Topics: Vectors and the geometry of space, vector functions, functions of several variables and partial derivatives
Prerequisites: Math UN1101: Calculus I or an equivalent. For more information on calculus: http://www.math.columbia.edu/programs-math/undergraduate-program/calculus-classes/
Instructor: Chen-Chih Lai
Email: cl4205 at math dot columbia dot edu
Office: 307A Mathematics Building
Office hours provide you with opportunities to ask questions about course material or mathematics in general.
Office Hours: Tue 1:10pm–2:25pm and Wed 10:10am–11:25am, or by appointment (in-person or via Zoom)
Teaching assistant(s):
Graduate TA: Juan Muñoz-Echániz (Help room hours: Tue 6pm–9pm in Room 406 Mathematics, Extra office hour: Th 1pm–2pm in Room 406 Mathematics, or by appointment)
Undergraduate TA: Amina Shindy (Help room hours: Thu 4pm–6pm in 502 Milstein at Barnard Campus)
Textbook: Calculus: Early Transcendentals, 8th Edition, by James Stewart
Grading: Homework (30%), Midterm 1 (20%), Midterm 2 (20%), Final Exam (30%).
There will be no makeup exams under any circumstances. However, the lowest score of the two midterms will be replaced by the final exam score if this increases your total score. So you can miss one midterm without too much damage. On the other hand, missing both midterms or missing the final will seriously harm your grade. Please check the exam dates now (see below) to make sure that you have no unavoidable conflicts!
Important websites for this course:
Lecture:
Days & Times: Tue, Thu 11:40am–12:55pm
Room: 207 Mathematics Building
Class dates: Sep 9, 2021–Dec 13, 2021
Exam Dates:
You are encouraged to take advantage of the math Help Rooms. The schedule is available at https://www.math.columbia.edu/general-information/help-rooms.
This schedule will be updated as we go along.
| Tuesday | Thursday |
|---|---|
| Sep 9: Brief overview, coordinate systems (§12.1, 10.3, 15.7, 15.8) | |
| Sep 14: Vectors (§12.2) | Sep 16: Dot product (§12.3)/HW1 due |
| Sep 21: Cross product (§12.4) | Sep 23: Equations of lines and planes (§12.5)/HW2 due |
| Sep 28: Parametric curves, conic sections (§10.1, 10.5) | Sep 30: Cylinders and quadric surfaces (§12.6)/HW3 due |
| Oct 5: Review | Oct 7: Miterm 1 |
| Oct 12: Vector functions and space curves (§13.1) | Oct 14: Derivatives and Integrals of vector functions (§13.2)/HW4 due |
| Oct 19: Arc length and curvature (§13.3) | Oct 21: Motion: velocity and acceleration (§13.4)/HW5 due |
| Oct 26: Functions of several variables, continuity (§14.1, 14.2) | Oct 28: Partial derivatives (§14.3)/HW6 due |
| Nov 2: No class | Nov 4: Tangent planes and linear approximations (§14.4) |
| Nov 9: Review/HW7 due | Nov 11: Midterm 2 |
| Nov 16: Chain rule (§14.5) | Nov 18: Directional derivative, gradient (§14.6) |
| Nov 23: Directional derivative, gradient (§14.6)/HW8 due | Nov 25: No class |
| Nov 30: Maximum and minimum (§14.7)/HW9 due | Dec 2: Maximum and minimum (§14.7) |
| Dec 7: Lagrange multipliers (§14.8)/HW10 due | Dec 9: Complex numbers (Appendix H) |
| Dec 14: Review/HW11 due | Dec 16: Final Exam (4:10pm-7:00pm) |
Disability Services facilitates equal access for students with disabilities by coordinating accommodations and support services, and cultivating a campus culture that is sensitive and responsive to the needs of students.
In order to receive disability-related academic accommodations, CC and GS students must first be registered with Disability Services (DS). More information on the DS registration process is available online at https://health.columbia.edu/ods.
Faculty must be notified of registered students' accommodations before exams or other accommodations will be provided. Students who have, or think they may have, a disability are invited to contact Disability Services for a confidential discussion at (212) 854-2388 (Voice/TTY) or by email at disability@columbia.edu. Barnard students are invited to visit the Center for Accessibility Resources & Disability Services (CARDS).
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If you are concerned about your classroom or out of classroom experiences, the Office of Equal Opportunity and Affirmative Action (EOAA) is available to advise and assist students who may be experiencing any equity, accessibility, inclusion, harassment, discrimination or sexual violence concerns. To make an appointment, or file a report, or find more information for students, visit the Student Conduct and Community Standards webpage.