Calculus III

 

S1201  Section 001  Summer 2007

Time and Place: MTWR 1:00pm-2:35pm 417 Mathematics Building
Instructor: Qi Li

Teaching Assistant: Min Lee (enoia at math.columbia.edu)
Office: 408 Mathematics 
Email:  liqi at 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

The homework is due Monday in class.

The midterm will be on ??.

The final exam will be on ??.

 

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.

20% for the weekly homework. 10% for the quiz. The lowest grade of the homework will be dropped. Late homework will NOT be accepted.

 

Help

The Math Help Room is 406 Math on Columbia Campus. Graduate students will answer your questions.

Schedule

Day

Topic

Section

Homework/ Practice Exams

Solutions

    

Week 1

 

 

 

05/21

Cartesian coordinates in three dimensions. Vectors.

12.1,12.2

12.1:6,7,17,40

12.2:8,11,18,24

12.1,12.2

05/22

Vectors. Dot Product. Cross product.

12.2-12.4

12.3:2,8,24,27,40

12.3

05/23

Matrices, determinants, cross product.

12.4

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

12.4

05/24

Lines and Planes

12.5

12.5:4,10,22,26,33

12.5

 

Week 2

 

 

 

05/29

Lines and Planes,

12.5

12.5:32,42,48,54,66,72

12.5.2

05/30

Cramer’s rule

 

 

 

05/31

Cylinders and Quadric Surface

Cylindrical and Spherical Coordinates

12.6,12.7

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

12.7

06/01

Vector Functions and Space Curves

Derivatives and Integrals of Vector Functions

13.1,13.2

13.1:2,6,18,33

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

13.1, 13.2

 

Week 3

 

 

 

06/04

Arc Length and Curvature

13.3

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

13.3

06/05

Motion in Space

13.4

13.4:12,16,34,36

13.4

06/06

Function of Two variables

14.1

 

 

06/07

Limit of Functions of Two variables and Continuous Functions

14.2

Sample Midterm

 

 

Week 4

 

 

 

06/11

REVIEW

 

 

 

06/12

Midterm

 

 

 

06/13

Partial Derivatives

14.3

14.1:6,11,15,30,32

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

14.3: 1, 5, 16, 19, 21, 36, 51, 66, 83

14.1, 14.2, 14.3

06/14

Tangent Planes and Linear Approximations

14.4

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

14.4

 

Week 5

 

 

 

06/18

Chain Rule

14.5

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

14.5

06/19

Directional derivatives

14.6

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

14.6

06/20

Max and Min

14.7

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

14.7

06/21

Lagrange Multipliers

14.8

14.8: 4, 10, 14, 18, 23, 39 

14.8

 

Week 6

 

 

Sample Final

06/25

 

 

 

 

06/26

 

 

 

 

06/27

REVIEW

 

 

 

06/28

FINAL