Calculus
III, sections 6 and 7
Room: TBA
Time: Tuesday and Thursday, 1:102:25 PM (section 6), 2:403:55 PM
(section 7)
Instructor: Michael
Harris
Office Hours: Tuesday 4:305:30, Thursday, 1112 and by appointment, room
number 521
Teaching
Assistants: Monica Marinescu (marinescu@math.columbia.edu)
Office hours T 10:00am  1:00pm
Robin
Zhang (rzhang@math.columbia.edu) Office
hours MW 1:00pm  2:30pm
Lina
Tian (yt2511@columbia.edu) Office
hours W 4:00pm  6:00pm
Lekha
Yesantharao (lvy2002@columbia.edu) Office
hours T 10:00am  12:00pm
All
office hours in the Help Room at 502 Milstein (Barnard)
Homework will be graded and
will count for 20% of the final grade.
Homework is due on Tuesday the week after it is assigned, except where
otherwise indicated. Late homework
will not be accepted.
The
two lowest grades (of 12 assignments) will be dropped.
Grades will be computed as
follows:
Homework
(and occasional quizzes): 20%
Final
exam: 40%
Midterms: 20% each
A
provisional schedule with homework assignments is indicated below; it will be
updated regularly. You can find a
sample syllabus, with reading assignments, at this
page. More complete
information about the course is on the department's Calculus
III page.
Textbook: The course textbook is James Stewart, Calculus: Early Transcendentals (8th edition)
WebAssign: WebAssign will not be required for the course. However, students who wish to take
advantage of features of WebAssign can use the class key
columbia 8235 9880
Prerequisites: The sole prerequisite for the course is Calculus I. Familiarity with the material of
Calculus II is helpful but not essential.
Class and reading schedule
Date 
Topics (chapters
in Stewart) 
Homework 
Optional HW 
9/4, 9/6 
Vectors, coordinate systems (§12.12, 10.3, 15.78) 
Due 9/12 12.1: 1, 4, 6, 15, 20, 35 12.2: 1, 4, 8, 21, 22 10.3: 3, 6 15.7: 2, 3, 6 
12.1: 3, 5, 14, 19, 38 12.2: 5, 914 10.3: 4, 5 15.7: 7, 8 
9/11, 9/13 
Dot products, cross products (§12.3, 12.4) 
Due 9/18 15.8: 2, 4, 7, 8 12.2: 24, 28, 44, 46 12.3: 1, 2, 5, 8, 17, 23,
31, 43, 54, 64 12.4: 4, 6, 13, 14, 25, 45,
53 
12.3: 11, 13, 62, 63 12.4: 15, 29, 42, 46, 47, 54 For students comfortable with
firstyear physics: 12.2: 3040, 12.3: 4953,
12.4: 912, 3941 
9/18, 9/20 
Equations of lines and planes (§12.5) 
Due 9/26 12.5: 1, 2, 4, 10, 14, 18,
19, 22, 26, 34, 40, 53, 55, 64, 65, 77 
12.5: 5, 12, 13, 21, 33, 35,
37, 46, 62, 80 
9/25, 9/27 
Review of conic sections, cylinders and quadric surfaces
in 3space (§10.5, 12.6); parametric curves, vectorvalued functions (§10.1,
13.1) 
Due 10/3 12.5: 73, 74, 77, 78, 79 10.5: 2, 8, 14, 22, identify
the conic sections in 2530 12.6: 1, 4, 5, 10, 15, 16,
19, 2128, 36, 47 
10.5: All oddnumbered
exercises. 12.6: Unassigned
oddnumbered exercises 120, 3138, 4346, 49. 
