M 408L (Integral Calculus), Fall 2017

This is the course page for my sections of the fall 2017 iteration of M 408L, unique numbers 53880, 53885, 53892, 53894.

A nicer syllabus page, created by course coordinator Pedro Morales, is available, customized by section: 53880, 53885, 53892, 53894.

Vital information

Andrew Neitzke
Office: RLM 9.134
Office hours: M 2:00-3:00, Th 5:00-6:00
Teaching Assistant
53880, 53885: Thomas Gannon, email: gannonth@math.utexas.edu
53892, 53894: Arun Debray, email: a.debray@math.utexas.edu
Class meetings
53880, 53885: TTh 2:00 pm-3:15 pm in WRW 102
53892, 53894: TTh 12:30 pm-1:45 pm in PHR 2.110
Discussion sessions
53880: MW 12:00-1:00 pm in CPE 2.212
53885: MW 3:00-4:00 pm in CPE 2.216
53892: MW 1:00-2:00 pm in ETC 2.136
53894: MW 3:00-4:00 pm in RLM 6.104
Calculus: Early Transcendentals, 8th Edition by James Stewart
Pre-class assignments (learning modules) will be due every Saturday, Monday and Wednesday night at midnight. Post-class assignments will be due every Tuesday morning at 3am. All these will be administered using the online Quest system.
Midterm exams
Tuesday Oct 3, 7:00-9:00pm
Tuesday Oct 31, 7:00-9:00pm
Tuesday Dec 5, 7:00-9:00pm
Final exam
The scheduling of the final exam is determined by the Registrar's Office, and will not be known until partway through the semester.
Grade weights
Pre-class homework (lowest 6 dropped)5%
Post-class homework (lowest 3 dropped)5%
Discussion sections3%
Midterm exam 119%
Midterm exam 219%
Midterm exam 319%
Final exam30%

Course description

M408L is an introductory course in integral calculus. It includes most of the basic topics of integration of functions of a single real variable: the fundamental theorem of calculus, applications of integration, techniques of integration, sequences, and infinite series.

The emphasis in this course is on problem solving, not on the presentation of theoretical considerations. While the course includes some discussion of theoretical notions, these are supporting rather than primary.

This course carries the Quantitative Reasoning flag. Quantitative Reasoning courses are designed to equip you with skills that are necessary for understanding the types of quantitative arguments you will regularly encounter in your adult and professional life. You should therefore expect a substantial portion of your grade to come from your use of quantitative skills to analyze real-world problems.

Other sites

Course announcements will be handled through Canvas.

We will use Piazza for class discussions; our class pages are at 53892, 53894 and 53880, 53885. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza.

Schedule & Notes

We will have 28 Tue/Thu class meetings and 27 M/W discussion sessions. Here is a tentative schedule, which may be adjusted as the semester goes on. Some notes from the class meetings may also be posted here, shortly after the meeting.

