Instructor: Akram Alishahi
Email: alishahi@math.columbia.edu
Webpage: courseworks.columbia.edu and math.columbia.edu/~alishahi/CalcIII.html
Office hours: Monday: noon-1p and Wednesday: 3p-4p or by appointment; at Math 613
Teaching Assistants:
TA's office hours is available at
http://www.math.columbia.edu/general-information/help-rooms/333-milbank/
Helproom: Milstein Center for Teaching and Learning Room: 502
Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition. For more information: http://www.math.columbia.edu/programs-math/undergraduate-program/calculus-classes/#textbook
An earlier edition of the book is also fine and much cheaper, but the homework references come from the 8th edition. Please get the correct problems from the library or a friend.
Prerequisite: Math. UN1101 (Calculus I) or equivalent. For more information: http://www.math.columbia.edu/programs-math/undergraduate-program/calculus-classes/#placement
Overview: Welcome to Calculus III! The topics you will be learning about this semester are
The prerequisite material for this course is covered in Calculus I. Familiarity with the material of Calculus II is helpful but not essential. Please let me know if you have any questions regarding whether this is the right course for you.
Homework: There will be problem sets every week, due at the beginning of class on Mondays, unless otherwise noted. If you can't make it to the class, put it in the assigned box outside of 410 Math.
You are welcome to work on the assignments together, but you must write up in your own words.
Late homeworks are not accepted. Solutions of homeworks will be posted on Courseworks after each assignment is due.
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Homework 10
Homework 11
Homework 12
Exam: There will be two 75-minute in-class midterm exams, and a final exam.
Midterm 1: October 3
Midterm 2: October 31
Final (Tentative schedule):
If you have a conflict with any of the exam dates, you must contact me ahead of time so we can make arrangements. (At least a week ahead is preferable.) If you are unable to take the exam because of a medical problem, you must go to the health center and get a note from them -- and contact me as soon as you can.
Grading: The final course grade will be determined by:
Homework: 10%
Midterm 1: 25%
Midterm 2: 25%
Final: 40%
The lowest homework score will be dropped.
Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles. But if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours and the course TA in the help room. Talking to your other classmates can also be helpful. Finally, there is information about tutoring resources through CC / SEAS, GS, and Barnard at http://www.math.columbia.edu/general-information/tutoring-services/.
Student with disabilities: Students must register with the Disability Services and present an accomodation letter before the exam or other accomodations that can be provided. More information is available on the Disability Services webpage: http://health.columbia.edu/disability-services
Tentetive Syllabus
| Date | Book Section(s) | Homework | Notes |
|---|---|---|---|
| 09/05 | Brief overview, coordinate systems (12.1,10.3,15.7,15.8) | ||
| 09/10 | Vectors (12.2) | HW 1 due | |
| 09/12 | Dot product (12.3) | ||
| 09/17 | Cross Product (12.4) | HW 2 due | |
| 09/19 | Equations of lines and planes (12.5) | ||
| 09/24 | Parametric curves, conic sections (10.1, 10.5) | HW 3 due | |
| 09/26 | Cylinders and quadric surfaces (12.6) | ||
| 10/01 | Review | ||
| 10/03 | Midterm 1 | ||
| 10/08 | Vectors functions and space curves (13.1) | HW 4 due | |
| 10/10 | Derivatives and integrals of vector functions (13.2) | Drop Date:Barnard, CC, GS, SPS | |
| 10/15 | Arc length and curvature (13.3) | HW 5 due | |
| 10/17 | Motion in space: velocity and acceleration(13.4) | ||
| 10/22 | Functions of several variables, limits, continuity (14.1, 14.2) | HW 6 due | |
| 10/24 | Partial derivatives (14.3) | ||
| 10/29 | Review | HW 7 due | |
| 10/31 | Midterm 2 | ||
| 11/05 | Academic Holiday | ||
| 11/07 | Tangent planes and linear approximations (14.4) | ||
| 11/12 | The chain rule (14.5) | HW 8 due | |
| 11/14 | Directional derivatives and the gradient vector (14.6) | ||
| 11/19 | More on Directional derivatives and the gradient vector (14.6) | HW 9 due | |
| 11/21 | Thanksgiving! | ||
| 11/26 | Maxima and minima (14.7) | HW 10 due | |
| 11/28 | More Maxima and minima (14.7) | ||
| 12/03 | Lagrange multipliers (14.8) | HW 11 due | |
| 12/05 | Complex numbers (Appendix H) | ||
| 12/10 | Review | HW 12 due |