Wed 12/5: Workshop 13.
Workshop 13 (back to the correct numbering) is a set of comprehensive review problems for the final exam. Solutions.
Wed 12/5: Final Exam Equation Sheet.
- You will be given the following equation sheet on the final exam.
Wed 12/5: Wrap up and review.
- Review for final exam
- Final exam is Monday 12/10, 3:30-6:30pm in HNS 168.
Mon 12/3: Divergence Theorem.
- Reading: Section 16.9
- Homework: (16.9): #1, 3, 5, 7, 9, 11.
Sun 12/2: Quiz 9 Solutions.
Fri 11/30: Stokes’ Theorem.
- Quiz 9 in class: covering problems from section 16.4-16.7
- Reading: Section 16.8
- Homework: (16.8): #3, 5, 7, 9, 13, 15.
Wed 11/28: Workshop 11.
Questions and solutions for Workshop 11, held on 11/28.
Wed 11/28: Surface integrals of vector fields.
- Reading: Rest of Section 16.7
- Homework: (16.7): #21, 23, 25, 27, 29.
Mon 11/26: Surfaces, Part II.
- Reading: Rest of Section 16.6, Section 16.7, through p. 1166.
- Homework: (16.6): #33, 35, 39, 43, 45, 47, (16.7): #5, 7, 9.
Wed 11/21: Workshop 10.
Questions and solutions for Workshop 10.
Wed 11/21: Surfaces, Part I.
- Reading: Section 16.6, through surfaces of revolution
- Homework: (16.6): #1, 3, 5, 7, 9, 19, 21, 23, 25.
- To help visualize parametric surfaces, you can use Wolfram Alpha and enter the plot as in the following example: 3d parametric plot (u,v,u^2 + v^2), u = -1 to 1, v = -1 to 1
Mon 11/19: Curl and Divergence.
- Reading: Section 16.5
- Homework: (16.5): #1, 3, 5, 7, 13, 15, 17.
Fri 11/16: Quiz 8 Solutions.
Fri 11/16: Major Erratum for Friday 11/16.
- Important Note: I completely goofed the sign in the statement of Green’s Theorem in lecture today, which says that the line integral of Pi + Qj over a closed curve bounding a region R is the double integral of Qx -Py, and not the other way around, as I stated it. This means that all the examples done in class are off by a minus sign!
- Please accept my sincerce apologies for this major error and correct your notes as neccessary.
Fri 11/16: Green’s Theorem.
- Quiz 8 in class: covering problems from section 16.3.
- Reading: Section 16.4
- Homework: (16.4): #3, 5, 7, 9, 11, 13.
Wed 11/14: Workshop 9.5.
Questions and solutions for Workshop 9.5, which was held on Wednesday 11/14.
- Note that the numbering got messed up. This was originally workshop 10, but I forgot to post it, and the next two workshops got numbered 10 and 11, respectively, so I retroactively renumbered this one to 9.5.
Wed 11/14: Exam 2 Solutions.
Wed 11/14: Fundamental Theorem for Line Integrals.
- Reading: Section 16.3
- Homework: (16.3): #3, 5, 7, 13, 15, 17.
Fri 11/9: Exam 2.
- Exam 2 in class, covering sections 15.1-15.8, 16.1, 16.2.
Wed 11/7: Workshop 9.
Questions and solutions for Workshop 9.
Wed 11/7: Review for Exam 2.
- Review session for Exam 2: Covering sections 15.1-15.8 (for the applications chapter 15.4, just mass and center of mass), and 16.1, 16.2.
Mon 11/5: Line Integrals.
- Reading: Section 16.2
- Homework: (16.2): #1, 3, 9, 11, 17, 19, 21
Fri 11/2: Quiz 7 Solutions.
Fri 11/2: Vector Fields.
- Quiz 7 in class: covering problems from sections 15.7 and 15.8.
- Reading: Section 16.1
- Homework: (16.1): #1, 3, 5, 7, 9, 11-14, 21, 23, 25.
Wed 10/31: Workshop 8.
Questions and solutions for Workshop 8.
Wed 10/31: Exam 2 moved to Friday November 9.
Wed 10/31: Triple integrals recap.
- Reading: Section 15.6, 15.7, 15.8
- Homework: No new homework problems
Mon 10/29: Spherical Coordinates.
- Reading: Section 15.8
- Homework: (15.8): #1, 5, 9, 11, 13, 21, 23, 25.
Sun 10/28: Quiz 6 Solutions.
Fri 10/26: Cylindrical Coordinates.
- Quiz 6 in class: covering problems from sections 15.4 (#1, 3, 11, 13) and 15.6 (#3, 5, 7, 13, 21, 41).
- Reading: Section 15.7
- Homework: (15.7): #1, 3, 5, 7, 17, 23, 25.
