Math 53 – Section 1 – Multivariable Calculus – Fall 2017

Denis Auroux – MWF 2-3pm, Room 155 Dwinelle

Instructor: Denis Auroux (

Office: 817 Evans.
Office hours: Mondays and Tuesdays, 10:30-12.

Lectures: Mondays, Wednesdays and Fridays, 2–3pm, 155 Dwinelle
Discussion sections: Mondays, Wednesday and Fridays, at various times. See list.

See below for important course information and policies.


Course information and policies

Section enrollment/changes are performed via CalCentral. Instructors have no control over the enrollment process. Due to serious issues with the new Student Information System's waitlist handling, the math department no longer uses waiting lists for lower-division classes; once the class fills up you will need to keep checking in CalCentral and hope that some space opens up.


The textbook for Math 53 is: Stewart, Multivariable Calculus: Early Transcendentals, UC Berkeley custom edition, 8th edition, Cengage Learning. (ISBN: 978-1-305-75645-8)

This is a custom edition containing chapters 10 and 12-16 of Stewart's "Calculus: Early Transcendentals", 8th edition; the regular edition is also fine. The 7th edition is also acceptable, but you will need to watch for differences in the numbering of assigned homework problems.

Other resources:

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.

Frequently asked questions

Q: I really want to get into the class, but the sections that fit my schedule are full, please help me!

A: Instructors have no control over the enrollment process. I cannot get you into the class magically if it is full. Keep in mind that, even if there is space in the lecture, you cannot enroll in a discussion section that is full. Due to serious issues with the new Student Information System's waitlist handling, the math department no longer uses waiting lists for lower-division classes; once the class fills up you will need to keep checking in CalCentral and hope that some space opens up.
If you really need to take this class, you should look for any remaining spaces at the less popular discussion section times, or look into Math 53 Section 2 with Prof. Frenkel, and/or consider rearranging your schedule of classes as needed. The math department is aware that both sections of Math 53 are full as of mid-July, and is working to add sections. See this page for updates on the department's attempts to keep up with demand. Keep checking CalCentral regularly to see if any space has opened up; there is always a bit of movement at the start of the semester, though I do expect that many discussion sections will remain full. In cases of genuine hardship (rather than personal preference), try to meet with a student services advisor to discuss your scheduling constraints; the math department's advisors are in 964-965 Evans.

Q: Can I attend a different discussion section than the one I'm registered for, which doesn't fit my schedule?

A: Unfortunately not. GSIs for this class already face a very heavy workload, and cannot reasonably be asked to deal with additional students. In addition, many discussion classrooms are not large enough to accommodate extra students.

Q: Can I use an older edition of the textbook?

A: The 7th edition of Stewart is fine; watch for alternative problem numbers in footnotes of homework assignments. The non-"early transcendentals" version should also be okay, you will just need to shift all chapter numbers by one (and adjust page numbers). Older editions of Stewart are not recommended because you'll need to borrow someone else's book to figure out what problems are assigned.

Q: I don't have my final exam schedule yet. How can I tell if there is a conflict?

A: As a general rule, final exams for classes with lectures at different times in the week are scheduled at different times during finals week. See the registrar's website for final exam groups. Final exams for MWF 2-3pm classes are scheduled for Tuesday Dec 12, 11:30-2:30pm. If you don't have a conflict for the lecture then you shouldn't have a conflict for the final. Unfortunately, the math department does not have the resources to provide alternative exam times; if you are worried about multiple back-to-back finals, check your schedule carefully and make the necessary adjustments to your course selections.

Q: What are your policies about assignments, midterms, and grading?

A: See here.

Q: Why is the homework harder than the quizzes and midterms?

A: Quizzes test your ability to quickly apply the concepts seen in class to routine problems. Homework is an occasion to think more deeply about the material, going slightly beyond the content of the lectures and exams. This is key to achieving a greater level of understanding, and to ensuring that you really master the concepts. This difference is also the reason why quizzes take place before the homework due date: by Monday you should have reviewed the week's material, attempted the homework problems, and solved at least the straightforward ones, but the more challenging homework problems may require some clarifications from your GSI in Monday's discussion or in office hours.

Q: Do you have any study tips?

A: First and foremost, stay on top of the material. If you fall behind, it is very hard to catch up in this class. Do the homework in installments, attempting it early on so you can ask questions at the Friday and Monday discussions if needed. Make use of resources available to you: office hours (both mine and your GSI's), study groups, etc. If you need extra help, look into extra resources such as the Student Learning Center. If you work with others, make sure that you arrive at your own understanding and can do the work yourself (you'll be on your own for exams!).

If you are worried about exam stress or time pressure on midterms and final exams, practice under real conditions, with a timer and without study materials, possibly together with a classmate, whenever you get the chance. Try to finish your GSI's weekly quizzes as fast as you can (then use the leftover time to make sure you got it right). Replicating test-taking situations as closely as possible even when you are not taking a test can go a long way towards overcoming testing anxiety.

After quizzes and midterms, review your answers to understand what you missed: not just what the correct solution was, but also how you went wrong, what clues in the statement of the problem or along your path of solution should have alerted you that something was wrong, or, if you were stuck, how you should have gotten started. Ask yourself if there were multiple ways to approach the question -- which ones were correct, which ones weren't, and why. And, once again, if you are confused about something, ask about it in office hours, in discussion, etc.

Q: Are grades curved?

