Calculus III

Summer 2008 Mathematics S1201 Section 1

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.


Schedule of Lectures

Day   

Topic

Homework

Due Date

May 27

10.1 Curves defined by parametric equations
10.2 Calculus with parametric curves

10.1: 7, 37, 40; 10.2: 14, 43, 65

June 2

May 28

10.3 Polar coordinates
10.4 Areas and lengths in polar coordinates

10.3: 1, 13, 51; 10.4: 5, 46

May 29

12.1 Three-dimensional coordinate systems
12.2 Vectors

12.1: 3, 34, 38; 12.2: 6, 9, 38

May 30

12.3 The dot product
12.4 The cross 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 9

June 3

12.6 Cylinders and quadric surfaces

12.6: 1, 21-28, 43, 49

June 4

10.5 Conic sections
10.6 Conic sections in polar coordinates

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 16

June 10

13.3 Arc length and curvature

13.3: 16, 45, 56, 60

June 11

Review


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

June 25

14.6 Directional derivatives and the gradient vector

14.6: 10, 16, 22, 31, 42, 49

June 26

14.6 Directional derivatives and the gradient vector


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.