Calculus III

 

S1201  Section 002  Summer 2007


Time and Place: MTWR 4:30pm-6:05pm 417 Mathematics Building
Instructor: Xinyi Yuan

Teaching Assistant: Min Lee (enoia@@math.columbia.edu)
Office: 408 Mathematics
Office hours: Mon 3:30pm-4:40pm, 405 Mathematics
Email:  yxy@@math.columbia.edu

 


Course Description

 

 

Textbook: Calculus Early Transcendentals, Fifth Edition, by James Stewart

 

Syllabus:

  • Vectors and Matrices, Coordinate Systems
  • Dot Product and Cross Product
  • Vector-valued Functions, Arc-length and Curvature
  • Multivariable Functions
  • Partial and Directional Derivatives
  • Local Extrema and Lagrange Multipliers
  • Complex Numbers and the Exponential Functions

 

Grading

The exams count for 70% of the final grade. The division is: 40% the final and 30% midterm. No make up exams will be given. 30% for the weekly homework. The lowest grade of the homework will be dropped. The homework is due Monday in class.  Late homework will NOT be accepted.

 

Help

The Math Help Room at 406 Math is available Mon-Fri. Graduate students will answer your questions.


Schedule

Day

Topic

Section

Homework/ Practice Exams

 

Week 1

 

 

05/21

Cartesian coordinates in three dimensions.

12.1

12.1:6,7,17,40

05/22

Vectors.

12.2

12.2:8,11,18,24

05/23

Dot product.

12.3

12.3:2,8,24,27,40

05/24

Matrices, determinants, cross product.

12.4

12.4:2,6,12,26,30,32

 

Week 2

 

 

05/29

Lines and Planes.

12.5

12.5:4,10,22,26,33

05/30

Cylinders and Quadric Surface

Cylindrical and Spherical Coordinates

12.6, 12.7

12.7:10,20,25,26,30,56

05/31

Vector Functions and Space Curves

13.1

12.5:32,48,54,72

13.1:2,6,18,33

06/01

Derivatives and Integrals of Vector Functions

13.2

13.2:10,14,20,25,36,40

 

Week 3

 

 

06/04

Arc Length and Curvature

13.3

13.3: 4,10,16,18,24,40

06/05

Functions of Several Variables

14.1

14.1: 6, 11, 15, 30, 32

06/06

Review

 

 

06/07

Midterm

 

MidtermSample

 

Week 4

 

 

06/11

Limits, continuity.

14.2

14.2: 7, 10, 11, 28, 37, 39

06/12

Partial derivatives.

14.3

14.3: 5, 16, 21, 36, 66, 83

06/13

Tangent planes, linear approximation

14.4

14.4: 2, 12, 19, 24, 31, 36

06/14

Chain rule

14.5

14.5: 4, 8, 9, 22, 28, 36

 

Week 5

 

 

06/18

Directional derivatives, gradient.

14.6

14.6: 8, 9, 15, 23, 27, 32

06/19

Max and min

14.7

14.7: 1, 3, 6, 11, 28, 40, 46

06/20

Max and min

14.7

No new homework

06/21

Lagrange multipliers

14.8

14.8: 4, 10, 14, 18, 23, 39

 

Week 6

 

 

06/25

Review

 

 

06/26

Review

 

 

06/27

Review

 

 

06/28

FINAL: 507 Math, 4:30-7:30pm

 

 FinalSample