Instructor: Eric
Urban, Office 521 Math, urban@math.columbia.edu
TA: Tae Gyu Lee
Time and Place: TR 9:10-10:25 in Math. 417.
Text: James Stewart - Calculus, Early Transcendentals (6th Edition)
Material Covered: Chapters 12, 13 and 14 + Appendix G.
Homework: The homework assignments and due dates are listed below. You must hand in the homework by 1 pm each Tuesday before class. There is a box for homework next to my office and the graded homework will be placed in a similar box nearby. Late homework will not be accepted under any circumstances.
Calculators: Calculators of any kind are not required for this course and won’t be allowed for the exams.
Midterm Exams. The midterm exams are on Thursday, February 21 and Thursday, March 27. Makeups will not be given for the midterm exams. Students can be excused from the midterms only because of serious illness or a family emergency of comparable gravity. To be excused you will need a note from your doctor or dean.
Final Exam: The Final Exam date is scheduled by the university on Thursday, May 15th from 9am to noon. All students must take the final exam at the time scheduled by the University; no final exams can be given earlier or later.
Grading: The course grade is apportioned as follows: Final exam 40%; each midterm exam 20%; homework 20%.
Help: My office hours are 10:30-11:30 pm on TR. The help rooms 406 Mathematics and 333 Milbank are open with people to answer calculus questions all day long on weekdays.
Method of Study: Your work for every class should have five components:| Class | Topic | Read | Homework problems |
Due
date |
| Jan 22 |
3D coordinate systems |
§12.1 | Ex: 4, 8, 11, 14, 19, 29, 33, 34 |
Jan 29 |
| Jan 24 |
Vectors and their coordinates | §12.2 | Ex: 3, 4, 5, 18, 20 , 31 |
Jan 29 |
| Jan 29 |
Dot product | §12.3 | Ex: 23, 27, 43, 46, 49, 51, 56, 58 |
Feb 5 |
| Jan 31 |
Cross product | §12.4 | Ex: 2, 3, 10, 14, 30, 38 |
Feb 5 |
| Feb 5 |
Equations of lines and planes | §12.5 | Ex: 3, 8, 11, 18, 33, 47, 57, 62 |
Feb 12 |
| Feb 7 |
Cylinders and quadric surfaces |
§12.6 | Ex: 4, 8, 12, 13, 21- 28, 33, 35 |
Feb 12 |
| Feb 12 |
Polar coordinates (review), Complex numbers |
§10.3 App. H |
Ex: 17, 25, 33, 37 Ex: 2,5,7,11,13,15,19, 23, 27, 33, 35 |
Not due Feb 26 |
| Feb 14 |
Complex exponentials |
App. H |
Ex: 41, 43, 44 |
Feb 26 |
| Feb 19 |
Review. I will go over some of the problems listed here. Let me know if there are problems you want me to cover. |
Chapter 12 |
Review, p.844-846 : Concept Chech : 1 to 12, True-False
Quiz, Ex: 1,2,3,4,5,7,8,9,11,12,13,15,17,19,26,27,37,47 |
Not due |
| Feb 21 |
Midterm I |
Ch. 12+ App. H |
Sample Midterm I |
|
| Feb 26 |
Vector functions and space curves | §13.1 | Ex: 1,2,3,15,19-24 |
Mar 4 |
| Feb 28 |
Derivative of vector functions | §13.2 | Ex: 3,4,5,6,8,9,12,15 | Mar 4 |
| Mar 4 |
Integral of vector functions, Arc length. |
§13.2 §13.3 |
Ex: 33,34, 40 Ex: 1,2,3,4,5,6,9,10,12 |
Mar 11 |
| Mar 6 |
Curvature | §13.3 | Ex: 21, 23, 24 | Mar 11 |
| Mar 11 |
Osculating circle. Velocity and acceleration | §13.3 §13.4 |
Ex: 39, 40, 41, 42 Ex: 3, 4, 5, 11, 13, 15, 19 |
Mar 25 Mar 25 |
| Mar 13 |
The tangential and normal components of acceleration | §13.4 | Ex: 20, 22, 25, 35 |
Mar 25 |
| Mar 25 |
Review. I will go over some of the problems listed here. Let me know if there are problems you want me to cover. |
Chapter 13 | Review, p881-883 : Concept Chech : 1 to 9, True-False
Quiz, Ex: 1, 3, 6, 9, 12, 15, 17, 20, 21. |
Not due |
| Mar 27 |
Midterm II | Sample Midterm II | ||
| Apr 1 |
Functions of several variables. Limits and continuity. | §14.1 §14.2 |
Ex: 7, 13, 17, 19, 23, 35, 61 Ex: 7, 11, 19, 27, 37, 39 |
Apr 8 Apr 8 |
| Apr 3 |
Partial derivatives. Tangent Planes. | §14.3 §14.4 |
Ex: 15,21,35,47,55,59,89 Ex: 3,5,11,17,29 |
Apr 8 Apr 15 |
| Apr 10 |
Linear approximations. |
§14.5 | Ex: 5,7,21,23,27,33,40 |
Apr 15 |
| Apr 15 |
Directional derivatives. The gradient vectors. | §14.6 | Ex: 5,7,11,19,29, 39, 49, | Apr 24 |
| Apr 17 |
Maximum and minimum values. | §14.7 | Ex: 1,2,3,5,6,7,8,15 ,28, 29, 39, 41, 45 | Apr 24 |
| Apr 22 |
Lagrange multipliers | §14.8 | Ex: 1,3,4,6,7,8,9,23,24 |
Apr 24 |
| Apr 24 |
Lagrange multipliers | §14.8 | Ex: 33, 39 | Not due |
| Apr 29 & May 1 |
Review. I will go over some of the
problems listed here. Let me know if there are problems you want me to cover. |
Chapter 14 |
Review, p 974-977 : Concept Chech : 3, 4, 7, 8, 9, 12, 15,
16. True-False Quiz, Ex: 1, 5, 9, 15, 25, 39, 43, 51, 52, 55, 60, 64 |
|
| May 15 |
Final exam
9:00am- noon in Math 417 |
|
Sample Final |