Instructor Office: 694 PGH2. Goals and Objectives:
Office Hours: Tu, Th 11:30-12:30 or by appointment
Phone Number: (713) 743-3492
E-mail address: dlabate@math.uh.edu
Homepage: http://www.math.uh.edu/~dlabate
This course is the second part of a 2-semester sequence and is concerned with selected applications of real analysis motivated by problems in applied mathematics, science and engineering. It is assumed that the student is familiar with the material of Math 4331, including properties of real numbers, limites, differentiability and Riemann integration. The main topics of this course are: metric spaces, approximations by polynomials, differential equations, Fourier series, convexity.3. Textbook: K. Davidson and A. P. Donsig, Real Analysis and Applications: Theory in Practice (Undergraduate Texts in Mathematics) 2010 Edition, Springer. ISBN-13: 978-0387980973 ISBN-10: 9780387980973
4. Homework and Examinations:
The only way to understand and master the material presented in class is by working out the homework problems on your own. You are strongly encouraged to work out the homework problems that are assigned regularly and carefully. Copying the homework from someone else or watching someone else doing the work for you will bring you minimal benefit. The homework will count 30% towards the final grade. There will be (almost) weekly homework assignments posted at the link below. At the end of the semester, your worst HW score will be dropped.Homework submission and evaluation policy: Every week I will collect the homework and I might administer a short quiz (10 min) based on the homework. The homework and possibly quiz collection will be on the DUE DATE AT THE BEGINNING OF THE LECTURE (10:05AM). No late homework submissions will be accepted. A late or missed HW will receive a 0 score. Homework should be submitted in a "professional" form which allows a grader to read your solutions without unnecessary effort or ambiguity. In particular, your solution should either be typed or handwritten in a neat and legible form; if you submit scanned pages, they should be perfectly legible; submitted pages should be ordered with clear indication of which problem is being solved; if your homework solution consists of more than one page, pages must be stapled. Collected homework which does not satisfy these guidelines might receive up to a 30% penalty in the score. You are allowed to e-mail your homework before class if you know you will miss class (note that attachments above 5MB may be filtered out by the UH mail server. You are encouraged to use a free app like camscanner on the cellphone rather than sending pictures).
HOMEWORK PROBLEMS: (the list below will be updated during the semester) 5. Topics and lectures allocated to each topics:
HW1 - Chap.7: 7.1: C,D,E; 7.2: B,D,G,H - DUE: Jan 26 - Solution.
HW2 - Chap.7: 7.3: A,D; 7.4: B,I,J; 7.5: A - DUE: Feb 2 - Solution.
HW3 - Chap.7: 7.6: B,F(a),G,I; 7.7: C,G; 8.1: A,H - DUE: Feb 21 - Solution.
HW4 - Chap.8: 8.2: D,G; 8.3: C; 8.4: E; 8.5: C; 8.6: A - DUE: Mar 2 - Solution.
HW5 - Chap.10: 10.2: A,D,F; 10.8: C,D - DUE: Mar 28 - Solution.
HW6 - Chap.11: 11.1: B,E,I; 11.2: H; 11.3: A - DUE: Apr 6 - Solution.
Suggested problems - Chap.12: 12.1 B, 12.3 A, 12.4 A(a), 12.5 A; Chap. 15: 15.1 B,C,F, 15.2 C,D,E. [No solutions will be posted]
Chapter Sections Covered so far Lectures Topics 7 1-7 1-7 4 Norms, inner products, Hilbert spaces 8 1-8 1-8 4 Limits of functions 9 1-3 1 2 Metric spaces 10 1-10 1-9 5-6 Approximations by polynomials 11 1-7 1-4 4-5 Dynamical systems 12 1-8 1-8 4-5 Differential equations 13-14 1-9 and
1-96-7 Fourier series 15 1-9 1-3 4-5 Wavelets
Tests. There will be three tests in class counting 40% towards the final grade (tentatively) on THU FEB 9, THU MAR 9, TUE APR 18. The worst of your 3 tests will be half-dropped; that is, the 3 tests counts 40% towards the final grade, where the best two tests will count 16% each, the worst one will count 8%.
Final exam. The final exam counts 30% towards the final grade. This is scheduled on THU May 4 at 11 am.
Makeup tests will be allowed only for justified and unavoidable absences. In this case, if possible, previous authorization should be obtained from the Instructor. In all other cases, you will get a zero score for a missed test.
Here are the tests with solutions: (I will post the information for current tests when available)
Test #1 with Solution -- Test #2 with Solution -- Test #3 with Solution
5. Grading:
The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).