MATH 451 Advanced Calculus, Autumn, 2007

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: 1 MWF, 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

REFERENCES:

Assessment: All assessment will be based on both the correctness of your results and the quality of your presentation.

Assessment Category

Weights

Homework

40%

Midterm test

25%

Final examination

35%

Grade

Percent

Grade

Percent

Grade

Percent

Grade

Percent

A

90-100%

B

75-84%

C

60-64%

D

45-49%

A-

85-89%

B-

70-74%

C-

55-59%

D-

40-44%

B+

80-84%

C+

65-69%

D+

50-54%

F

0-39%

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.

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 12, at noon.  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

H1

Logic,  preliminaries Completeness Axiom

Section 1.1 #1abe, 2abc, 3, 11a, 15, supplementary logic problems

H2

  Integers, rationals, and dense sets

Section 1.2 #1, 2, 4, 5

H3

  Familiar inequalities and identities  

Section 1.3 #4, 14, 15, 18a, 21, 22

 

Convergent sequences

Section 2.1 #1, 2b, 8, Supplementary problems

 

H4

 

Sequences and sets Monotone Convergence Theorem Compactness Theorem

Section 2.2 #1, 2, 3

 

H4

Section 2.3 #1, 2, 3, 4

 

H5

Continuous functions

Section 2.4 #1 (Very brief reasons -- full proofs not required), #8, 12

 

 H5  

 

Extreme Value Theorem

Section 3.1 #2, 8, 11, 13

 

Intermediate Value Theorem

Section 3.2 #2a,3,7

H6

 

Section 3.3 #4,7,8

 

H7

 

Uniform continuity

Section 3.4 #1, 3; Supplementary problems on infinite sets

 

H8 

 

The epsilon-delta criterion

Section 3.5 #1, 5, 8

 

  H9  

 Images and Inverses

Section 3.6 #2 (Proofs not necessary), 4

 

 Limits

Section 3.7 #1ac, 2a, 4a

 

 Derivatives

Section 4.1 #1, 4a, 5bc, 8, 14

 

H10  

   

 Differentiating inverses and compositions

Section 4.2 #3, 9

 

 Mean Value Theorem

Section 4.3 #2a, 3, 5, 11, 12, 20

 

 

Section 4.4 #3a, 5, 7

 

 

Section 5.2 #1, 3, 5

 

1

Final Examination Review