MATH V1202.001 & V1202.002: Calculus IV
  Fall 2013

Section 1: MW 8:40am - 9:55am, Mathematics 312
Section 2: MW 10:10am - 11:25am, Mathematics 312


All important course announcements will appear in Courseworks.

Course Details

Instructor:  Michael Woodbury
Phone: x4-4988
Office: 427 Mathematics

Office Hours: Friday 4:30pm-6:00pm, Monday 1pm-2:30pm or by appointment.

Teaching Assistant:
Undergrad TAs: Min-hwan Oh, Siqi Cao
Grad TAs: Tristan Collins, Pak Hin Lee

Text: James Stewart Calculus: Early Transcendentals, seventh edition, Brooks/Cole, 2008.

Course description: We will cover chapters 15 (Multiple Integrals) and 16 (Vector Calculus). The main topics are:

  1. multiple integrals (using rectangular coordinates)
  2. integrals using polar, cylindrical, and spherical coordinates
  3. vector fields
  4. line integrals
  5. gradients, curl, and divergence.
  6. Green's Theorem, Stoke's Theorem, Divergence Theorem

We will also cover topics from basic complex analysis. The required material will be presented in class. Additional reference materials will also be provided.

Here are course notes written by Prof. Herve Jacquet. This (together with the lectures) is the main reference for the section on complex numbers.
Complex Numbers
Complex Functions and the Cauchy Riemann Equations
Contour Integrals and Cauchy's Theorem

If you feel like you would benefit from additional reading material, here is an online book on complex analysis:
Complex Analysis by George Cain
It is pretty readable and has a number of good exercises for practice.

Prerequisites: All material covered in Calculus I-III (Stewart chapters 1-14, except those involving differential equations) will be assumed. In particular, knowing the theory of integration in one variable well will be especially important.

Important Dates:

  1. September 3: First day of classes
  2. October 8: Drop date (most colleges)
  3. October 2: Midterm 1 (This is the tentative date and is subject to change.)
  4. November 4-5: University holiday (Remember to vote)
  5. November 13: Midterm 2 (This is the tentative date and is subject to change.)
  6. December 9: Last day of classes
  7. December 16 or 18: Final exam. (The final exam for section 2 is on Monday, and section 1 is on Wednesday.)

Advice: Previous experience suggests that students find Calculus IV much more challenging than Calculus I-III. Do everything you can to not fall behind. Here are some suggestions:

  1. Be an active learner. Watching me or a TA do math without doing work on your own will not be enough to be able to reproduce the work yourself on quizzes or exams.
  2. Ask questions in class, and utilize office hours if needed.
  3. Read the book. Look at the book before class to get an idea of the material we are going to cover, then reread it more carefully after class.
  4. Attend class. (Not everything we cover will be from the book).
  5. Do the homework. Besides being graded, this is your best resource for learning the math. Also, keep in mind that the point of homework is not to get the right answer; rather, it is a learning tool. As such, don't cheat yourself by racing through the problems or leaving out justification of each step. Also, be sure to avoid relying on a solutions manual-resources such as a solution manual can give the false impression of understanding.
  6. Do problems that aren't assigned.

Resources: Help is always available from the Help Room (Mathematics 406, 10am-5pm Mon-Fri), me, or the TAs.
If there's something you don't understand, ASK.

Written Homework: Written homework will be assigned every week except when there is a Midterm. This means there will be 12 homework assignments. Assigned problems can be found in the schedule below. Problems in parentheses are optional.

Web-based Homework: You are also responsible for WebAssign homework. This is an online homework system that will give you the instant feedback of knowing whether your answers is correct or not.

Exams: We will have 2 midterms, and one final

Grading: The grading scheme is as follows:

Class Schedule and Homework Assignments

This schedule is tentative and I expect that it WILL change. Please check regularly for the most accurate information.
Date Topics/Sections covered Remarks Homework Date Due
September 3Cartesian, polar, cylindrical and spherical coordinate systemsHW1: 10.3 #7-12,(54); 15.8 #8,12,13; 15.9#14,15 September 9
September 9,11(15.1-3) Integrals over rectangles and more general regionsHW2: 15.1 #2,(8,10),14; 15.2 #24,(40) 15.3#12,14,16,38,(56,62) September 16
Sept 16,18(15.4-5) Polar Coordinates; Applications; Triple IntegralsHW3: 15.4 #1-4,6,10,14,(39,40); 15.5 #28,(32); 15.6#(22,24) September 23
Sept 23,25(15.6-8) Cylindrical and spherical coordinatesHW4: 15.7#28,30,34,48,(55a); 15.8#16,30September 30
Sep 30, Oct 2(15.9) Change of coordinates; Review
Oct 7,9(16.1) Midterm 1; Vector FieldsHW5: 15.9#18,20,(47); 15.10#8,14; 16.1#4,6,26,(35),36October 14
Oct 14,16(16.2-3) Line Integrals; Fundamental theorem for line integralsHW6: 16.2#18,34,40,(45,49,50); 16.3#11,26,28,(29,35) October 21
Oct 21,23(16.4-6) Green's theorem; Curl and divergenceHW7: 16.4#2,19,(21,22),28; 16.5#9-11,12,20,(30,32,37,39); 16.6#20,(22),24,(64)October 28
Oct 28,30(16.7-8) Surface integrals; Stoke's theorem
HW8: 16.7#39,40,44; 16.8#16,17,(20) November 6
Nov 6(16.9) Divergence theoremHW9: 16.9#2,4,18,(19),20,24November 11
Nov 11,13Review; Midterm 2
Nov 18,20Complex Functions 1HW10: The problems from Complex Numbers notes.November 25
Nov 25Complex Functions 2: Cauchy-Riemann equationsHW11: Problems from Complex Functions and the Cauchy Riemann Equations plus extra problems.December 2
Dec 2, 4Complex Functions 3:Contour integrals and Cauchy's theoremHW12: Problems from Contour Integrals and Cauchy's TheoremDecember 9
Dec 10Review
December 16/18Final Exam 

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