MATH
452 Advanced Calculus, Winter, 2014
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.
INSTRUCTOR: Dr. Ken Wiggins, 336 KRH, 527-2088
Office Hours: 2 TuWTh, 3 M, 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 functions, integrals, infinite series, and other selected topics.
TEXT: Advanced Calculus, A Course in Mathematical Analysis, Second Edition, by
Patrick M. Fitzpatrick, 2006, The Brooks Cole Series in Advanced Mathematics
Assessment: All assessment will be based on both the correctness
of your results and the quality of your presentation.
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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 typewritten 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. To encourage careful reading of the textbook, the first student
to report an error in the textbook via email will be given 1 point of extra credit in the homework category. To see the current list of errors
go to textbook errors.
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!
TESTS: These tests will cover the lectures and homework exercises.
FINAL EXAMINATION: This comprehensive test will be given on Wednesday, March 19, at 8 AM.
SPECIAL CONSIDERATION FOR EXTRA EFFORT: Your lowest test grade will be dropped and replaced with your final examination grade if you meet the following conditions: You must
· Be present, on time, and attentive for at least 28 of the 29 scheduled class sessions
· Turn in all of the homework on time.
· Make a higher grade on the final examination than you did on your lowest test.
DISABILITIES: If you have a physical and/or learning disability and
require accommodations, please contact your instructor or the Special Services
office at 527-2090. This syllabus is available in alternative print formats
upon request. Please ask your instructor.
Approximate Schedule:
Week Topic Assignment
1 New functions
New functions and the area problem
Logic supplement
Good questions
Methods of Proof
H1: 5.2 #1, 3, 6; 5.3 #4, 7, 16; 5.4 #1
2 More Integrals
H2: 6.1 #2,4,6; 6.2 #4, 7;
3 Even More Integrals
H3: 6.3 #1,3; 6.4 #1 (very brief and informal justification, not detailed proofs),
4 Review problems for test 1 H4: 6.4 #6; 6.5 #4, 5; 6.6 #1c, 2b; 8.1 #2c (Give the 201st Taylor Polynomial.)
5 The number e. H5: 8.2 #1, 3, 8 Due Monday
6 H6: 8.3 #1; 8.4 #1,2; Due Wednesday
7 Cauchy Remainder Theorem H7: 8.5 #4, 6; Due Monday
8 Nonanalytic function H8: 8.6 #2, 4; 8.7 #2, 8
Bernstein polynomials The Approximation Theorem
9 The Approximation proof H9: 9.1 #1df, 6, Test #2, Monday
10 Pointwise and Uniform Convergence, More Uniform Convergence H10: 9.2 #4, 6; 9.3 #4,7; 9.4 #2, 4