SYLLABUS

Course: M3220, Foundations of Analysis II

Instructor: Dr. A.D. Roberts, JWB 312, 581-6710; message: 581-6851

e-mail: aroberts@math.utah.edu

Classes: MWF, 8:35am - 9:25am, JTB 120

Office Hours: MWF, 9:40am - 10:30am

Text: An Introduction to Analysis, William R. Wade

Prerequisite: M1210-1220; M2210

Course Description

The course will examine topics in Multivariable Calculus from a more advanced point of view. We begin by considering the algebraic and topological structure of Rn, continue on to examine the concepts of differentiation and integration on Rn, and conclude with Green's Theorem and Stokes's Theorem, the fundamental theorems of Multivariable Calculus. Throughout the course there will be an emphasis an reading mathematics and on writing simple proofs.

Grading

Assignments/Quizzes (best 5 out of 6) 30%

Midterms ( 2 ) 40%

Final Examination 30%

Total 100%

Notes:

1. The Final Examination is comprehensive and is scheduled for Monday, May 3, 1999 from 7:30am to 9:30am.

2. The Midterms are tentatively scheduled for: February 19th, April 2nd. We'll make these dates firm a week prior to the midterm.

3. The Assignments/Quizzes will be due generally on Fridays: 1/22, 2/5, 3/5, 3/26, 4/14 (Wed), 4/23. Assignments will be handed out in class a week before the assignment is due and any changes necessary in the above schedule will be announced in class.

Assignments will generally consist of questions to consider outside of class but may also involve a brief in-class quiz on the day the assignment is due. Students may discuss the assignment outside of class but each student is to turn in their own independent write-up. Selected problems will be graded on each assignment and a portion of the total possible points will be given for a complete assignment (ie., all problems show significant effort). While late assignments may occasionally be accepted, 15% of the grade will be deducted for each day late and no late assignments will be accepted after the graded assignments are returned to the class.

Course Schedule (Tentative)

Week

1-4 Ch 5: Algebraic structure and basic topology of Rn

4-8 Ch 6: Differentiation on Rn

8-13 Ch 3 & 7: Integration on Rn

13-16 Ch 8 : Curves, Surfaces, Green's Theorem, Stokes's Theorem