10/2, 10/4 
Review for first midterm (through 12.6); first midterm 
Due 10/10 (note change of date!) 10.1: 7, 8, 11, 14, 24, 28 Exercises
24 and 28 are designed to develop geometric intuition: using a graphic
calculator defeats the purpose 13.1: 1, 4, 5; 9, 10 (for the last
two find a oneword description for the graph) 
10.1: 10, 1922, 33; also
43, 44, 48, 52 (for fun) 13.1: 12, 13, 14, 28, 31 
10/9, 10/11 
Integrals of vectorvalued functions, normal and binormal
vectors, arc length, curvature
(§13.23) 
Due 10/16 13.1: 16, 2126. 13.2: 6, 7, 1012, 16, 21,
26, 27, 34, 37, 42 13.3: 1, 4, 11, 13 
13.2: 15, 1720, 28, 41 13.3: 2, 3, 5, 79, 16 
10/16, 10/18 
Physical applications (§13.4, time permitting); functions
of several variables:
definitions and continuity (§14.12) 
Due 10/23 13.3: 19, 20, 22, 32, 47 14.1: 3, 12, 13, 22, 25, 28,
29, 32, 46, 48, 6166, 67, 70 
13.3: 21, 25, 4245 14.1: 5, 8, 10, 16, 20, 33,
36, 49, 52, 71 
10/23, 10/25 
Partial derivatives and tangent planes (§14.34) 
Due 10/30 14.2: 6, 10, 11, 14, 17, 18,
25, 32, 33, 37, 41 14.3: 58, 10, 18, 20, 21, 29, 36, 47 
14.2: 2, 520 (those not
assigned), 29,38 14.3: 25, 27, 31, 33, 35,
37, 43, 48 
10/30, 11/1 
Chain rule (§14.5);
Directional derivatives and the gradient (§14.6) 
Due 11/13 (note the date!) 14.3: 64, 65, 72, 78, 88, 94 14.4: 2, 4, 12, 18, 21, 25,
28, 32 14.5: 2, 3, 6, 7, 12, 13 
14.3: 75, 76, 86, 95 14.4: 1, 3, 5, 26, 27, 29 14.5: 1, 4, 5, 8, 9, 11, 19 
11/8 
Review for second midterm (through 14.4) 
Second midterm (no HW) 

11/13, 11/15 
Second midterm; Maximum/minimum problems (§14.7,
beginning) 
Due 11/20 14.5: 22, 23, 27, 30, 31,
42, 49 14.6: 5, 7, 13, 21, 22, 29 
14.5: 28, 29, 32, 44, 50 14.6: 6, 11, 27 
11/20 
Complex numbers (Appendix) 
Due 11/29 (note the date!) 14.7: 1, 2, 3, 6, 9, 11, 16 (graphing not
necessary), 21, 32, 35, 36,
39 (graphing
not necessary) Appendix H: 4, 8, 9, 12, 16, 22, 29, 39 
14.7: 13, 19, 31, 33, 37 Appendix H: 24, 34, 44, 45 
11/27, 11/29 
The gradient (§14.6), Maximum/minimum problems and Lagrange multipliers
(§14.78) 
Due 12/4 14.6: 9, 15, 41, 43, 52, 55, 60, 64(a) 14.7: 41, 43, 44, 46, 54, 57 14.8: 4, 6, 7, 8, 12, 22, 31, 33, 34, 36 
14.6: 10, 16, 24, 56, 63 14.7: 42, 47, 49, 50, 55, 56,
59 14.8: All odd problems 123,
3143 
12/4, 12/6 
Maximum/minimum problems and Lagrange multipliers, continued; Review for final exam 


Midterms: October
4, November 13 (in class) Note change of date!
Final: date to be announced by
the registrar
If you have a conflict with
any of the exams, you must inform the instructor as soon as possible and at
least one month before the exam. Makeup exams
will not be given unless the student has two other exams scheduled the same
day. Students with three exams
scheduled on the same day should visit the Student Service Center in 205 Kent
Hall to fill out a form which can then be submitted to each instructor or
department. An attempt will then
be made to arrange for one of the instructors to schedule a makeup exam on a
different day. Students can only
be excused from the exams because of serious illness or family emergency; documentation from your doctor or dean
must be provided.
No electronic devices (laptops, calculators,
telephones) are allowed during exams.
Academic integrity:
Students are encouraged to work together on homework but any assignments
handed in should be the work of the person whose name appears at the top of the
page. Collaboration during exams
is considered cheating and is taken very seriously. Cheating during a midterm or final entails failing the
course. Students are advised to
consult the Columbia
University Undergraduate Guide to Academic Integrity.
Disability services:
In order to ensure their rights to reasonable accommodations, it is the
responsibility of students to report any learningrelated disabilities, to do
so in a timely fashion, and to do so through the Office of Disability Services.
Students who have documented conditions and are determined by DS to need
individualized services will be provided an DScertified ‘Accommodation
Letter’. It is students’ responsibility to provide this letter to all their
instructors and in so doing request the stated accommodations.
More information on the DS
registration process is available online at https://health.columbia.edu/content/disabilityservices.
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