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Math 135: General Course Outline |
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Catalog Description
135. Ordinary Differential Equations.
(4) Lecture, three hours; discussion, one hour. Requisites: courses 33A,
33B. Selected topics in differential equations. Laplace transforms, existence
and uniqueness theorems, Fourier series, separation of variable solutions to
partial differential equations, Sturm-Liouville theory, calculus of variations,
two point boundary value problems, Green's functions. P/NP or letter grading.
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Textbook
G. Simmons, Differential Equations
with Applications and Historical Notes, 2nd Ed., McGraw-Hill.
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Schedule of Lectures
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CommentsFootnotes 1. The book does not include a review of partial fractions. Most calculus textbooks provide a suitable discussion of the technique. 2. The book only states a limited form of the Heavyside expansion theorem in problem 5 of section 53. The more general statement can be found in standard texts devoted to Laplace transforms. 3. The book provides a limited description of the use of the unit-step function and unit impulse functions. A better treatment can be found in Redheffer's book Differential Equations. 4. The proof of Theorem B is easier than Theorem A (the local existence theorem) since one doesn't have to worry about the Picard iterates leaving the domain where f(x,y) is Lipschitz. Thus, discussing and proving Theorem B before Theorem A is recommended. 5. The book glosses over some of the mathematical details required by the convergence proofs so one must supplement the material in the text as needed. Additional Notes An energetic instructor may want to cover two point boundary value problems and Green's functions in more depth instead of spending the last three lectures on the calculus of variations. Alternately, one could replace the lectures on the calculus of variations with lectures on regular perturbation theory. A reference for this latter topic is Bender and Orszag, Advanced Mathematical Methods for Scientists and Engineers, Chapter 7. Outline update: C. Anderson, 5/05 NOTE: While this outline includes only one midterm, it is strongly recommended that the instructor considers giving two. It is difficult to schedule a second midterm late in the quarter if it was not announced at the beginning of the course. |
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For more information, please contact
Student Services, ugrad@math.ucla.edu. |
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