Math 53 - Multivariable Calculus

Math 53 - Section 1 - Multivariable Calculus - Fall 2011

Denis Auroux - MWF 1-2pm, Room 155 Dwinelle

[Announcements] [Textbook] [Grading policy] [Homework] [Exams] [Syllabus] [Resources] [Sections]

Instructor: Denis Auroux (auroux@math.berkeley.edu)

Office: 817 Evans.
Office hours: Mondays 4-5:30pm (except on midterm days), Wednesdays 2:30-4pm

Lectures: Mondays, Wednesdays and Fridays, 1-2pm, 155 Dwinelle
Discussion sections: Tuesdays and Thursdays, at various times, see list.
Section enrollment/changes are performed through TeleBears.

Announcements

(11/26) A practice final has been posted below, as well as information about the final exam.
(11/26) Note a slight change to class schedule: in-class final reviews will be Friday Dec 2 and Monday Dec 5. Course evaluations will be handed out at end of lecture on Wed Nov 30.
(11/21) Midterm 2 has been graded. Solutions are posted below, as well as statistics. All the scores are posted on bSpace.
(11/16) Additional office hours on Friday Nov 18, 4-5:30pm. No office hours on Monday Nov 21 or Wed Nov 23 (sorry).
(11/13) Midterm 2 will take place on Monday November 21 at 1pm (usual class time). Review lecture on Friday Nov 18. Due to shortage of seats: on the day of the midterm, if your last name begins with E, F or G please go to 740 Evans; else come to 155 Dwinelle (usual classroom). Midterm 2 covers the material seen in class since midterm 1.
(11/6) Practice exams for midterm 2 are posted below. We haven't covered all the material yet.
(10/31) I'll be out of town next week (Nov 7-11). Prof. Williams will teach the lectures; office hours are cancelled.
(10/31) Office hours on Wed 11/2 are moved to: 3:30-4:30pm.
(10/14) Office hours on Wed 10/19 are cancelled -- sorry.
(10/10) Midterm 1 has been graded. Solutions are posted below, as well as statistics; all the scores are on bSpace.
(10/2) My office hours on Monday Oct 3 are cancelled; they are rescheduled on Tuesday Oct 4, 4:30-6pm; additional office hours before Midterm 1 on Friday Oct 7, 2-4:30pm (first half in lecture hall, second half at my office).
(9/28) Due to midterm 1 on Monday 10/10, the due date for Homework 6 is extended to Thursday 10/13 (instead of Tuesday 10/11).
(9/28) Here is a link to the applet shown in class to illustrate directional derivatives. It may not work with recent browsers (or require downgrading Java to 1.5).
(9/27) Midterm 1 will take place on Monday October 10 at 1pm (usual class time). No documents, no calculators. More information will be given in the review lecture (Fri Oct 7). Due to shortage of seats: on the day of the midterm, if your last name begins with F or G please go to 740 Evans; else come to 155 Dwinelle (usual classroom).
(9/24) Practice midterms for midterm 1 (longer than the actual midterm) have been posted below. But I recommend waiting until next weekend (and until you have reviewed the material) to look at them. After Friday 9/30 the only missing topic will be Lagrange multipliers, so you'll be able to do all but Problem 9 on each practice exam.
(9/20) Reminder: ASUC Lecture Notes are available for this class (by subscription).
(9/19) Here are the slides shown in today's lecture.
Office hours on Wednesday (9/21) will be from 3:10pm to 4pm (instead of 2:30) due to a department meeting. Sorry!
(9/14) Here are the slides shown in today's lecture.
(9/6) Homework 1 solutions are available below, as well as the next two homework assignments. Grades are being posted on bSpace at regular intervals.
(8/19) The first section meetings are on Thursday 8/25. The first lecture is on Friday 8/26. Students on the wait list should look for an open section. If you cannot find one to fit your schedule, you should talk to Barbara Peavy (967 Evans). Students with questions about Concurrent Enrollment can also ask Barbara Peavy.
Important: You MUST attend the section for which you are registered. If you are enrolled and wish to switch sections, you can do so yourself on TeleBears. However you cannot switch into a section that is full.
(8/19) Make sure to read the course policy and the detailed syllabus.

Textbook

The textbook for this course is: Stewart, Multivariable Calculus: Early Transcendentals for UC Berkeley. (ISBN: 978-1-4240-5499-2, Cengage).

(This is a custom edition containing chapters 10 and 12-16 of Stewart's "Calculus: Early Transcendentals", 6th edition).

Grading and course policy

Weekly homework and quizzes 25%; two midterms 25% each; final exam 25%; the lowest midterm can be dropped and replaced by the final exam grade. There will be no make-up exams. This grading policy allows you to miss one midterm, but check your schedule to make sure you have no conflict for the final exam.

