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***

• Final exam is Tuesday, May 13, 12-1:50pm, room 101 Warren Weaver Hall
• No office hours on Thursday
• Office hours will be held Monday from 4:30-6:30pm
• No notes or calculator are allowed on the exam. You will be provided will this formula sheet .

Course description

• Trigonometric, Inverse Trigonometric, Logarithmic and Exponential Functions.

• Derivatives, Antiderivatives and Integrals of functions of one real variable.

• Applications including graphing, maximizing and minimizing functions.

• Areas and Volumes.

Textbook

Calculus, Early transcendentals,  by James Stewart.

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

 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.

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 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.