Calculus I: V63.0121.015


Information

Mon/Wed 6:20-8pm, Goddard A
Instructor: Miranda Holmes, office 809 WWH
Email: holmes at cims dot nyu dot edu
Office Hours: Monday 5-6pm, Thursday 2-3pm

***ANNOUNCEMENTS***


Course description


Textbook

Calculus, Early transcendentals,  by James Stewart.

It will be very helpful to read the textbook before the classroom discussion of each topic.


Grading

 Homework  20%
 Midterm 1, Wed Feb 27  20%
 Midterm 2, Wed Apr 9  20%
 Final Exam, Tues May 13, 12-1:50pm, room 101  40%

Midterm 2 will cover all sections up to and including section 5.5. (This is all the material covered in class up to and including Wednesday, April 2.)


Tutoring

Free tutoring is available in the Undergraduate Math Tutoring Center.
See http://math.nyu.edu/degree/undergrad/tutor_schedule.html for a schedule.

Syllabus / Homework

Homework will be collected every Wednesday, for the Monday and Wednesday of the preceeding week.
If you can't make it to class, please arrange to have someone hand it in for you, or else put it in my box (in the lobby of WWH).
Homework received after Thursday morning at 8am will receive 0.

(Homework problems in brackets do not need to be handed in; they are there for practice and solutions will be handed out with the rest.)

  Jan 23 (Wed)  1.1
 1.2
 Functions and their representations
 A catalog of essential functions
 1.1: 19, 21, 23, 25, 37, 53, 57
 1.2: 18, 28, 39, 43, 49, 62
  due Wednesday, January 30
  Jan 28 (Mon)  1.3
 1.4
 The limit of a function
 Calculating limits
 1.3: 3, 7, 13, 33, (4, 11, 16, 39)
 1.4: 2, 10, 11, 13, 20, 23, 31 (24, 35, 36)
  due Wednesday, February 6
  Jan 30 (Wed)  1.5
 1.6
 2.1
 Continuity
 Limits involving infinity
 Derivatives and rates of change
 1.5: 13, 20, 24, 29, 35
 1.6: 14, 18, 21, 26, 29, 47, 49
  due Wednesday, February 6
  Feb 4 (Mon)  2.1
 2.2
 Derivatives and rates of change
 The derivative as a function
 2.1: 23, 24, 25, 28
 2.2: 1, 3, 9, 14, 16, 17, 18, 19, 20, 28, 33, 35
  due Wednesday, February 13
  Feb 6 (Wed)  2.3
 2.4
  Basic differentiation formulas
  The product and quotient rules
  2.3: 4, 11, 16, 26, 32, 39, 48, 52, 62
  2.4: 3, 11, 23, 29, 38, 43, 46, 52
  due Wednesday, February 13
  Feb 11 (Mon)  2.5
 2.6
 The Chain rule
 Implicit Differentiation
  2.5: 3, 11, 21, 34, 37, 45, 51, 54, 64
  2.6: 5, 13, 14, 17, 23, 32, 36, 38
  due Wednesday, February 20
  Feb 13 (Wed)  2.7
 2.8
 Related Rates
 Linear Approximations and Differentials
  2.7: 3, 7, 11, 14, 20, 36
  2.8: 3, 10, 13, 18, 20, 21, 23, 28
  due Wednesday, February 20
  Feb 18 (Mon)     No class  
  Feb 20 (Wed)   3.1
  3.2
  3.3
  Exponential Functions
  Inverse Functions and Logarithms
  Derivatives of logarithms and exponential functions
  3.1: 11, 16, 18, 25, 30, 31, 32
  3.2: 48, 53, 63, 66, 73
  3.3: 7, 23, 24, 30, 38
  due Wednesday, February 27
  Feb 25 (Mon)  3.2
 3.3
 3.4
  Inverse functions and logarithms
  Derivatives of logarithms and exponential functions
  Exponential Growth and Decay
  3.2: 4, 17, 22, 30, 36, 39
  3.3: 50, 51, 57, 63
  3.4: 1, 4, 5, 9, 12, 18, 20
  due Wednesday, March 5
  Feb 27 (Wed)     MIDTERM (60 minutes) SOLUTIONS
 
  Mar 3 (Mon)  3.5
 3.7
  Inverse trignometric functions
  Indeterminate forms and L'Hospital's rule
  3.5: 4, 8, 10, 11, 13, 17, 20, 28, 32
  3.7: 6, 12, 24, 30, 31, 35, 40, 41, 49
  due Wednesday, March 12
 Mar 5 (Wed)  3.7
 4.1
  Indeterminate forms and L'Hospital's rule
  Maximum and minimum values
  3.7: 6, 12, 24, 30, 31, 35, 40, 41, 49
  4.1: 8, 14, 28, 29, 36, 43, 44, 55, 61
  due Wednesday, March 12
 Mar 10 (Mon)   4.2
  4.3
  The Mean Value Theorem
  Derivatives and shapes of graphs
  4.2: 4, 13, 15, 18, 27, 30, 32, 36
  4.3: 4, 24, 30, 34, 35, 37, 48, 53
  due Wednesday, March 26
 Mar 12 (Wed)   4.3
  4.5
  Derivatives and shapes of graphs
  Optimization Problems
  4.5: 6, 9, 12, 24, 28, 32, 43
  due Wednesday, March 26
 Mar 24 (Mon)   4.6
  4.7
  Newton's Method
  Antiderivatives
  4.6: 6, 8, 10, 12, 18, 22, 25, 29*
  4.7: 1, 2, 3, 4, 11, 23, 26
  due Wednesday, April 2
 Mar 26 (Wed)   5.1
  5.2
  Areas and Distances
  The Definite Integral
  5.1: 2, 8, 14, 16
  5.2: 2, 8, 14, 18
  due Wednesday, April 2
 Mar 31 (Mon)   5.2
  5.3
  The Definite Integral
  Evaluating Definite Integrals
  5.2: 29, 32, 39, 50
  5.3: 3, 12, 15, 20, 32, 37, 43, 62
  due Wednesday, April 9
 April 2 (Wed)   5.4
  5.5
  The Fundamental Theorem of Calculus
  The Substitution Rule
  5.4: 2, 4, 8, 20, 22, 24, 27, 28, 33
  5.5: 6, 15, 21, 31
  due Wednesday, April 9
 April 7 (Mon)   5.5
  6.1
  The Substitution Rule
  Integration by Parts
  5.5: 39, 47, 55, 62
  6.1: 2, 8, 14, 19, 26, 31, 40, 43
  due Wednesday, April 16
 April 9 (Wed)     MIDTERM
 
  Practice Midterm
  Solutions to practice midterm
 April 14 (Mon)   6.2   Trigonometric Integrals and Substitutions   6.2: 8, 12, 20, 28, 34, 42, 51, 52, 58
  due Wednesday, April 23
 April 16 (Wed)   6.3   Partial Fractions   6.3: 19, 22, 28, 38, 41
  due Wednesday, April 23
 April 21 (Mon)   6.6   Improper Integrals   6.6: 7, 10, 14, 22, 28, 32, 41, 46
  due Friday, May 2 9am
 April 23 (Wed)   6.5   Approximate Integration   6.5: 7, 8, 10, 15, 16, 18, 26
  due Friday, May 2 9am
 April 28 (Mon)   7.1   Areas between curves   7.1: 5, 6, 7, 8, 14, 15, 18, 20, 25, 33
  due Friday, May 2 9am
 April 30 (Wed)     Review   Review Problems
 May 5 (Mon)     Review   Bring book to class
* second part only. To find non-zero root, start with x_1 = 0.01.