Make sure to read the detailed course policy for important information.

Homework

Homework assignments are due each Tuesday in section; they will be posted here.

Homework 1 (due Tuesday 9/6) and solutions.
Homework 2 (due Tuesday 9/13) and solutions.
Homework 3 (due Tuesday 9/20) and solutions.
Homework 4 (due Tuesday 9/27) and solutions.
Homework 5 (due Tuesday 10/4) and solutions.
Homework 6 (due Thursday 10/13) and solutions.
Homework 7 (due Tuesday 10/18) and solutions.
Homework 8 (due Tuesday 10/25) and solutions.
Homework 9 (due Tuesday 11/1) and solutions.
Homework 10 (due Tuesday 11/8) and solutions.
Homework 11 (due Tuesday 11/15) and solutions.
Homework 12 (due Tuesday 11/22) and solutions.
Homework 13 (due Thursday 12/1) and solutions.

Exams

The midterms will take place on Monday October 10 and Monday November 21 (1-2pm) in the usual lecture room. The final exam will be on Wednesday 12/14 (7-10pm) in the Rec. Sports Facility Field House.

Directions to RSF Field House: The RSF Field House is located on the west end of the Recreational Sports Facility (on Bancroft Way). Please arrive promptly, and enter through the exterior double doors that lead directly into the Field House from outside. During the exam (restroom access etc.): to minimize disruption, exit/enter through the RSF Atrium doors at East end of the Field House. See aerial view (click on image to enlarge)

Practice exams and solutions to midterms will be posted here. Please note: the practice midterms are longer (80-90 minutes) than the actual midterms (50 minutes, during regular class time).

Midterm 1 score distribution: the quartiles are 61, 73, 82. (i.e.: 25% of the class got above 82, 25% got between 73 and 82, 25% got between 61 and 73, 25% got below 61).

A very rough estimate of what this might mean in terms of letter grades: cut-off between A- and B+ = somewhere around 80-82; cut-off between B- and C+ somewhere around 66-68; cut-off between C- and D somewhere around 55-57.

Midterm 2 score distribution: the quartiles are 65, 79, 87. (i.e.: 25% of the class got above 87, 25% got between 79 and 87, 25% got between 65 and 79, 25% got below 65).

A very rough estimate of what this might mean in terms of letter grades: cut-off between A- and B+ = somewhere around 86-88; cut-off between B- and C+ somewhere around 72-74; cut-off between C- and D somewhere around 56-58.

Remember your lowest midterm score will be dropped and replaced by your final exam score if that one is better; so, if you are unhappy with how you did, don't despair, but make sure to go over the things you missed, review any concepts that may be giving you trouble, and come regularly to section and to office hours.

Syllabus

Date	Topics	Book
Fri 8/26	Parametric equations	§ 10.1, 10.2
Mon 8/29	Polar coordinates	§ 10.3
Wed 8/31	Polar coordinates continued	§ 10.4
Fri 9/2	Vectors, dot product	§ 12.1, 12.2, 12.3
Mon 9/5	NO CLASS (Labor Day)
Wed 9/7	Dot product continued; determinant	§ 12.3
Fri 9/9	Cross product	§ 12.4
Mon 9/12	Equations of lines and planes	§ 12.5
Wed 9/14	Parametric equations and vector functions	§ 13.1
Fri 9/16	Velocity, acceleration	§ 13.2, 13.4
Mon 9/19	Functions of several variables	§ 14.1
Wed 9/21	Partial derivatives	§ 14.2, 14.3
Fri 9/23	Tangent plane, linear approximation	§ 14.4
Mon 9/26	Chain rule	§ 14.5
Wed 9/28	Gradient, directional derivatives	§ 14.6
Fri 9/30	Max-min problems	§ 14.7
Mon 10/3	Max-min problems continued	§ 14.7
Wed 10/5	Lagrange multipliers	§ 14.8
Fri 10/7	Review
Mon 10/10	MIDTERM 1
Wed 10/12	Double integrals	§ 15.1, 15.2, 15.3
Fri 10/14	Double integrals in polar coordinates	§ 15.4
Mon 10/17	Applications of double integrals	§ 15.5
Wed 10/19	Change of variables in double integrals	§ 15.9
Fri 10/21	Triple integrals	§ 15.6
Mon 10/24	Triple integrals in cylindrical coordinates; applications	§ 15.7
Wed 10/26	Triple integrals in spherical coordinates	§ 15.8
Fri 10/28	Vector fields	§ 16.1
Mon 10/31	Line integrals	§ 16.2
Wed 11/2	Gradient fields, fundamental theorem for line integrals	§ 16.3
Fri 11/4	Green's theorem	§ 16.4
Mon 11/7	Curl and divergence, Green's theorem revisited	§ 16.5
Wed 11/9	Surface area	§ 16.6
Fri 11/11	NO CLASS (Veterans' Day)
Mon 11/14	Surface integrals and flux	§ 16.7
Wed 11/16	The divergence theorem	§ 16.9
Fri 11/18	Review
Mon 11/21	MIDTERM 2
Wed 11/23	More about the divergence theorem	§ 16.9
Fri 11/25	NO CLASS (Thanksgiving)
Mon 11/28	Stokes' theorem	§ 16.8
Wed 11/30	Stokes' theorem continued; applications to physics	§ 16.8
Fri 12/2	Optional review (first half of the course)
Mon 12/5	Optional review (second half of the course) (RRR week)
Wed 12/14	FINAL EXAM (7-10pm) (RSF field house)