Wed 10/24: Workshop 7.
Questions and solutions for Workshop 7.
Wed 10/24: No Lecture.
- No lecture today
- There will be a workshop from 2-3:30 as usual in Heieser 106.
Mon 10/22: Triple integrals.
- Reading: Section 15.6
- Homework: (15.6): #3, 5, 7, 13, 21, 41.
Sat 10/13: Quiz 5 Solutions.
Fri 10/12: Applications of double integrals.
- Quiz 5 in class: covering sections 15.1, 15.2, 15.3.
- Reading: Section 15.4
- Homework: (15.4): #1, 3, 11, 13.
Wed 10/10: Double integrals in polar coordinates.
- Reading: Section 15.3
- Homework: (15.3): #1-4, 5, 7, 9.
Mon 10/8: Double integrals over general regions.
- Reading: Section 15.2
- Homework: (15.2): #3, 5, 7, 11, 23, 25, 45, 49
Fri 10/5: Double Integrals.
- Reading: Section 15.1
- Homework: (15.1): #1, 9, 11, 13, 15, 17, 19.
Thu 10/4: Exam 1 Solutions.
Wed 10/3: Exam 1.
- Exam 1 in class.
- No workshop today.
Mon 10/1: Review.
- Review for midterm exam.
- Midterm exam will take place Wednesday during the class hour. It will cover all material we’ve discussed thus far. The types and difficulty of questions will be similar to those of the weekly quizzes.
Fri 9/28: Quiz 4 Solutions.
Fri 9/28: Global optimization, Lagrange multipliers.
- Quiz 4 in class: covering assigned problems from 14.4-14.7 (except problems (14.7) #31 and 33).
- Reading: Section 14.8
- Homework: (14.7): #31, 33, (14.8): #3, 5, 7.
Wed 9/26: Workshop 5.
Here are solutions for Workshop 5.
Wed 9/26: Workshop 5.
Here are solutions for Workshop 5.
Wed 9/26: Local extrema.
- Reading: Section 14.7
- Homework: (14.7): #3, 5, 7, 11, 31, 33.
Mon 9/24: Gradient.
- Reading: Section 14.6
- Homework: (14.6): #7, 9, 11, 13, 15, 23, 33, 41, 43.
Wed 9/19: Workshop 4.
Questions and solutions for Workshop 4.
Tue 9/18: Quiz 3 Solutions.
Fri 9/14: Tangent planes, chain rule.
- Quiz 3 in class: covering assigned problems from 13.1, 13.2, 14.1, 14.2, and 14.3.
- Reading: Section 14.4, 14.5.
- Homework: (14.4): #1, 3, 5, 11, (14.5): #1, 3, 7, 9, 11.
Wed 9/12: Workshop 3.
Questions and answers for Workshop 3 are here.
Wed 9/12: Limits, continuity and partial derivatives.
- Reading: Section 14.2, 14.3
- Homework: (14.2): #29, 31, 33, 34, (14.3): #10, 11, 12, 17, 19, 31, 37, 53.
Mon 9/10: Multivariable functions.
- Reading: Section 14.1
- Homework: (14.1): #25, 29, 31, 45, 47, 49, 61, 63, 64.
Sat 9/8: Quiz 2 Solutions.
Fri 9/7: Curves.
- Quiz 2 in class: covering assigned problems from 12.5 (#51, 53), and 12.6.
- Reading: Section 13.1, 13.2
- Homework: (13.1): #7, 9, 11, 21, 23, 25, (13.2): #9, 11, 23.
Wed 9/5: Workshop 2.
Questions and answers for Workshop 2 are here.
Wed 9/5: Quiz 1 Solutions.
Wed 9/5: Surfaces.
- Reading: Section 12.6
- Homework: (12.6): #3, 5, 11, 15, 21-28.
Fri 8/31: Planes.
- Quiz 1 in class: covering assigned problems from 12.1-12.5 (except (12.5): #23, 33)
- Reading: Section 12.5 on planes
- Homework: (12.5): #23, 33, 51, 53.
Wed 8/29: Workshop 1.
Questions and answers for Workshop 1 are here.
Wed 8/29: .
- Note: Since the west wing of Heiser is closed this week, the workshop will take place in the LETRA classroom in Pritzker Marine Lab from 2-3:30 today.
Wed 8/29: Cross product, lines and planes.
- Reading: Sections 12.4, 12.5
- Homework: (12.4): #1, 3, 13, 28, 29, (12.5): #3, 5, 7, 23, 33.
Mon 8/27: Euclidean space, vectors and vector algebra.
- Reading: Sections 12.1-12.3
- Homework: (12.1): #2, 5, 6, (12.2): #15, 17, 19, 21, (12.3): #1, 4, 8, 23, 24, 27.