Math 532 Modern Analysis II Spring, 2006
Meetings: TR 4:30-5:45, Engr 177
Instructor: Greg Morrow
Office: Engr 271, (719) 262-3184
E-mail: gjmorrow@math.uccs.edu
Hours: TR: 10:15-10:45, 2:00-2:50, or by appointment
Prerequisite: Advanced Calculus in one real variable (Math 431)
Text: Advanced Calculus by Patrick M. Fitzpatrick. (First edition)
Description: Pointwise and uniform convergence of sequences and series of functions, power series, differentiation and integration of uniform limits, topology of Euclidean space, continuity and the extreme value theorem, topology of metric spaces, completeness, the contraction mapping principle, compactness in a metric space, differentiation of functions of several real variables, the mean value theorem, the chain rule, the second derivative test in several variables, and the inverse function theorem in several variables.
Homework and Tests: Homework will be assigned and collected weekly; see the assignments and due dates on the syllabus. Late homework will not be accepted. The lowest homework score will be dropped. There will be two mid-semester tests and a final exam. The final exam will cover material primarily from the material after the second midterm test. The following percentages may be used to compute the final grade: homework, 25%, midterms 25% each and final test 25%.
Grading: 90’s => grade of A , 80’s => grade of B or better, 70’s => grade of C or better.
1/17 – 1/19 9.2
1/24 – 1/26 9.3 Notes 2 HW I, Jan. 26
1/31 – 2/2 9.4 Notes 3 HW II, Feb. 2
2/7 – 2/9 10.1, 10.2 Notes 4 HW III, Feb.9
2/14 – 2/16 10.3, 11.1 HW IV, Feb. 16 Review Test 1
2/21 – 2/23 11.2 Notes 5 HW V, Feb. 23
2/28– 3/2 Test over Chps. 9,10 is due on 3/2 Notes 6
3/7– 3/9 12.1, 12.2 Notes 7 HW VI, Mar. 9
3/14–3/16 12.4, 12.5 Notes 8 HW VII, Mar. 16
3/21 – 3/23 13.1-13.3 Review Test 2 HW VIII, Mar. 23
3/28-3/30 Spring Break
4/4 – 4/6 Test 2 over Chps. 11,12 is due on 4/11 Notes 9
4/11 – 4/13 14.1-14.3 Notes 10 HW IX, Apr. 18
4/18– 4/20 15.2, 15.3 Notes 11 HW X, Apr. 25
4/25 – 4/27 16.1, 16.3 Notes 12 HW XI, May 2
5/2 – 5/54 Review Review Final Exam (extra) HW XII, May 9
5/9 Final Exam on 5/9, 4:30-7:00 pm
I. 9.2: 1, 3, 4, 5, 6, 7.
II. 9.2: 10 (Grad); 9.3: 1, 2, 4, 5.
III. 9.4: 1, 4 ( the sign should be (-1)^(k+1) in both exercises 3 and 4), 7, 8, 13.
IV. 10.1: 7, 9, 10, 13; 10.2: 3, 8 (Grad).
V. 10.3: 2, 6, 12(extra credit), 13; 11.1: 4, 8, 12.
VI. 11.2: 1, 2, 5, 7, 8.
VII. 12.1: 1, 4, 11(a),(b), 11(c) (extra credit: show a counterexample); 12.2: 1, 10.
VIII. 12.4: 2, 3, 6, 8, 9(extra credit), 10.
IX. 13.1: 6, 12; 13.2: 6, 13; 13.3: 6, 9.
X. 14.1: 5, 15; 14.2: 1; 14.3: 4, 9(extra credit), 11. (NOTE CHANGE)
XI. 15.2: 6; 15.3: 1, 3, 5, 7.