DateTopicNotes 1Notes 2
Aug. 30 (W) Fundamental Theorem of Calculus (5.3)
Aug. 31 (Th) Fundamental Theorem of Calculus (5.3) Lecture 01-1 Lecture 01-2
Sep. 5 (T) Indefinite integrals, net change (5.4) Lecture 02-1 Lecture 02-2
Sep. 6 (W) Substitution (5.5)
Sep. 7 (Th) Substitution (5.5) Lecture 03-1 Lecture 03-2
Sep. 11 (M) Areas between curves (6.1)
Sep. 12 (T) Areas between curves (6.1) Lecture 04-1 Lecture 04-2
Sep. 13 (W) Volumes (6.2)
Sep. 14 (Th) Volumes (6.2) Lecture 05-1 Lecture 05-2
Sep. 18 (M) Integration by parts (7.1)
Sep. 19 (T) Integration by parts (7.1) Lecture 06-1 Lecture 06-2
Sep. 20 (W) Trigonometric integrals (7.2)
Sep. 21 (Th) Trigonometric integrals (7.2) Lecture 07-1 Lecture 07-2
Sep. 25 (M) Trigonometric integrals (7.2)
Sep. 26 (T) Trigonometric integrals (7.2) Lecture 08-1 Lecture 08-2
Sep. 27 (W) Trigonometric substitutions (7.3)
Sep. 28 (Th) Trigonometric substitutions (7.3) Lecture 09-1 Lecture 09-2
Oct. 2 (M) Trigonometric substitutions (7.3)
Oct. 3 (T) Trigonometric substitutions (7.3) Lecture 10-1 Lecture 10-2
Oct. 4 (W) Partial fractions (7.4)
Oct. 5 (Th) Partial fractions (7.4) Lecture 11-1 Lecture 11-2
Oct. 9 (M) Strategy for integration (7.5)
Oct. 10 (T) Strategy for integration (7.5)
Oct. 11 (W) Improper integrals (7.8)
Oct. 12 (Th) Improper integrals (7.8) Lecture 13-1 Lecture 13-2
Oct. 16 (M) Partial derivatives (14.3)
Oct. 17 (T) Partial derivatives (14.3) Lecture 14-2
Oct. 18 (W) Double integrals (15.1)
Oct. 19 (Th) Double integrals (15.1) Lecture 15-1 Lecture 15-2
Oct. 23 (M) Double integrals over general regions (15.1-15.2)
Oct. 24 (T) Double integrals over general regions (15.1-15.2)
Oct. 25 (W) Double integrals over general regions (15.1-15.2) Lecture 17-1 Lecture 17-2
Oct. 26 (Th) Double integrals over general regions (15.1-15.2)
Oct. 30 (M) Sequences (11.1)
Oct. 31 (T) Sequences (11.1) Lecture 18-1 Lecture 18-2
Nov. 1 (W) Series (11.2)
Nov. 2 (Th) Series (11.2) Lecture 19-1 Lecture 19-2
Nov. 6 (M) Integral tests and estimating sums (11.3)
Nov. 7 (T) Integral tests and estimating sums (11.3) Lecture 20-1 Lecture 20-2
Nov. 8 (W) Comparison tests and alternating series (11.4-5)
Nov. 9 (Th) Comparison tests and alternating series (11.4-5)
Nov. 13 (M) Absolute convergence and ratio/root tests (11.6)
Nov. 14 (T) Absolute convergence and ratio/root tests (11.6) Lecture 22-1 Lecture 22-2
Nov. 15 (W) Strategy for testing series (11.7)
Nov. 16 (Th) Strategy for testing series (11.7) Lecture 23-1 Lecture 23-2
Nov. 20 (M) Power series (11.8)
Nov. 21 (T) Power series (11.8) Lecture 24-1 Lecture 24-2
Nov. 27 (M) Power series and functions (11.8-11.9)
Nov. 28 (T) Power series and functions (11.8-11.9) Lecture 25-1 Lecture 25-2
Nov. 29 (W) Functions as power series (11.9)
Nov. 30 (Th) Functions as power series (11.9) Lecture 26-1 Lecture 26-2
Dec. 4 (M) Taylor series (11.10)
Dec. 5 (T) Taylor series (11.10) Lecture 27-1 Lecture 27-2
Dec. 6 (W) Applications of Taylor polynomials (11.11)
Dec. 7 (Th) Applications of Taylor polynomials (11.11)

Post-class homework

Weekly post-class homework assignments will be posted on Quest. The post-class homework contributes 5% to the final grade. The three lowest post-class homework scores will be dropped when computing the final grade. No late homework will be accepted, and no make-up homework will be given. Because the three lowest scores are dropped, you can miss a few 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 $30 charge per student per class for its use, with no student being charged more than $60 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.


No books, notes, or calculators may be used on the midterm or final exams.

The three midterm exams will be held on Tuesday Oct 3, Tuesday Oct 31, and Tuesday Dec 5, all from 7:00-9:00 pm in JES A121A.

The final exam will be offered only at the time and date set by the Registrar. This time and date will be posted here as soon as they are fixed. 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.

Discussion sessions

The teaching assistants will lead discussion sessions on Monday and Wednesday. Each discussion session will begin with a set of discussion problems, which count for course credit (total of 3% of the course grade), administered through Canvas. Please bring a device which is able to access Canvas over campus wi-fi (phone, laptop, tablet etc.) During these sessions, there will also 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.

Learning modules

Your first contact with the new material in this course will come through "learning modules" administered through Quest. The learning modules contain text, videos and a few problems to do. One learning module is due before each in-class meeting, and one during each weekend. The deadline will be set at midnight (so midnight Monday night, Wednesday night, Saturday night). The learning modules make up 5% of the course grade (with your lowest six grades dropped.)


The primary textbook for this course is Calculus: Early Transcendentals, 8th 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.

It is possible to purchase an ebook edition of the part of the text needed for this course, more cheaply than you could buy the whole paper book. Some more details about this are posted in a Canvas announcement. One drawback is that if you choose this method you will not own a book: rather what you will own is the right to use the ebook while you are enrolled at UT.

The differences between the 8th edition and the 7th edition of this book are relatively minor, and I believe you should be able to use the 7th edition if you prefer.

Other resources

There is an undergraduate computer lab in RLM 7.122, and it is open to all students enrolled in math courses. Any student can sign up for an individual account in the computer lab: all you need is your UT EID. These computers have a large assortment of powerful commercial math software: this includes Mathematica, Maple, MATLAB, magma, and an assortment of open source programs.

The Math Department Calculus Lab will be open weekday afternoons in the STEM Learning Center on the ground floor of PCL (Perry-CastaƱeda Library), beginning on Wed Sep 6. This is a joint TA session for all calculus classes taught at UT, staffed by TAs and undergraduate Learning Assistants. No matter what your question, you can get help at Calc Lab.

Another valuable resource is the Counselling and Mental Health Center, which is open from M-F 8-5, in the Student Services Bldg (SSB), 5th Floor, or at 512-471-3515. More information is available at www.cmhc.utexas.edu.

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