Calculus I –Section 10,  Fall 2007

Instructor:   Prof. Shou-Wu Zhang (szhang@math.columbia.edu, x4-6362 )

Office Hour:   1:10-2:10 pm Tuesday and Thursday, Math 608

TA:  Xinyi Yuan (yxy@math.columbia.edu), Sixuan Li (sl2414@columbia.edu), and Padmavati Sridhar (ps2267@columbia.edu).

Time and Place:  2:40-3:55 pm Tuesday and Thursday, Math 203.

Text: Calculus (early transcendental) by James Stewart, 6th Edition.

Exams:  The midterm exams are on Oct 4 and November 8. The final exam   is on December 20.

Make-ups will not be given   for the midterm;   no final exams can be given earlier or later.

Homework: Homework will be assigned every Tuesday and Thursday will be due the following Tuesday. 

There is a pickup basket on a table in front of  rooms 410, math building,

 The later homework will NOT be accepted under any circumstances.

Grading: Final exam 40%, each midterm exam 20%, and homework grades 10%, webwork 10%

Help:. The help room Math 406   and Barnard Help Room is open on weekdays.

 

 

                                            Schedule of lectures

This schedule is tentative and may be modified as necessary.

 

Date

Reading

Homework

  Sept.4, 6

  1.1: Four ways to represent a function

  1.2:A catalog of essential functions,

  1.3: New functions from old functions,

 

  1.1: 30,  44, 45,  64

  1.2: 2,  8,  18
  1.3: 3, 39, 41

  Solution

  Sept. 11,13

  1.5: Exponential functions

  1.6:  Inverse functions and logarithms

  2.1: The tangent and velocity problems

  2.2: The limit of a function

  1.5: 14, 25
   1.6: 24, 38, 48

   2.1: 2, 7
   2.2:  5, 12,  28

  Solution

  Sept. 18,20

  2.3: Calculating limits using limit laws

  2.4: Precise definition of a limit

  2.5: Continuity

  2.3: 2, 10, 13,  36

  2.4: 1, 20, 32

  2.5: 4, 37, 42, 45

 Solution

  Sept. 25,27

  2.6: Limits at infinity

  2.7: Derivatives and rates of change

  2.8: The derivative as a function

  3.1:  Polynomials and exponentials

  2.6: 3, 22, 36
  2.7: 6, 14, 28
  2.8: 20, 24

  3.1: 34, 50(a,b),  67

 Solution

  Oct. 2

  3.2: The product and quotient rules

  3.3: Derivatives of trigonometics

  3.2: 12, 14, 34
   3.3: 10, 16, 39

Solution

  Oct. 4

1st Midterm

Solution

  Oct. 9,11

  3.4: The chain rule

  3.5: Implicit differentiation,

  3.6: Derivatives of logarithmic functions,

  3.4:  12, 20, 26, 41

  3.5:  23, 26, 50,
  3.6:  3,  25, 33, 45

Solution

  Oct.16, 18

  3.9: Related rates

  3.10: Linear approximations

  3.11: Hyperbolic functions

  4.1:  Maximum and minimum values,

  3.9: 3, 16

   3.10: 2, 23

   3.11: 31, 43

   4.1:  7, 44, 47, 59

Solution

  Oct. 23, 25

  4.2: The Mean Value Theorem

  4.3:  Shape of a graph,

  4.4:  L'Hospital's rule,

  4.2: 14, 17, 27, 32

  4.3: 10, 15,  21, 47
  4.4: 13, 46, 52, 60

Solution

  Oct. 30

  Nov 1

  4.5: Summary of curve sketching

  4.7: Optimization problems

  4.8: Newton's method

  4.5: 22, 31, 32, 54

   4.7: 11, 18, 38, 41
   4.8: 5, 40

Solution

  Nov. 8

 2nd Midterm

Solution

  Nov.13, 15

  4.9: Antiderivatives

  5.1: Areas and distances

  5.2: The definite integral

  4.9: 9, 12, 15, 34, 46

  5.1: 4, 12, 17, 20
  5.2: 7, 17, 34, 36

Solution

  Nov. 20

  5.3: The Fundamental Theorem of Calculus

  5.4: Indefinite integrals

  5.3: 2, 7, 14,  29,  41

  5.4: 12, 30, 32, 44, 47

Solution

  Nov.27, 29

  5.5: The substitution rule,

  6.1: Areas between curves

  6.2: Volumes

  5.5: 4, 5, 22, 30, 69
  6.1: 6, 27, 32

  6.2: 3, 6,  50

Solution

  Dec. 4

   6.3:, Volumes by cylindrical shells,

   6.5: Average value of a function

   6.3: 14, 18, 42, 43
   6.5: 5, 10

Solution

  Dec. 6

Review

 Old Final