A: Yes and no. Curves are used to compare scores on midterms and on the final, and to adjust for their relative difficulty levels, so that "dropping the lowest midterm" means the midterm on which you performed worst relatively to the class as a whole. Curves are also used to adjust quiz scores so that discussion sections with harder quizzes are not penalized. See detailed policy. On the other hand, overall course grades are not curved on any fixed scale, and the grade cut-offs are not predetermined in any manner. If the class performs strongly as a whole, there will be more A's. However, the grade distribution is usually centered on B-, consistent with other lower-division math classes. Please do not try to second-guess the grading process, instead ask me if you think there may be an error and want a detailed accounting of your grade in the course.


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


There will be two midterms, on Monday 10/2 and Wednesday 11/15 (2-3pm) in the usual lecture room.
The final exam will be on Tuesday December 12, 11:30-2:30pm.

Practice exams and solutions to midterms will be posted here. I recommend that you first review the material carefully, and only attempt the practice midterms, with the indicated time limits, once you feel ready. Attempting a practice midterm under conditions that closely replicate an actual exam (closed book, no documents, with time limit) is a good way to prepare, but only works if you already know the material.


Wed 8/23 Vectors, dot product § 12.1, 12.2, 12.3
Fri 8/25 Dot product continued; determinant § 12.3
Mon 8/28 Determinant and cross product § 12.4
Wed 8/30 Equations of lines and planes § 12.5
Fri 9/1 Parametric equations and vector functions § 10.1, 13.1
Mon 9/4 NO CLASS (Labor Day)
Wed 9/6 Parametric equations: velocity, acceleration § 10.2, 13.2, 13.4
Fri 9/8 Parametric equations: arc length; further examples § 10.2, 13.3
Mon 9/11 Functions of several variables § 14.1
Wed 9/13 Partial derivatives § 14.2, 14.3
Fri 9/15 Tangent plane, linear approximation § 14.4
Mon 9/18 Chain rule § 14.5
Wed 9/20 Gradient, directional derivatives § 14.6
Fri 9/22 Partial differential equations; max-min problems § 14.7
Mon 9/25 Max-min problems continued § 14.7
Wed 9/27 Non-independent variables, Lagrange multipliers § 14.8
Fri 9/29 Review
Mon 10/2 MIDTERM 1
Wed 10/4 Polar coordinates § 10.3, 10.4
Fri 10/6 Double integrals § 15.1, 15.2
Mon 10/9 Double integrals in polar coordinates § 15.3
Wed 10/11 Applications of double integrals § 15.4
Fri 10/13 Change of variables in double integrals § 15.9
Mon 10/16 Triple integrals § 15.6
Wed 10/18 Triple integrals in cylindrical coordinates; applications § 15.7
Fri 10/20 Triple integrals in spherical coordinates § 15.8
Mon 10/23 Vector fields § 16.1
Wed 10/25 Line integrals § 16.2
Fri 10/27 Gradient fields, fundamental theorem for line integrals § 16.3
Mon 10/30 Green's theorem § 16.4
Wed 11/1 Curl and divergence, Green's theorem revisited § 16.5
Fri 11/3 Surface area § 16.6
Mon 11/6 Surface integrals and flux § 16.7
Wed 11/8 The divergence theorem § 16.9
Fri 11/10 NO CLASS (Veterans' Day)
Mon 11/13 Review
Wed 11/15 MIDTERM 2
Fri 11/17 Stokes' theorem § 16.8
Mon 11/20 More on partial differential equations
11/22, 11/24 NO CLASS (Thanksgiving Break)
Mon 11/27 More on divergence and Stokes; applications
Wed 11/29 Final review
Fri 12/1 Final review
Tue 12/12 FINAL EXAM (11:30-2:30)

Discussion sections

SecTimeRoomInstructor E-mailOffice hours
101MWF 8-9am70 Evans Nima Moininima Tu 9-11 / 1010 Evans
102MWF 8-9am105 Latimer Ritwik Ghoshritwikghosh TuTh 9-10 / 866 Evans
103MWF 9-10am70 Evans Nima Moininima Tu 9-11 / 1010 Evans
104MWF 9-10am105 Latimer Ritwik Ghoshritwikghosh TuTh 9-10 / 866 Evans
105MWF 10-11am105 Latimer Kyeonsik Namnamgoood MW 12:30-1:30 / 1020 Evans
106MWF 10-11amB51 Hildebrand Jasper Dengwindowsuser TuTh 11:30-12:30 / 781 Evans
107MWF 11-12pmB51 Hildebrand Jasper Dengwindowsuser TuTh 11:30-12:30 / 781 Evans
108MWF 11-12pmB56 Hildebrand Kyeonsik Namnamgoood MW 12:30-1:30 / 1020 Evans
109MWF 12-1pm105 Latimer Michael Yehyehm TuTh 12-1 / 1064 Evans
110MWF 12-1pm70 Evans Jingyi Wangjingtian MF 3-4 / 866 Evans
111MWF 1-2pm105 Latimer Michael Yehyehm TuTh 12-1 / 1064 Evans
112MWF 1-2pm70 Evans Jingyi Wangjingtian MF 3-4 / 866 Evans
113MWF 3-4pm70 Evans Jeffrey Hicksjeff.hicks Tu 12-1, F 1-2 / 853 Evans
114MWF 3-4pm105 Latimer Justin Breretonjbrere TuTh 2:10-3:15 / 835 Evans
115MWF 4-5pm70 Evans Jeffrey Hicksjeff.hicks Tu 12-1, F 1-2 / 853 Evans
116MWF 5-6pm70 Evans Justin Breretonjbrere TuTh 2:10-3:15 / 835 Evans
117MWF 5-6pm105 Latimer Ahmad Zareeizareei M 6-8pm, Hesse Hall GSI Rm
118MWF 4-5pm4 Evans Ahmad Zareeizareei M 6-8pm, Hesse Hall GSI Rm
All e-mail addresses