Calculus IV - Spring 2012

Section 3: Tuesday, Thursday 11:00am - 12:15pm, Mathematics 207
Course website: math.columbia.edu/~tosatti/calc4.html

Instructor:

Valentino Tosatti
Email: tosatti@math.columbia.edu
Office: Mathematics 625

Office hours:

Tuesdays 4:30pm - 6:30pm

TAs:

Nicholas Chan - nc2372@columbia.edu
Peter Krawczyk - ppk2109@columbia.edu
Zhengyu Xiang - xiangzy@math.columbia.edu

Textbook:

J.Stewart - Calculus, Early Transcendentals (Seventh edition), available in the university bookstore.

Prerequisites:

Calculus II and III or equivalent.

Grading:

Homework 20%; Midterm I 20%; Midterm II 20%; Final 40%

Midterms:

There will be two midterm exams during class. Make-up exams will not be given unless a written excuse for missing the exam is provided from either a doctor in the case of illness or from a dean in other exceptional circumstances.

Midterm 1 : Thursday Feb. 16
Midterm 2 : Thursday Apr. 5

Final:

The projected final exam date is Tuesday May 8 from 9:00am to 12:00pm. All students must take the final at the time scheduled by the university.

Homework:

There will be weekly written assignments which can be found below along with the due date and time. Problem sets are due on Tuesdays in class. The solutions will be posted on Courseworks.
Graded homework can be picked up in room Mathematics 405. Old homeworks are discarded after 2 weeks!

Help room:

Mathematics 406. There is more information here.

Calculators:

Calculators are not needed for this course, and they will not be allowed in the exams.

Honesty:

Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Any cheating during midterms or finals will result in you failing the course and the matter being reported to your dean.

Important Dates:

January 17: first day of class
February 16: first midterm
February 21: drop date
March 12-16: Spring break
April 5: second midterm
April 26: last day of class
May 8: projected final exam

Syllabus

This is a tentative syllabus and it is likely to change as the course progresses.

Date Reading Homework
Jan. 17, 19 15.1, 15.2, 15.3: Double integrals, Iterated integrals, General regions
Short review of basic one-variable integration techniques		 #1 due 1/24 in class
15.2: 4, 8, 20, 28
15.3: 6, 8, 18, 22, 24, 46, 48, 50
Jan. 24, 26 15.4, 15.5: Polar coordinates, Applications of double integrals #2 due 1/31 in class
15.4: 4, 6, 8, 12, 14, 16, 24
15.5: 2, 6, 10, 18
Jan. 31, Feb. 2 15.7, 15.8: Triple integrals, Cylindrical coordinates #3 due 2/7 in class
15.7: 8, 10, 16, 20, 34, 46
15.8: 12, 16, 18, 20, 30
Feb. 7, 9 15.9, 15.10: Spherical coordinates, Change of variable #4 due 2/14 in class
15.9: 8, 12, 24, 26, 30, 36, 40
15.10: 8, 18, 24, 26
Feb. 14 Review Practice Midterm A
Practice Midterm A Solution
Feb. 16 Midterm 1
 Practice Midterm B
Practice Midterm B Solution
Feb. 21, 23 16.1, 16.2: Vector Fields, Line Integrals #5 due 2/28 in class
16.1:
16.2:
Feb. 28, Mar. 1 16.2, 16.3: Line Integrals, Fundamental theorem for line integrals #6 due 3/6 in class
16.2:
16.3:
Mar. 6, 8 16.4, 16.5: Green's theorem, Curl and divergence #7 due 3/20 in class
16.4:
16.5:
Mar. 13, 15 Spring Break!
Mar. 20, 22 16.6, 16.7: Parametric surfaces, Surface integrals #8 due 3/27 in class
16.6:
16.7:
Mar. 27, 29 16.8, 16.9: Stokes' theorem, Divergence theorem #9 due 4/3 in class
16.8:
16.9:
Apr. 3 Review
Apr. 5 Midterm 2
Apr. 10, 12 Complex Functions 1,2 - Prof. Friedman's notes 1 notes 2
See also Appendix H in the textbook 		#10 due 4/17 in class
HW questions from notes:
Notes 1:
Notes 2:
Apr. 17, 19 Complex Functions 2,3 - Prof. Friedman's notes 2 notes 3 #11 due 4/24 in class
HW questions from notes:
Notes 2:
Notes 3:
Apr. 24 Complex Functions 3 - Prof. Friedman's notes 3 #12 due 4/26 in class
HW questions from notes:
Notes 3:
Apr. 26 Review
May 8 Projected Final exam