Instructor Office:  694 PGH
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 (part of a 2-semester sequence) provides a solid introduction to deeper properties of the real numbers, continuous functions, differentiability and integration needed for advanced study in mathematics, science and engineering. It is assumed that the student is familiar with the material of Math 3333, including an introduction to the real numbers, basic properties of continuous and differentiable functions on the real line, and an ability to do epsilon-delta proofs. The main topics of this course are: Open and closed sets, compact and connected sets, convergence of sequences, Cauchy sequences and completeness, properties of continuous functions, fixed points and the contraction mapping principle, differentiation and integration.

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 (11:05PM). 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)

HW1 - Chap.1-2: Homework 1 - DUE: Sept 1 - Solution.    Additional notes about Ch.2: Notes Ch.2
HW2 - Chap.2: Sec.2.4:C,G; Sec.2.5:C,D; Sec.2.6:B; Sec.2.7:H,J; Sec.2.8:A,B. (pages from textbook)) - DUE: Sept 8 - Solution.
HW3 - Chap.2-3: 2.8:C, 2.9:A,C, 3.1: A,C - DUE: Sept 22 - Solution.
HW4 - Chap.3-4: 3.2: F,G,M,N, 4.1: D,E,F,I - DUE: Sept 29 - Solution.
HW5 - Chap.4: 4.2: A,B,E, 4.3: B,G,J,L - DUE: Oct 6 - Solution.
HW6 - Chap.4: 4.4: C,D,F,I - DUE: Oct 18 - Solution.
HW7 - Chap.5: 5.1: E,F,J; 5.2: F,G,H - DUE: Oct 27 - Solution.
HW8 - Chap.5: 5.3: F,I,K,N; 5.4: E,H,L; 5.5: F - DUE: Nov 3 - Solution.
HW9 - Chap.5: 5.5: I,K; 5.6: D,F,H(a); 5.7: A,B - DUE: Nov 10 - Solution.
HW10 - Chap.6: 6.1: E,R; 6.2: B,L; 6.3: C,F,I; 6.4: C - DUE: Nov 29 - Solution.

5. Topics and lectures allocated to each topics:
 
 

Chapter	Sections	Covered so far	Lectures	Topics
1	1-3	1+	1	Review
2	1-9	1-9	6-7	The Real Numbers
3	1-3	1-3	3	Series
4	1-4	1-4	4	Topology of Rn
5	1-7	1-7	7-8	Functions
6	1-4	1-4	4	Differentiations and Integrations
7	1-7		7-8	Norms and Inner Products
8	1-6	1-2	7-8	Limits of Functions

  Tests. There will be three tests in class counting 40% towards the final grade (tentatively) on THU SEPT 15, TUE OCT 18, TUE NOV 15 . 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 MON Dec 13 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).