fb0783300

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