Instructor

Name: Maksym Fedorchuk
Email: mfedorch@math.columbia.edu
Office: Math 613 
Tel.: 212-854-2192
Office hours: MW 2:30-3:30pm or by appointment

Location and time

Monday and Wednesday, 1:10-2:25pm in Math 312.
Attendance is strongly encouraged.

Teaching Assistants

Tim Heath (timheath@math), Alexander Boger ( ajb2163@) and Yuxiao Huang ( yh2419@)
TAs grade homeworks and hold regular office hours in Calculus Help Room

Textbook

Calculus, Early Transcendentals (6th ed.) by James Stewart. The book should be available at the Columbia bookstore.
Access to the WebAssign on-line homework system is not required.

Course Content

This course will offer an introduction to single variable calculus and particularly differentiation and integration techniques. We will cover Chapters 1-5 and a bit of Chapter 6.

Grading and Examinations

Your course grade will be determined as follows:
Component
 Date
 Percentage
Midterm I October 6, in class
 25
Midterm II November 22, in class
 30
Homework
 Weekly
 5
Final Exam
 projected date
Monday, December 20, 1:10-4pm
 40

Homework

Weekly homework will be assigned and is an essential part of the course. Problem sets are to be submitted in the designated dropbox on the 4th floor of Math Hall on the due date (usually Wednesdays). Show your work and provide sufficient justification to receive full credit. Partial credit will be provided. No late homework will be accepted and no extensions given but two lowest homework scores will be dropped at the end. Please staple your work.

Collaboration Policy

All homework solutions have to be your own work written in your own words. If you discuss solutions to the homework assignment with other students, please list the names of your collaborators on the write up. No collaboration or use of an outside aid is permitted during exams. Cheating on an exam will result in a grade of F and will be reported to a dean.

Calculators

Calculators will not be permitted during the exams.
Date

 Topics covered

 Assigned reading
Sep. 8
 1.1: Four ways to represent a function
1.2: A catalog of essential functions
1.1, 1.2
Sep. 13
 1.2: A catalog of essential functions
1.3: New functions from old functions
1.5: Exponential functions
 1.3, 1.4, 1.5
Sep. 15
 1.6: Inverse functions and logarithms
 1.6
Sep. 20
 2.1: The tangent and velocity problems
2.2: The limit of a function
 2.1, 2.2
Sep. 22
 2.3: Calculating limits using limit laws
The Squeeze Theorem
 2.3
Sep. 27
 2.5: Continuity
The Intermediate Value Theorem
 2.5
Sep. 29
 2.6: Limits at infinity: horizontal asymptote
2.7: Derivatives and rates of change
 2.6, 2.7
Oct. 4
 2.7: Derivatives and rates of change
2.8: The derivative as a function
 2.7, 2.8
Oct. 6
 Midterm I

Oct. 11
 3.1: Derivatives of polynomials and exponentials
 3.1
Oct. 12
 Last Day to Drop Class for Barnard, CC, GS, GSAS, and CE.
Oct. 13
 3.2: The product and quotient rules
3.3:Derivatives of trigonometic functions
 3.2, 3.3
Oct. 18
 3.4: The chain rule
 3.4, 3.5
Oct. 20
 3.5: Implicit differentiation
3.6: Derivatives of logarithmic functions
 3.5, 3.6
Oct. 25
 3.9: Related rates
3.10: Linear Approximations and differentials
 3.9, 3.10
Oct. 27
 3.11 Hyperbolic Functions
4.1: Maximum and minimum values
 3.11, 4.1
Nov. 1

 Academic Holiday.  November 2 is Election Day.



Nov. 3

4.1: Maximum and minimum values
4.2: The Mean Value Theorem
4.1, 4.2
Nov. 8
 4.3: How derivatives affect the shape of a graph
 4.3
Nov. 10
 4.4: Indeterminate forms and L'Hopital’s Rule
4.4
Nov. 15
 4.5: Summary of curve sketching
4.7: Optimization problems
 4.7
Nov. 17
 Midterm Review.
 3.1--3.10, 4.1--4.4
Nov. 22
 Midterm II

Nov. 24
 4.8: Newton’s method.
Nov. 29
 4.9: Antiderivatives
 4.9, 5.1
Dec. 1
 5.1: Areas and distances
5.2: The definite integral
 5.1-5.2
Dec. 6
5.3: The fundamental theorem of calculus
5.4: Indefinite integrals
 5.3, 54
Dec. 8
 5.5: The substitution rules

Dec. 13
 6.1 Areas between curves
6.2 Volumes
 5.5, 6.1

 
 6.1, 6.2
Monday,
Dec. 20
 Final Examination
 All of the above
Due Date
 Assigned Exercises
8-10 randomly chosen problems will be graded
Suggested Exercises (not to be turned in)
Sep. 15, 5pm
1.1: 2, 24, 30, 44, 46, 68, 70
1.2: 2, 4, 8, 12
1.3: 4
1.1: 5, 28, 64, 69
1.2: 9, 11, 18
Sep. 22, 5pm

 1.3: 34, 38, 42, 48, 50
1.5: 15, 16, 18, 19
1.6: 10, 18, 24, 38, 48
1.3: 3, 12, 30, 39, 51
1.5: 14, 25
1.6: 5, 9, 11, 15, 61, 73
Sep. 29, 5pm
 2.1: 2, 6 (use calculator)
2.2: 4, 6, 8, 12, 28, 32
2.3: 2, 8, 14, 26, 30
2.2: 2, 5, 14, 25, 26, 34
2.3: 7, 11, 25, 27, 29, 35, 37
Oct. 6, 5pm 2.5: 18, 36, 50
2.6: 10, 16, 18, 22, 32, 36

Oct. 20, 5pm



2.7: 30, 52
2.8: 3, 36, 38, 42, 44, 50(a)
3.1: 6, 8, 10, 12, 22, 30, 34
3.2: 4, 6, 8
2.7: 31--36, 51,
2.8: 6, 50(b,c,d), 51, 53
3.1: 32, 33, 35, 36
Oct. 27, 5pm
 3.3: 10, 12, 40
3.4: 8, 12, 34, 40, 44
3.5: 6, 12, 26
3.6: 12, 24, 40, 44

Nov. 3, 5pm
 3.10: 2, 4, 6
4.1: 30, 32, 36, 42, 44, 50 		3.10: 23, 4.1: 39, 41, 49, 78
Nov. 10, 5pm
 4.1: 54, 56, 60, 62
4.2: 12, 20, 24
4.3: 10, 15, 20, 34
Nov. 17, 5pm
 4.4: 10, 14, 18, 22, 40, 42, 46, 52, 56, 60
Chapter 3 review: 8, 12, 26, 60
Chapter 4 review: 4, 6, 45
Dec. 6, 5pm
 4.9: 2, 5, 18, 20, 21, 23, 32, 50
5.1: 2, 18, 20, 21, 22
5.2: 17, 18, 30, 36, 56
Dec. 13, 5pm
 5.3: 19, 24, 35, 38, 40
5.5: 12, 13, 14, 19, 30, 43, 44

Midterm I, October 6

The midterm will cover material of Lectures 1-8 (Sections 1-2).

Midterm II, November 22

The midterm will cover material in Sections 3.1-4.4

Final Examination, December 20

 The final is cumulative.

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