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: 614 Mathematics Building
Office hours provide you with opportunities to ask questions about course material or mathematics in general.
Office Hours: Mon 2:40pm–3:55pm and Tue 10:10am–11:25am, or by appointment (in-person or via Zoom)
Teaching assistant(s):
Graduate TA:
Juan Muñoz-Echániz (Help room hours: Mon 5:00pm-7:00pm and Wed 5:00pm-6:00pm in Room 406 in the Mathematics Building at Columbia)
Undergraduate TAs:
Celine De Lager (Help room hours: Mon and Wed 10:00am-11:00am in 502 Milstein at Barnard Campus);
Ronit Kathuria (Help room hours: Tue 4:00pm-6:00pm in 502 Milstein at Barnard Campus)
Textbook: Calculus: Early Transcendentals, 9th 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: Mon, Wed 11:40am–12:55pm
Room: 312 Mathematics Building
Class dates: Jan 18, 2023–May 1, 2023
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.
| Monday | Wednesday |
|---|---|
| Jan 18: Brief overview, coordinate systems (§12.1, 10.3, 15.7, 15.8) | |
| Jan 23: Vectors (§12.2) | Jan 25: Dot product (§12.3)/HW1 due |
| Jan 30: Cross product (§12.4) | Feb 1: Equations of lines and planes (§12.5)/HW2 due |
| Feb 6: Parametric curves, conic sections (§10.1, 10.5) | Feb 8: Cylinders and quadric surfaces (§12.6)/HW3 due |
| Feb 13: Review | Feb 15: Miterm 1 |
| Feb 20: Vector functions and space curves (§13.1) | Feb 22: Derivatives and Integrals of vector functions (§13.2)/HW4 due |
| Feb 27: Arc length and curvature (§13.3) | Mar 1: Motion: velocity and acceleration (§13.4)/HW5 due |
| Mar 6: Functions of several variables (§14.1) | Mar 8: Limit and continuity (§14.2)/HW6 due |
| Mar 15: No class | Mar 17: No class |
| Mar 20: Partial derivatives (§14.3) | Mar 22: Tangent planes and linear approximations/HW7 due |
| Mar 27: Review | Mar 29: Midterm 2 |
| Apr 3: Chain rule (§14.5) | Apr 5: Directional derivative, gradient (§14.6) |
| Apr 10: Directional derivative, gradient (§14.6)/HW8 due | Apr 12: Maximum and minimum (§14.7) |
| Apr 17: Maximum and minimum (§14.7)/HW9 due | Apr 19: Maximum and minimum (§14.7) |
| Apr 24: Lagrange multipliers (§14.8)/HW10 due | Apr 26: Lagrange multipliers (§14.8) |
| May 1: Review/HW11 due | May 3: No class |
| May 8: Final Exam (9:00am–12:00pm) |
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.