Day/Time: MTWR 1:00pm-2:35pm (Note: Friday, May 30 is the
make-up date for May 26 which is the Memorial Day holiday. Class will
meet on May 30.)
Location: 417 Mathematics
Building
Instructor: Chenyan Wu
Teaching Assistant:
Adam Jacob (ajacob "at" math.columbia.edu) Help room
schedule is available here.
Contact
Information: chenyan "at" math.columbia.edu
Office
Hours: 2.35pm - 3.35pm Wednesdays at 528
Textbook:
CALCULUS, EARLY TRANSCENDENTALS (6th edition) by James Stewart
Material Covered: This course covers chapters 12, 13 and 14 of the textbook. Simply put the goal is to study multivariable calculus and its application. We will see a generalization of what you have learnt in Calculus I: continuity, partial derivative, chain rule... However we need to be cautious as multivariable functions sometimes exhibit strange behaviours. As application and motivation we will study various surfaces, parametric curves and some optimization problems.
Prerequisites: Calc I, Calc II. Know how to take limit and derivative and know vector space.
Homework: Assignments will be posted on courseworks and here. Students are encouraged to discuss the problem but are required to write their own solutions. Copying other's homework is not allowed and not good for you. Homework is due on Mondays in class (2.35pm). You lose 10% of points for each day you are late. Please write clearly and include only the relevant parts. You get no credit or even lose points for irrelevant parts even if what you write is true. Before applying a theorem please show that the conditions are all satisfied. Learn to manipulate the symbols and plug in the numbers at the last step. Most of the times the numbers tend to obliterate the structure. Calculator is not allowed in exams. It is encouraged that you not use one while doing homework.
Grading: The final grade is produced using the following recipe: 30% HW + 30% Midterm Exam + 40% Final Exam. All the grading information is available on Courseworks.
|
Day |
Topic |
Homework |
Due Date |
|
May 27 |
10.1 Curves defined by parametric equations |
10.1: 7, 37, 40; 10.2: 14, 43, 65 |
June 2 |
|
May 28 |
10.3 Polar coordinates |
10.3: 1, 13, 51; 10.4: 5, 46 |
|
|
May 29 |
12.1 Three-dimensional coordinate systems |
12.1: 3, 34, 38; 12.2: 6, 9, 38 |
|
|
May 30 |
12.3 The dot product |
12.3: 41, 49, 53; 12.4: 5, 13, 18,49 |
|
|
June 2 |
12.5 Equation of lines and planes |
12.5: 10, 26, 44, 63, 75 |
|
|
June 3 |
12.6 Cylinders and quadric surfaces |
12.6: 1, 21-28, 43, 49 |
|
|
June 4 |
10.5 Conic sections |
10.5: 31, 41, 46, 51; 10.6: 1, 5, 27 |
|
|
June 5 |
13.1 Vector functions and space curves. |
13.1: 9, 28, 41 |
|
|
June 9 |
13.2 Derivatives and integrals of vector functions |
13.2: 17, 32, 37, 39 |
|
|
June 10 |
13.3 Arc length and curvature |
13.3: 16, 45, 56, 60 |
|
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June 11 |
Review |
|
|
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June 12 |
Midterm |
Sample Midterm available on Courseworks. Click Assignment and there it is. |
|
|
June 16 |
13.4 Motion in space: velocity and acceleration |
13.4: 29, 31(You don't need to graph.) |
June 23 |
|
June 17 |
14.1 Functions of several variables |
14.1: 30, 73(If you don't have graphing software, just discuss what surfaces you get for varying c's. |
|
|
June 18 |
14.2 Limits and continuity |
14.2: 1, 6, 8, 10, 16, 41, 44, 45 |
|
|
June 19 |
14.3 Partial derivatives |
14.3: 28, 48, 50, 75, 95(You don't need to graph.) |
|
|
June 23 |
14.4 Tangent planes and linear approximations |
14.4: 4, 14, 28, 40, 42 |
June 30 |
|
June 24 |
14.5 The chain rule |
14.5: 14, 25, 26, 48 |
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|
June 25 |
14.6 Directional derivatives and the gradient vector |
14.6: 10, 16, 22, 31, 42, 49 |
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June 26 |
14.6 Directional derivatives and the gradient vector |
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|
|
June 30 |
14.7 Maximum and minimum values |
14.7: 4, 12, 15, 20, 30, 55 |
July 4? Just kidding. |
|
July 1 |
14.8 Lagrange multipliers |
14.8: 41, 46 |
|
|
July 2 |
Review |
Not satisfied with your scores? Here is the remedy if you put in work. Or this may prove to be poison? |
|
|
July 3 |
Final Exam |
Sample Final Exam is Online at Courseworks. |
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