M 408M (Multivariable Calculus), Fall 2014

This is the course page for M 408M, unique numbers 55325 and 55330.

Vital information

TTh 11:00-12:30 pm in CPE 2.214
Instructor: Andrew Neitzke
Email: neitzke@math.utexas.edu
AN's Office: RLM 9.134
AN's Office hours: M 11:00-12:00, W 11:00-12:00
Discussion Session
MW 8:00-9:00 am in UTC 1.116
MW 2:00-3:00 pm in CPE 2.220
Teaching Assistant: Dan Kubala
Email: dkubala@math.utexas.edu
DK's Office: RLM 12.146
DK's Office hours: M 3:00-4:30, F 1:00-2:30
Calculus: Early Transcendentals, 7th Edition by James Stewart.
M 408L or M 408S with a grade of at least C-.
Homework assignments will be due on Tuesdays at 3am. The Quest system will be used to assign and submit the homework.
Midterm Exams
Oct. 2 (in class)
Nov. 4 (in class)
Final Exam
Dec. 13 (Saturday), 9am-12pm in CPE 2.214 (same room as lecture)
Grade Weights
Optionally, one midterm exam score may be dropped and replaced with the final exam score.
Homework (lowest 2 dropped)15%
Midterm Exam 125%
Midterm Exam 225%
Final Exam35%

Course Description

M 408M is directed at students in the natural and social sciences and at engineering students. In comparison with M408D, it covers fewer chapters of the text. However, some material is covered in greater depth. This is not a course in the theory of calculus.

The content includes an introduction to the theory and applications of differential and integral calculus of functions of several variables, including parametric equations, polar coordinates, vectors, vector calculus, functions of several variables, partial derivatives, gradients, and multiple integrals.

Schedule & Notes

Here is a tentative schedule, which may be adjusted as the semester goes on. The notes from the lectures will also be posted here, shortly after the lecture.

DateTopicLecture NotesRemarks
Aug. 28 (Th)Parametric curves, tangents (10.1, 10.2) Lecture 01
Sep. 2 (T)Area and arclength (10.2) Lecture 02
Sep. 4 (Th)Polar coordinates, tangents, areas, arclengths (10.3, 10.4) Lecture 03
Sep. 9 (T) Conic sections and their polar forms (10.5,10.6) Lecture 04
Sep. 11 (Th) 3D coordinate systems (12.1) Lecture 05 Sep. 12 is the 12th class day
Sep. 16 (T)Vectors (12.2) Lecture 06
Sep. 18 (Th)Equations of lines, dot products (12.3, 12.5) Lecture 07
Sep. 23 (T)Cross products, equations of planes (12.4, 12.5) Lecture 08
Sep. 25 (Th)Quadric surfaces (12.6) Lecture 09
Sep. 30 (T)Vector functions and space curves (13.1) Lecture 10
Oct. 2 (Th)Exam 1
Oct. 7 (T)Calculus of vector functions, arclength (13.2, 13.3) Lecture 11
Oct. 9 (Th)Velocity and acceleration (13.4) Lecture 12
Oct. 14 (T)Curvature and intrisic properties of curves (13.3) Lecture 13
Oct. 16 (Th)Functions of several variables, limits (14.1, 14.2) Lecture 14
Oct. 21 (T)Limits, partial derivatives (14.3) Lecture 15
Oct. 23 (Th)Tangent planes and linear approximation (14.4) Lecture 16
Oct. 28 (T)The chain rule (14.5) Lecture 17
Oct. 30 (Th)Directional derivatives, gradients (14.6) Lecture 18
Nov. 4 (T)Exam 2 Nov. 4 is the Q-drop deadline
Nov. 6 (Th)Maximum and minimum values (14.7) Lecture 19
Nov. 11 (T)Lagrange multipliers (14.8) Lecture 20
Nov. 13 (Th)Double integrals, iterated integrals (15.1, 15.2) Lecture 21
Nov. 18 (T)Double integrals over general regions (15.3) Lecture 22
Nov. 20 (Th)Double integrals in polar coordinates (15.4) Lecture 23
Nov. 25 (T)Change of variables in double integrals (15.10) Lecture 24
Dec. 2 (T)Change of variables cont'd, Triple integrals (15.10, 15.7) Lecture 25
Dec. 4 (Th)Triple integrals cont'd (15.7) Lecture 26


Weekly homework assignments will be posted on Quest, and you will submit your homework using the same website. The homework contributes 15% to the final grade. The two lowest homework scores are dropped when computing the final grade. No late homework will be accepted, and no make-up homework will be given. Because the two lowest scores are dropped, you can miss one or two assignments without penalty.

