Calculus IV - MATHV1202 - Fall 2010

Section 2:  TUESDAY, THURSDAY   09:10A - 10:25A
MATHEMATICS  312

Instructor: Fabio Nironi


Email: nironi@math.columbia.edu
Office: Mathematics 415
Tel:  (212) 854 4354

Office hours:

  6:00pm - 7:00pm Wednesday ;  9:30am-10:30am Friday ; and by appointment

TA:

  Sahil Shah
  Email: sds2145@columbia.edu
  Office hours: Wednesday and Thursday from 3 pm to 4 pm in the Math building help room

Textbook:

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

Suggested Reading:

For what concernes the last part of the course (elements of functions of one complex variable) we will be following Prof. Friedman's notes; however I would like to suggest some extra reading. In my opinion a good choice could be: "Schaum's Outlines: Complex Variables (With an Introduction to Conformal Mapping and Its Applications)". A used copy of the book can be found for a couple of bucks (including delivery expenses). We will only cover a small selection of the arguments presented in the book, and I can even provide copies of the parts that we will use. 

Prerequisites:

This is a fourth semester course in Calculus and assumes familiarity with Calculus I-III or equivalent.

Grading:

Homework 20%; Best  Midterm  25%; the Midterm Not Necessarily as Good as the Best  15%; 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 : October 7th (in class)
Midterm 2 : November 18th (in class)

Final:

The final exam projected date is Thursday Dec 16-th from 9.00am to noon. 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. Problem sets are due on Friday by 5.00pm and can be dropped in my drop-box. The solutions will be posted on Courseworks.

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:

Monday, Sep 6: Labor Day - University Holiday
Tuesday, Sep 7: First Day of Classes
Tuesday, Oct 12: Last Day to Drop Class
Monday, Nov 1: Academic Holiday
Tuesday, Nov 2: Election Day - University Holiday
Thursday, Nov 25: Thanksgiving Day - University Holiday
Friday, Nov 26: University Holiday
Monday, Dec 13: Last Day of Classes
Tuesday, Dec 14 - Wednesday, Dec 15: Study Days
Thursday, Dec 16 - Thursday, Dec 23: Final Examinations

Syllabus

Date Reading Homework
Sep. 7, 9 15.1, 15.2, 15.3: Double integrals, Iterated integrals, General regions.
Short review of basic one-variable integration techniques		 #1 due 9/17
15.1: 12, 14
15.2: 4, 8, 20, 22, 28
15.3: 6, 8, 18, 20, 46, 50
Sep. 14, 16 15.4, 15.5: Polar coordinates, Applications of double integrals #2 due 9/24
15.4: 4, 6, 8, 12, 16, 24
15.5: 2, 6, 10, 16, 18
Sep. 21, 23 15.6, 15.7: Triple integrals, Cylindrical coordinates #3 due 10/1
15.6: 8, 10, 16, 20, 34, 44
15.7: 16, 18, 20, 28
Sep. 28, 30 15.8, 15.9: Spherical coordinates, Change of variable #4 due 10/8
15.8: 8, 12, 24, 26, 30, 44
15.9:  8, 14, 20, 22, 24
Oct. 5 Review
Oct. 7 Midterm 1

 Practice Midterm
Solution
Practice Midterm2
Solution2
Oct. 12, 14
 16.1, 16.2: Vector Fields, Line Integrals #5 due 10/22
16.1: 22, 24, 26
16.2: 10, 14, 34, 42
16.3: 8, 18, 22
Oct. 19, 21
 16.2, 16.3: Line Integrals, Fundamental theorem for line integrals #6 due 10/29
16.3: 16, 20, 26, 32
16.4: 6, 8, 10, 14, 18, 21
Oct. 26, 28
 16.4, 16.5: Green's theorem, Curl and divergence #7 due 11/5
16.5: 14, 18, 20, 26,30, 38
16.6:  4, 13-18, 24, 26, 34, 58, 60(a, c)
Nov.  4
 16.6, 16.7: Parametric surfaces, Surface integrals #8 due 11/15
16.7: 6, 10, 20, 24, 30, 36
16.8: 4, 6, 8, 12(a), 18
Nov. 9, 11 16.8, 16.9: Stokes' theorem, Divergence theorem #9 due 11/22
16.8: 10, 14, 16, 17
16.9: 4, 6, 8, 12, 17, 18, 24, 32
Nov. 16 Review
Nov. 18 Midterm 2

Practice Midterm
Solution
Practice Midterm
Solution
Nov. 23
 Complex Functions 1,2 - Prof. Friedman's notes 1
See also Appendix H in the textbook 		#10 due 11/29
HW questions from notes:
Notes 1: ALL
Nov. 30, Dec. 2 Complex Functions 2,3 - Prof. Friedman's notes 2 notes 3 #11 due 12/10
HW questions from notes:
Notes 2: 2, 3, 5, 7, 8, 10
Notes 3: 4, 5, 6, 7, 8
Dec. 7 Complex Functions 3 - Prof. Friedman's notes 3
Dec. 9 Review
Dec. 16
 Final exam Practice Problems
Solutions
Practice Final
Practice Solutions