Math 431 Modern Analysis I Fall 2005
Meetings: TR 4:30 pm – 5:45 pm, DWIR 243
Instructor: Greg Morrow
Office: EN 271, (719) 262 –3184, gjmorrow@math.uccs.edu
Hours: TR: 10:00 – 10:30 and 1:40-2:55, or by appointment
Webpage: http://mathweb.uccs.edu/gmorrow
Prerequisite: Calculus III and Discrete Math. (Math 341 strongly recommended.)
Text: Advanced Calculus (1996), by Patrick Fitzpatrick. Boston: PWS Publishing Company (first edition)
Description: Course covers the theory of calculus on the real line. Topics include the real numbers, convergence of sequences, continuous functions and the Intermediate Value Theorem, differentiation and the Mean Value Theorem, the Riemann integral, infinite series of numbers, and Taylor series. While the student will have familiarity with many of the basic topics, the problems, lectures, and exams will require attention to abstracted formulations and rigor. In particular, the mathematical proof in this subject will be emphasized and required.
Homework and Tests: Homework will be assigned weekly. Homework will count 25% of the course grade. There will be two midterm tests and a final test each counting 25% of the course grade.
Final exam: Tuesday, Dec. 13, 4:30 – 7:00 p.m.
Grading. 90’s = A, 80’s = B, 70’s = C. Half grades (e.g. B+) are possible.
Math 431 Modern Analysis I Morrow, Fall 2005
Syllabus (subject to change; revised 04/18/06)
8/23 – 8/25 HW I 9/1 Review for Chap. 1 Notes-01
8/30-9/1 HW II 9/8 Review Chp 2-1 Notes-02 Notes-03
9/8 HW III 9/15 Notes-04 Notes-05
9/13 – 9/15 HW IV 9/22 Notes-06 Notes-07
9/20 – 9/22 HW V 9/29 Notes-08 Notes -09
9/27 – 9/29 HW VI Note Change 10/6 Notes-10
10/4 – 10/06 .HW VII 10/20 Review Test 1
10/11– 10/13 Test 1 on Chapters 1, 2 & 3 on 10/13 Sample Solution Review Test 1
10/18- 10/20 HW VIII 10/27 Notes-11 Notes-12 Notes-13
10/25- 10/27 HW IX 11/03 Notes-14 Notes-15
11/01 – 11/03 HW X 11/10 Notes-16
11/08 – 11/10 HW XI Dec. 1 Notes-17
11/15 – 11/17 midterm Chp 4&6 due 11/17 Hints for Test 2 Notes-18
11/22 HW XII Dec. 8 Notes-19 Review Final Exam
11/29 – 12/1 9.1, review Notes-20 Notes-20b
12/6 – 12/8 review Solution Review Final
Final exam, Tuesday, Dec. 13, 4:30 – 7:00 pm
HOMEWORK ASSIGNMENTS:
HW I. 1.1: 6, 9. 1.2: 5. 1.3: 1, 11, 19.
HW II. 2.1: 4, 5, 7, 10, 16, 17.
HW III. 2.2: 1, 3, 5, 6, 8, 12 (extra credit).
HW IV. 3.1: 4, 5, 7. 3.2: 3, 7 (assume further that f is non-negative)
HW V. 3.3: 1, 3, 6, 8. 3.4: 3, 7
HW VI. 3.5: 1, 4, 6 (instead of problem 9), 10. 3.6: 9(a)
HW VII. 4.1: 7, 9, 11, 16, 18.
HW VIII. 4.2: 8, 9(extra credit). 4.3: 3, 5, 14, 15, 20 (extra credit)
HW IX. 6.2: 1, 4, 6, 7, 12
HW X. 6.3: 3, 6.4: 2, 3, 7, 8.
HW XI. 8.1: 3, 8.2: 1, 5, 8, 12.
HW XII. 8.3: 2, 4(extra credit). 9.1: 1, 2, 7, 8.