Instructor

Name: Maksym Fedorchuk
Email: mfedorch@math.columbia.edu
Office: 613 Math Hall
Tel.: 212-854-2192
Office hours: Tuesday 1-3pm or by appointment

Location and time

Monday and Wednesday, 9:10-10:25am in Math 207

Teaching Assistants

Graduate: Zhengyu Xiang ( xiangzy@math)
Undergraduate: Nopphon Weeranoppanant (odd homeworks) <nw2193> and Juinn Ho (even homeworks) <sh2502>
TAs hold regular office hours in Calculus Help Room

Monday and Wednesday, 09:10-10:25 am

Mathematics Building, Room 207
Attendance is strongly encouraged.

Textbook

Calculus, Early Transcendentals (6th 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 12-14 of the textbook with some additional sections selected from other chapters.

Grading and Examinations

Your course grade will be determined as follows:
Component
 Date
 Percentage
Midterm I February 22, in class
 20
Midterm II March 24, in class
 20
Homework
 Weekly
 20
Final Exam
 Wednesday, May 12
9:00am-noon
 40

Homework

Weekly homework will be assigned and is an essential part of the course. Problem sets are to be submitted in the designated mailbox on the 4th floor of the math hall across from office 410 by 5pm 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 worst 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. 20 Introduction. Two and three dimensional coordinate systems. Polar coordinates in the plane. 12.1, 10.3
Jan. 25 Vectors. Dot product.
 12.2, 12.3
Jan. 27 Applications of vectors. Cross product.
 12.3, 12.4
Feb. 1
 Cross product. Equations for lines and planes in the space.
 12.5, 12.5
Feb. 3
 More on lines and planes in the space.
 12.5, 10.5
Feb. 8
 Quadric surfaces in the space.
 10.5, 10.6, 12.6
Feb. 10
 Vector functions. Caclulus of vector functions.
 13.1, 13.2
Feb. 15
 Derivatives and integrals of vector functions: arc length and curvature; velocity and acceleration.
 13.2, 13.3, 13.4
Feb. 17 Review.
Feb. 22
 Midterm I.
Feb. 24
 Functions of several variables.
14.1
Mar. 1
 Continuity and limits of functions of several variables.
 14.1, 14.2
Mar. 3
 Partial derivatives.
 14.3, 14.5
Mar. 8
 Tangent planes and linear approximations. 14.4, 14.5
Mar. 10
 The chain rule in several variables
14.5
Mar. 22
 Review.
Mar. 24
 Midterm II.
Mar. 29
 Directional derivatives. Gradient. 14.6
Mar. 31
 Maxima and minima. 14.7
Apr. 5
 Second order behavior near a critical point. Saddle points.
Apr. 7
 Lagrange Multipliers I.
 14.8
Apr. 12
 Lagrange multipliers, II.
 14.8
Apr. 14
 Complex numbers, Part I.
 Appendix H
Apr. 19
 Complex exponentials.
Appendix H
Apr. 21
 Derivatives of complex functions.  Differential equations.
 17.1
Apr. 26
 Nonhomogeneous differential equations. Cauchy-Riemann equations. 17.1
Apr. 28 Review: Vector functions (Chapters 12-13). Kepler's Laws.
 17.2
May 3
 Review: Calculus of vector functions. Optimization Problems. Differential Equations.
May, 12
 Final Examination
Due Date
 Assigned Exercises (to be turned in)
 Suggested Exercises (not to be turned in)
January 27 Section 10.3: 11, 13
Section 12.1: 3, 11, 13, 15, 35
Solutions
Section 12.1: 39
February 3 Section 12.2: 20, 22, 23, 30
Section 12.3: 20, 24, 38, 52
Section 12.4: 4, 12, 14
Solutions 		Section 12.2: 4, 16, 32
Section 12.3: 1, 5, 13, 56, 58
February 10
 Section 12.4: 20, 36
Section 12.5: 10, 20, 24, 50, 70
Section 10.5: 30
Solutions 		Section 12.4: 29, 38, 46

Section 10.5: 26, 29
February 17
 Section 13.1: 2, 12, 19 , 20, 21, 22, 23, 24, 28
Section 13.2: 10, 18, 20, 26
Section 13.3: 4, 14, 22
Solutions 		Section 13.1: 10, 42
Section 13.2: 4, 8
Section 13.3: 2, 25, 32, 40
March 3
 Section 14.1: 6, 8, 16 , 30, 31, 39, 40, 43, 61, 62
Solutions 		Section 14.1: 65, 66
March 10
 Section 14.2: 7, 8, 10, 16, 17, 18, 40
Section 14.3: 16, 18, 20, 22, 32, 34, 40, 46, 48, 54
Solutions 		Section 14.2: 11, 12, 13, 14, 15, 42
Section 14.3: 5--8,9, 10, 56
March 24
 Section 14.4: 2, 4, 6, 14, 42
Section 14.5: 10, 12, 22, 43, 34
Solutions 		Section 14.4: 11, 12
Section 14.5: 15, 55, 57
April 9
 Section 14.6: 7, 10, 12, 29, 34, 43
Section 14.7: 12, 17, 18, 20
Solutions 		Section 14.6: 48, 61
Section 14.7: 3, 4, 41, 43
April 16
 Section 14.8: 4, 9, 12, 18, 34, 39, 40, 21
Solutions 		Section 14.8: 46
April 23
 Appendix H: 8, 27, 32, 36, 38, 47
Section 17.1: 1, 2, 12, 17
Solutions
Appendix H: 1--14, 16, 25--28, 41, 43, 45, 47

Midterm I, February 22

The midterm will cover material from sections 10.5, 12.1--12.5 and 13.1--13.3.
To prepare, redo homeworks 1-4 and do the practice exams.
Midterm 1 Information
Practice Midterm 1 Solutions Problems 4-5 solutions
Practice Midterm 2 Solutions

Midterm II, March 24

The midterm will cover material from sections 14.1-14.5.
To prepare, redo homeworks 5-7 and do the practice exam.
Midterm 2 Information Solutions to suggested exercises
Practice Midterm Solutions

Final Examination, May 12

 The final is cumulative and covers Chapters 12.1--12.5, 13, 14, Appendix H (complex numbers) and 17.1--17.2 from the book. At least 50% of the final will be devoted to the topics covered since the 2nd midterm.
The formulae sheet for the final.
To prepare for the final do some of the following exercises:
Chapter 12 review exercises: 9, 10, 17, 19, 21, 25, 26*, 27
Chapter 13 review exercises: 6, 9, 12, 17, 18, 19, 21**
Chapter 14 review exercises: 6, 9, 10, 14, 22, 29, 36, 37, 41**, 46, 47, 48, 52, 53, 56, 59, 62, 63, 65
Chapter 17 review exercises: 1, 2, 3, 4, 5, 6, 11, 12
Review Exercises Solutions
Practice Final
Practice Final Solutions

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