Additional resources

MIT's OpenCourseWare project has a nice set of video lectures for MIT's multivariable calculus class, taught by a familiar instructor. The overall course topics are roughly the same, but they are covered in a different order and not quite in the same manner, so don't use this as a replacement for attending lectures!

Also, you can subscribe to ASUC Lecture Notes for this class.

Discussion sections

Section	Time	Room	Instructor	e-mail	Office hours
101	TT 8-9:30am	B51 Hildebrand	Andreas Voellmer	voellmer@math.berkeley.edu	F 10-12 / 1064 Evans
102	TT 8-9:30am	7 Evans	Elan Bechor	ebechor@math.berkeley.edu	M 4-5, W 3-4 / 858 Evans
103	TT 8-9:30am	3 Evans	Jae-young Park	jaypark@berkeley.edu	Tu 9:30-10:30, Th 1-2 / 1041 Evans (web page)
104	TT 12:30-2pm	B51 Hildebrand	Alexandru Chirvasitu	chirvasitua@math.berkeley.edu	Tu 2:30-3:30, Th 2-3 / 1010 Evans (web page)
105	TT 12:30-2pm	85 Evans	Elan Bechor	ebechor@math.berkeley.edu	M 4-5, W 3-4 / 858 Evans
106	TT 11-12:30pm	9 Evans	Andreas Voellmer	voellmer@math.berkeley.edu	F 10-12 / 1064 Evans
107	TT 11-12:30pm	7 Evans	Alex Kruckman	kruckman@math.berkeley.edu	Tu 10-11, Th 2-3 / 787 Evans
108	TT 12:30-2pm	5 Evans	Nam Trang	namtrang@math.berkeley.edu	TuTh 11-12 / 1043 Evans
109	TT 12:30-2pm	41 Evans	Alex Kruckman	kruckman@math.berkeley.edu	Tu 10-11, Th 2-3 / 787 Evans
110	TT 5-6:30pm	246 Dwinelle	Alexandru Chirvasitu	chirvasitua@math.berkeley.edu	Tu 2:30-3:30, Th 2-3 / 1010 Evans (web page)
111	TT 5-6:30pm	55 Evans	Christian Hilaire	hilaire@math.berkeley.edu	MW 5-6 / 840 Evans
112	TT 2-3:30pm	81 Evans	Natth Bejraburnin	natth@math.berkeley.edu	M 11:30-12:30, F 10-11 / 1093 Evans (web page)
113	TT 2-3:30pm	5 Evans	Nam Trang	namtrang@math.berkeley.edu	TuTh 11-12 / 1043 Evans
114	TT 2-3:30pm	3105 Etcheverry	Jae-young Park	jaypark@berkeley.edu	Tu 9:30-10:30, Th 1-2 / 1041 Evans (web page)
115	TT 2-3:30pm	179 Stanley	Kevin Wray	kwray@math.berkeley.edu	M 2:30-3:30, Th 3:30-4:30 / 854 Evans (web page)
116	TT 6-8pm	230D Stephens	Yuhao Huang	huang@math.berkeley.edu	MW 4-6:30 / 1041 Evans (PDP section) (web page)
117	TT 3:30-5pm	39 Evans	Natth Bejraburnin	natth@math.berkeley.edu	M 11:30-12:30, F 10-11 / 1093 Evans (web page)
118	TT 8-9:30am	325 LeConte	Christian Hilaire	hilaire@math.berkeley.edu	MW 5-6 / 840 Evans
119	TT 12:30-2pm	330 Evans	Kevin Wray	kwray@math.berkeley.edu	M 2:30-3:30, Th 3:30-4:30 / 854 Evans (web page)
120	TT 2-3:30pm	332 Evans	Elan Bechor	ebechor@math.berkeley.edu	M 4-5, W 3-4 / 858 Evans