The text is intended for a first course on the subject, to be taken by students who have had two years of calculus and an introduction to ordinary differential equations and vector spaces. Actually, there are two variants of the course which are interwoven in the text; they correspond to two different 10-week undergraduate courses at Georgia Tech in which the text has been used. The course emphasizing the integral operators and the method of Green's functions, Mathematics 4348, follows the "Green track" with the plan listed below, while the course emphasizing Fourier series and other orthogonal series, Mathematics 4582, follows the orthogonal track. The materials in the orthogonal track originated as class notes by Evans Harrell, while the ones in the Green track originated as class notes by James Herod. A good 15-week course could be made from all of one track and selected pieces of the other.
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Syllabus: An outline of the content and objectives of a course at Georgia Tech
A diagnostic homework assignment, which you should take before embarking on this course.
Other possibly useful links are to the usenet newsgroup devoted to mathematics and mail to other professors at Georgia Tech who teach these courses, Profs. Chafee, Loss, Neff, and Swiech,
CHAPTER II: BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS