Math 1202 S: Calculus IV (Summer B 2021)
The syllabus for this course is available here (Updated: 6/30/2021).
Lecture time: Monday, Tuesday, Wednesday, Thursday: 4:30 pm - 6:05 pm
Location: Zoom (See CourseWorks for links)
Instructor Email: ajp2239@columbia.edu
Instructor Office Hours: Wednesday and Friday, 1:00 - 2:00 pm
Teaching Assistant: Maya Merchant
Teaching Assistant Email: mnm2153@columbia.edu
Teaching Assistant Office Hours: Monday and Tuesday, 10:00 - 11:00 am
Problem Sets
All problem sets must be completed using WebAssign. I have listed the due dates here for reference.
- Problem Set 1
Due Tuesday, July 6th, 2021 at 4:00 pm
- Problem Set 2
Due Monday, July 12th, 2021 at 4:00 pm
- Problem Set 3
Due Monday, July 19th, 2021 at 4:00 pm
- Problem Set 4
Due Monday, July 26th, 2021 at 4:00 pm
- Problem Set 5
Due Monday, August 2th, 2021 at 4:00 pm
- Problem Set 6
Due Monday, August 9th, 2021 at 4:00 pm
Exams
- Quiz 1:
- Time: July 4th at 10 am - July 6th at 4 pm
- Sections covered: 15.1, 15.2, 15.3, 15.4, 8.5
- Practice Quiz, Practice Quiz Solutions
- Quiz, Quiz Solutions
- Quiz 2:
- Time: July 11th at 10 am - July 12th at 4 pm
- Sections covered: 15.5, 15.6, 15.7, 15.8
- Quiz, Quiz Solutions
- Quiz 3:
- Time: July 25th at 10 am - July 26th at 4 pm
- Sections covered: 16.1, 16.2, 16.3, 16.4
- Quiz, Quiz Solutions
- Quiz 4:
- Time: August 1st at 10 am - August 2nd at 4 pm
- Sections covered: 16.5, 16.6, 16.7, 16.8
- Quiz, Quiz Solutions
- Quiz 5:
- Time: Take home
- Sections covered: Complex analysis
- Quiz, Quiz Solutions
- Exam 1:
- Time: July 16 at 10 pm - July 18 at 4 pm
- Sections covered: 15.1, 15.2, 15.3, 15.4, 15.5, 15.6, 15.7, 15.8, 15.9, and all material covered in lecture.
- Stewart Chapter 15 Review Exercises: 6, 7, 20, 24, 27, 32, 34, 43a, 44, 45, 47, 48, 51, 54, 57
- Exam 1, Exam 1 Solutions
- Exam 2:
- Time: August 10 at 11:59 am - August 12 at 11:59 am EST
- Sections Covered: 16.1-16.9, all relevant material from chapter 15, and all material covered in lecture (excluding complex analysis)
- Stewart Chapter 16 Review Exercises: 1a, 4, 5, 7, 13, 17, 23, 26abc (but use grid lines to sketch the surface), 28, 29, 30, 33, 35, 36, 37, 38, 39
Course Schedule
This section will be updated after class to list the material that was covered and house the lecture notes. The material that will be covered is subject to change as the course progresses. For a tentative schedule, see the course syllabus.
- Week 1
- June 28, 2021:
- Double integrals over rectangles
- Section 15.1
- Lecture 1 Notes
- June 29, 2021:
- Double integrals over general regions
- Section 15.2
- Lecture 2 Notes
- June 30, 2021:
- Double integrals over polar regions
- Section 15.3
- Lecture 3 Notes
- July 1, 2021:
- Applications of double integrals - Probability
- Section 8.5, 15.4
- Lecture 4 Notes
- June 28, 2021:
- Week 2
- July 6, 2021:
- Surface area
- Section 15.5
- Lecture 5 Notes
- July 7, 2021:
- Triple integrals
- Section 15.6
- Lecture 6 Notes
- July 8, 2021:
- Cylindrical and spherical coordinates
- Sections 15.7, 15.8
- Lecture 7 Notes
- July 6, 2021:
- Week 3
- July 12, 2021:
- Change of variables in multiple integrals
- Section 15.9
- Lecture 8 Notes
- July 13, 2021:
- More change of variables, vector fields
- Sections 15.9, 16.1
- Lecture 9 Notes
- July 14, 2021:
- Gradient vector fields, line integrals
- Sections 16.1, 16.2
- Lecture 10 Notes
- July 15, 2021:
- Exam 1 review
- Lecture 11 Notes
- July 12, 2021:
- Week 4
- July 19, 2021:
- Line integrals of vector fields
- Section 16.2
- Lecture 12 Notes
- July 20, 2021:
- The Fundamental Theorem of line integrals
- Section 16.3
- Lecture 13 Notes
- July 21, 2021:
- Green's Theorem
- Section 16.4
- Lecture 14 Notes
- July 22, 2021:
- Curl and divergence
- Lecture 15 Notes
- July 19, 2021:
- Week 5
- July 26, 2021:
- Parametric Surfaces
- Section 16.6
- Lecture 16 Notes
- July 27, 2021:
- Surface area and surface integrals of functions
- Section 16.7
- Lecture 17 Notes
- July 28, 2021:
- Surface integrals of vector fields (and Skokes's Theorem?)
- Sections 16.7, 16.8
- Lecture 18 Notes
- July 29, 2021:
- Stokes's Theorem
- Lecture 19 Notes
- July 26, 2021:
- Week 6
- August 2, 2021:
- Divergence Theorem and complex numbers
- Section 16.9
- Lecture 20 Notes
- August 3 2021:
- Derivatives of complex functions
- Lecture 21 Notes
- August 4, 2021:
- Complex integration
- Lecture 22 Notes
- August 5, 2021:
- Exam 2 Review
- Lecture 23 Notes
- August 2, 2021: