Math 20500, Autumn 2007
"Integration in Several Variables"
Instructor: Yon-Seo Kim,
Class homepage: http://www.math.uchicago.edu/~yskim/a07M205.html
Class Hours: Sec 45] MWF 11:30am - 12:20pm at Eckhart 308,
Sec 55] MWF 12:30pm - 1:30pm at Eckhart 308
email: yskim@math.uchicago.edu
(please start the message title with Math205-)
Office: E306, Office Hours
MF 10:00am - 11:30am or by
appointments.
College Fellow: Francis Chung, email:
fjchung@math.uchicago.edu
OH W 1:30pm - 3:30pm
Office:
Basement of 5720
Woodlawn,
Discussion section: Thursdays 6pm-7pm at E203
Textbook: Advanced Calculus by Patrick M. Fitzpatrick, 2nd ed.
Course
Outline
This course will cover Chapters 6-8 and 18-20. Course materials include:
Integration of several variables, Taylor polynomial approximation, Change of variables, Line/Surface Integrals.
Homework will be assigned every week and will be collected one-week
after the homework is assigned.
There will be one midterm and the final exam. Midterm is scheduled at the end of 4th week.
Grading basis: Homework -30%, Midterm -30%, Final Exam -40%
Notes
and Comments on Past/Future Lectures
Sep 24th: 6.1-6.2; Darboux sums, Archimedes-Riemann Theorem, Integrability of a
function. Note
Sep 26th: 6.3-6.4; Properties and Applications of Integral. Note
Sep 28th: 6.5-6.6; The first and second Fundamental Theorems. Note
Oct 1st: Fundamental Theorems, Application to differential equations. Note
Oct 3rd: Integration by parts. Convergence theorems. Note
Oct 5th: Approximation formulas. Note
Oct 8th: Taylor polynomials. Note
Oct 10th: Taylor series expansion. Note
Oct 12th: Cauchy Integral Remainder Theorem. Note
Oct 15th: Binomial Expansion. Weierstrass Approximation Theorem. Note
Oct 17th: Weierstrass Approximation Theorem cont'd.
Oct 19th: Midterm Exam. Solutions: section
45, section 55
Oct 22nd: Integration in Several variables. Note
Oct 24th: Further properties of Integration in R^n. Note
Oct 26th: Set of Jordan content zero. Note
Oct 29th: Volume of a subset in R^n. Note
Oct 31st: Fubini's Theorem. Note
Nov 2nd: Fubini's Theorem cont'd. Note
Nov 5th: Change of Variables. Note
Nov 7th: Change of Variables cont'd. Note
Nov 9th: Line integral. Note
Nov 12th: Surface integral. Note
Nov 14th: Surface integral contd. Note
Nov 16th: Green's Formula. Note
Nov 19th: Green's Formula and Application.
Note
Nov 21st: Stokes Formula. Note
Nov 23rd: Stokes Formula contd.
Nov 26th: Review Session.
Nov 28th: Review Session.
Final Exam Solutions: Sec 45 Sec 55
Homework
Assignments
HW#1 (due Oct 5th): 6.1- 2,3,5,7. 6.2- 3,6,8,9,12. 6.3- 1,2,4,6.
6.4- 3,4,7. 6.5- 2,5,6. 6.6- 3,4,6,8,11.
HW#2 (due Oct 12th): 7.1- 2,3,5. 7.2- 2,3,5,8,9. 7.3- 1,3,6,10,13. 7.4-
3,7,10.
HW#3 (due Oct 22nd): 8.1- 2,4,5. 8.2- 2,5,7,8,11,12. 8.3- 2,5. 8.4- 3,5. 8.5-
4,6.
HW#4 (due Oct 29th): 8.6- 3,4. 8.7- 4,5,6. 18.1- 1,2,5,6,10,12.
HW#5 (due Nov 5th): 18.2- 1,2,4,5,6,8,10. 18.3- 1,2,5,6,9,12.
HW#6 (due Nov 12th): 19.1- 2,3,4,5,9. 19.3- 1,2,4,5,7,10,11.
HW#7 (due Nov 19th): 20.1- 1,3,6,7,8,9,10,11.
HW#8 (due Nov 28th): 20.2- 5,6,8,12,16,18. 20.3-
2,3,4,6,8,10,11,12,13,14,15,16.