Instructor

Maksym Fedorchuk
Email: mfedorch@math.columbia.edu
Office: 7th floor Mathematics Hall
Tel: 212-854-4759
Office hours: 5-6pm on Monday, 9:30-10:30am on Thursday, or by appointment

Location and time

Section 5: Tuesday and Thursday, 11:00am-12:15pm in Math 312
Section 6: Tuesday and Thursday, 1:10pm-2:25pm in Math 312

Teaching Assistants

Section 5: Philip Engel (pme2105), Chris McGinn (cfm2118), and Ruchi Gupta (rg2625)
Section 6: Andrew Kiluk (aek2140), James Diotte (jad2192), and Akshay Shah (ars2212)
TAs hold regular office hours in Calculus Help Room

Textbook

Calculus, Early Transcendentals (7th ed.) by James Stewart. The book should be available at the Columbia bookstore.

Course Content

This course will offer an introduction to multivariable calculus and particularly differentiation in several variables. We will cover most of the content in Chapters 10, 12-14 of the textbook with some additional sections selected from other chapters.

Grading and Examinations

There will be two midterm exams during class. Make-up exams will not be given. In case you miss a midterm because of a family or medical emergency, and the emergency is confirmed by a note from your dean, your other midterm will count for 40% of the course grade. Your course grade will be determined as follows:
Component Date Percentage
Midterm I February 16, in class 20
Midterm II March 22, in class 20
Homework Weekly 20
Final Exam Tuesday, May 08 40

All students must take the final at the time scheduled by the university. If you miss the final exam, you will need to petition the dean's office to receive a mark of INC (incomplete) and retake the final at a later day.

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 the math hall by 5pm on the due date (usually Tuesdays). 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 the 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 the 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
Jan. 17 Introduction. Two and three dimensional coordinate systems. Polar coordinates in the plane. 12.1, 10.3
Jan. 19 Vectors. Applications of vectors. 12.2, 12.3
Jan. 24 Dot product. Lengths and distances. 12.3, 12.4
Jan. 26 Cross product. Equations for lines and planes in the space. 12.5, 12.5
Jan. 31 More on lines and planes in the space. 12.5, 10.5
Feb. 2 Cylinders and quadric surfaces in the space. 10.5, 10.6, 12.6
Feb. 7 Vector functions. Calculus of vector functions. 13.1, 13.2
Feb. 9 Derivatives and integrals of vector functions. 13.2, 13.3
Feb. 14 Arc length and curvature. 13.3
Feb. 16 Midterm I.  
Feb. 21 Motion in space: velocity and acceleration. Kepler's laws. 13.4
Feb. 23 Functions of several variables. Continuity and limits of functions of several variables. 14.1, 14.2
Feb. 28 Partial derivatives. 14.3, 14.5
Mar. 1 Tangent planes and linear approximations. 14.4, 14.5
Mar. 6 The chain rule in several variables. 14.5
Mar. 8 Directional derivatives. The gradient vector. 14.6
Mar. 20 Review.  
Mar. 22 Midterm II.  
Mar. 27 Maxima and minima I. 14.7
Mar. 29 Maxima and minima II. 14.7
Apr. 3 Absolute extrema. Second order behavior near a critical point. Saddle points.  
Apr. 5 Lagrange multipliers, I. 14.8
Apr. 10 Lagrange multipliers, II. 14.8
Apr. 12 Lagrange multipliers, III. Appendix H
Apr. 17 Complex numbers, complex exponentials. Appendix H
Apr. 19 Review: Vectors in space (Chapter 12). Ch. 12
Apr. 24 Review: Vector functions (Chapters 13). Ch. 13
Apr. 26 Review: Optimization Problems (Chapter 14). Ch. 14
May 8 Final Examination  
Due Date Assigned Exercises (to be turned in) Suggested Exercises (not to be turned in)
Homework 1
January 24		 Section 10.3: 12, 14, 20
Section 12.1: 8, 12, 14, 16, 36
Section 12.2: 4, 8, 14		 Section 10.3: 25, 54
Section 12.1: 5, 13, 21, 27, 41
Homework 2
January 31		 Section 12.2: 22, 24, 42
Section 12.3: 18, 20, 26, 46
Section 12.4: 4, 14, 22		 Section 12.2: 3, 5, 7, 9, 15, 17
Section 12.3: 5, 7, 15, 17
Homework 3
February 7		 Section 12.4: 32, 36
Section 12.5: 10, 16, 34, 52, 58, 72, 74, 78		 Section 12.4: 19, 42, 45
Section 12.5: 75, 81
Homework 4
February 14		 Section 13.1: 2, 22, 24
Section 13.2: 18, 22, 26
Section 13.3: 4, 6, 14		 Section 13.1: 3, 5, 21, 23, 42
Section 13.2: 17, 21, 25
Section 13.3: 3, 5, 13, 19
Homework 5
February 28		 Section 13.3: 18, 20, 22, 24, 44, 46
Section 13.4: 12, 14, 28		  
Homework 6
March 6		 Section 14.1: 30, 31
Section 14.2: 8, 10, 16, 18
Section 14.3: 20, 22, 32, 34, 40, 46, 48, 54		 Section 14.1:38, 59--60
Section 14.2: 21, 42, 43
Section 14.3: 75, 76
Homework 7
March 20		 Section 14.4: 2, 4, 6, 14, 42
Section 14.5: 6, 10, 12, 22, 34, 42
Section 14.6: 10, 12, 28, 34, 46		 Section 14.4: 17, 21, 46
Section 14.5: 35, 55
Section 14.6: 7, 11, 48, 61
Homework 8
April 3		 Section 14.7: 6, 8, 10, 13, 14, 20 Section 14.7: 1, 2, 3, 4, 37, 38, 41, 43
Homework 9
April 10		 Section 14.7: 30, 32, 34, 48
Section 14.8: 4, 6, 8, 10		 Section 14.7: 31, 36, 37, 38, 55
Section 14.8: 35, 55
Homework 10
April 17		 Section 14.8: 14, 16, 18, 20
Appendix H: 8, 27, 32, 36, 38, 47		 Section 14.8: 11, 15, 19, 21, 22, 23, 25, 47
Homework 11 (final review)
April 30		 Section 12 Review Exercises: 4, 10, 17, 20, 22, 26
Section 13 Review Exercises: 4, 8, 9, 10
Section 14 Review Exercises: 16, 36, 48, 56, 64		 Section 14 Review Exercises: 26, 46, 55, 62

Midterm I

The first midterm takes place on Thursday of February 16th.
Topics covered
The following are practice exams:
Practice midterm #1 Solutions
Practice midterm #2 Solutions
Practice midterm #3 Solutions

Midterm II

The second midterm takes place on Thursday of March 22nd.
Topics covered
The following are practice exams:
Practice midterm #1 Solutions
Practice midterm #2 Solutions

Final Examination, May 8

Practice final #1 with solutions
Practice final #2 with solutions (solution of Problem 4 is fixed at 11:40am, May 3)

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