Quest cost notice

This course makes use of the web-based Quest content delivery and homework server system maintained by the College of Natural Sciences. This homework service will require a $25 charge per student per class for its use, with no student being charged more than $50 a semester. This goes toward the maintenance and operation of the resource. Please go to http://quest.cns.utexas.edu to log in to the Quest system for this class. After the 12th day of class, when you log into Quest you will be asked to pay via credit card on a secure payment site. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email quest.billing@cns.utexas.edu.


The two midterm exams will be given in class, at the usual time and location. All of the exams are cumulative.

Midterm Exam 1Thursday, October 2
Midterm Exam 2Tuesday, November 4
Final ExamSaturday, December 13, 9am-12pm, CPE 2.214

Exam policies

Unless otherwise specified, no books, notes, or calculators are permitted on the exams.

The final exam will be offered only at the time set by the Registrar. Extraordinary circumstances that cause a student to miss the final exam will be handled in accordance with the policies of the College of Natural Sciences and the University.

Students who require special accommodation for exams (e.g., for reasons of disability) should contact the instructor early in the semester to figure out those accommodations.


You can look at your grades on Quest. Homework contributes 15% to the final grade. The two lowest homework scores are dropped. The basic formula for the exams is that each midterm exam contributes 25%, and the final exam contributes 35%. An important exception is that one midterm score may be dropped and replaced with the final exam score. Thus, if your final score is lower than both of your midterm scores, the formula will be
Midterm Exam 1 = 25%Midterm Exam 2 = 25%Final Exam = 35%
But, if your final exam score is higher than either of your midterm scores, the formula will be
Your higher midterm exam score = 25%Your lower midterm exam score = 0%Final Exam = 60%
Attendance, in and of itself, does not contribute to the final grade.

Discussion Sessions

The teaching assistant will lead discussion sessions on Monday and Wednesday. During these sessions, there will be time to ask questions about the material and homework problems. This will also be a time to practice problem solving by working on problems not in the homework. These problems may be more challenging than the homework problems, and they are intended to stimulate discussion between the students and the TA.

Textbook & Other Resources

The primary textbook is Calculus: Early Transcendentals, 7th Edition by James Stewart. This textbook is of the highest quality, and you should read it. This does not mean that it is "easy" to read. Mathematics books in general are quite demanding on the reader, owing to the intrinsic difficulty of the material, so do not be surprised if you have to go slowly.

There are several sets of freely available online videos covering some of the material in this course. MIT OpenCourseWare has a course known as 18.02. Compared to M 408M, the MIT course moves faster and reaches more advanced material (corresponding to UT's M 427L), but there is a great deal of overlap. There is also a UC Berkeley multivariable calculus course whose syllabus seems to correspond closely to our own. Besides these, there are many other resources online.

There is an undergraduate computer lab in RLM 7.122, and it is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. These computers have most of the mainstream commercial math software: mathematica, maple, matlab, magma, and an asortment of open source programs.

The Math Department Calculus Lab is open M-F 2-7 in PAI 5.42 (except for a few days when the first hour will be down the hall in Painter 5.33). This is a joint TA session for all calculus classes taught at UT, and will be staffed at all times by at least two TAs and 3 undergraduate Learning Assistants. No matter what your question, you can always get help at Calc Lab.

Religious Holidays

In accordance with UT Austin policy, please notify the instructor at least 14 days prior to the date of observance of a religious holiday. If you cannot complete a homework assignment in order to observe a religious holiday, you will be excused from the assignment. If the holiday conflicts with an exam, you will be allowed to write a make-up exam within a reasonable time.

Special Needs

Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice), 232-2937 (video), or http://www.utexas.edu/diversity/ddce/ssd.

Academic Integrity