MATH
451 Advanced Calculus, Autumn, 2009
Walla
Walla University
BULLETIN DESCRIPTION: Study of functions of one and several variables including continuity, differentiation, infinite series, uniform convergence, and selected topics. Prerequisite: MATH 283 Offered odd years only. 3 credits (quarter)
INSTRUCTOR: Dr. Ken Wiggins, 338 KRH, 527-2088
Office Hours: 3 M; 2 TuWTh; 1 F, Other Office hours by appointment
OBJECTIVES: After finishing this course, students should be able solve problems and to organize and effectively communicate ideas involving the basic theory of real numbers, sequences of real numbers, continuous functions, limits, and differentiation.
TEXT: Advanced Calculus, A Course in Mathematical Analysis, 2nd edition. by Patrick M. Fitzpatrick, 2006, Thompson Brooks/Cole, ISBN 0-534-37603-7, errata
REFERENCES:
1.
Counterexamples
in Analysis, Bernard R. Gelbaum and John M. H. Olmsted, 1964, Holden-day, QA300 G4
2.
Learning
to reason: an introduction to logic, sets, and relations, Nancy Rodgers, 2000, Wiley, QA9.R7264
3.
Mathematical
thinking and writing: a transition to abstract mathemtics, Randall Maddox, 2002, Academic Press, QA9.54.M34
4.
Principles
of mathematical analysis, Walter Rudin, 1953, McGraw-Hill, QA300.R8
5. Proofs from the book, 3rd edition, Martin Aigner, Gunter M. Ziegler, 2004, Springer, QA36.A36
7. Advanced Calculus and Analysis by Ian Craw
8. Advanced Calculus by Tom Trench
Assessment: All assessment will be based on both the correctness of
your results and the quality of your presentation.
Assessment Category |
Weights |
|
Grade |
Percent |
Grade |
Percent |
Grade |
Percent |
Grade |
Percent |
|
|
A |
90-100% |
B |
75-84% |
C |
60-64% |
D |
45-49% |
|||||
Homework |
40% |
|||||||||||
A- |
85-89% |
B- |
70-74% |
C- |
55-59% |
D- |
40-44% |
|||||
Midterm test |
25% |
|||||||||||
B+ |
80-84% |
C+ |
65-69% |
D+ |
50-54% |
F |
0-39% |
|||||
Final examination |
35% |
|||||||||||
|
HOMEWORK: Homework exercises will be announced in class, and they will be collected once each week. Your instructor will be grading the homework, and because he wishes to return it to you promptly, homework that is more than one day late may not be accepted. Homework papers that are one day late will be assessed a 20% late penalty. Oral presentations may be included in your homework. Each day you must bring one printed (computer) question to class from the reading assignment. Some of these questions will be addressed during the class period. The questions will count as part of your homework grade.
Your homework exercises will be challenging, and you may need extra help from your instructor. Don't hesitate to ask for help when you need it!
MIDTERM TEST: This test will cover the lectures and homework exercises.
FINAL EXAMINATION: This comprehensive test will be given on Wednesday, December 16, at 8. Attendance is required, so make your travel plans with this appointment in mind.
DISABILITIES: If you have a physical and/or learning disability and
require accommodations, please contact your instructor or the Special Services
office at 527-2366. This syllabus is available in alternative print formats
upon request. Please ask your instructor.
MATH 451, Advanced Calculus Homework Schedule -- Subject
to change
Topic |
Weekly Assignment |
|
H1 |
Section 1.1 #1abe, 2abc, 3, 11a, 15, supplementary logic problems |
|
H2 |
Section 1.2 #1, 2, 4, 5 |
|
H3 |
Section 1.3 #4, 14, 15, 18a, 21, 22 |
|
H4 |
Sequences and sets Monotone Convergence Theorem Compactness Theorem |
Section 2.1 #1, 2b, 8, Supplementary problems Section 2.2 #1, 2, 3 |
H5 |
Section 2.3 #1, 2, 3, 4 Section 2.4 #1 (Very brief reasons -- full proofs not required), #8, 12 Section 3.1 #2, 8, 11, 13 |
|
H6 |
Section 3.2 #2a,3,7 Section 3.3 #4,7,8 |
|
H7 |
Section 3.4 #1, 3 Section 3.5 #1, 5, 8 |
|
H8 |
Section 3.6 #2 (Proofs not necessary), 4 Section 3.7 #1ac, 2a, 4a |
|
H9 |
Section 4.1 #1, 4a, 5bc, 8, 14 Section 4.2 #3, 9 |
|
H10 |
Section 4.3 #2a, 3, 5, 11, 12, 20 Section 4.4 #3a, 5, 7 |
1