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.
Instructor:
Michael Woodbury
Phone: x4-4988
Office: 427 Mathematics
email: MYLASTNAME at MATH dot COLUMBIA dot EDU
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:
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:
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:
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:
Date | Topics/Sections covered | Remarks | Homework | Date Due |
---|---|---|---|---|
September 3 | Cartesian, polar, cylindrical and spherical coordinate systems | HW1: 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 regions | HW2: 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 Integrals | HW3: 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 coordinates | HW4: 15.7#28,30,34,48,(55a); 15.8#16,30 | September 30 | |
Sep 30, Oct 2 | (15.9) Change of coordinates; Review | |||
Oct 7,9 | (16.1) Midterm 1; Vector Fields | HW5: 15.9#18,20,(47); 15.10#8,14; 16.1#4,6,26,(35),36 | October 14 | |
Oct 14,16 | (16.2-3) Line Integrals; Fundamental theorem for line integrals | HW6: 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 divergence | HW7: 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 theorem | HW9: 16.9#2,4,18,(19),20,24 | November 11 | |
Nov 11,13 | Review; Midterm 2 | |||
Nov 18,20 | Complex Functions 1 | HW10: The problems from Complex Numbers notes. | November 25 | |
Nov 25 | Complex Functions 2: Cauchy-Riemann equations | HW11: Problems from Complex Functions and the Cauchy Riemann Equations plus extra problems. | December 2 | |
Dec 2, 4 | Complex Functions 3:Contour integrals and Cauchy's theorem | HW12: Problems from Contour Integrals and Cauchy's Theorem | December 9 | |
Dec 10 | Review | |||
December 16/18 | Final Exam |
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