M 408C (Differential and Integral Calculus), Fall 2015

This is the course page for the fall 2015 iteration of M 408C, unique numbers 52655, 52660, 52705, 52710.

Vital information

Andrew Neitzke
Email: neitzke@math.utexas.edu
Office: RLM 9.134
Office hours: T 4:00-5:30
Teaching Assistant
52655, 52660: Yaoguang Zhu, email: yzhu@math.utexas.edu
52705, 52710: Yuri Sulyma, email: ysulyma@math.utexas.edu
52655, 52660: TTh 9:30 am-10:45 am in CLA 0.126
52705, 52710: TTh 11:00 am-12:15 pm in RLM 4.102
Discussion sessions
52655: MW 8:00-9:00 am in CPE 2.212
52660: MW 3:00-4:00 pm in CPE 2.210
52705: MW 8:00-9:00 am in CPE 2.210
52710: MW 1:00-2:00 pm in PHR 2.114
Calculus: Early Transcendentals, 7th Edition by James Stewart.
Homework assignments will be due every Wednesday morning at 3am. The Quest system will be used to assign and submit the homework.
Midterm exams
Sep 29 (in class)
Oct 29 (in class)
Dec 1 (in class)
Final exam
52655, 52660: Dec 12 9:00 am-12:00 noon, in CLA 0.126
52705, 52710: Dec 9 2:00 pm-5:00 pm, in RLM 4.102
Grade weights
Homework (lowest 2 dropped)15%
Midterm exam 120%
Midterm exam 220%
Midterm exam 320%
Final exam25%

Course description

M408C is our standard first-semester calculus course. It is directed at students in the natural sciences and engineering. The emphasis in this course is on problem solving, not the theory of analysis. There should be some understanding of analysis, but the majority of the proofs in the text will not be covered in class.

The syllabus for M408C includes most of the basic topics in the theory of functions of a real variable: algebraic, trigonometric, logarithmic and exponential functions and their limits, continuity, derivatives, maxima and minima, integration, area under a curve, and volumes of revolution.

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.

Schedule & Notes

We will have 28 lectures in total, including 3 taken up by midterm exams. 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.

DateTopicNotes 1Notes 2
Aug. 27 (Th) Generalities on functions; exponentials (1.5) Lecture 01-1 Lecture 01-2
Sep. 1 (T) Inverse functions; logarithms (1.6) Lecture 02-1 Lecture 02-2
Sep. 3 (Th) Tangents and velocities; limits and limit laws (2.1-2.3) Lecture 03-1 Lecture 03-2
Sep. 8 (T) What a limit is precisely, and continuity (2.4,2.5) Lecture 04-1 Lecture 04-2
Sep. 10 (Th) Limits at infinity (2.6) Lecture 05-1 Lecture 05-2
Sep. 15 (T) Derivatives (2.7,2.8) Lecture 06-1 Lecture 06-2
Sep. 17 (Th) Derivatives of polynomials and exponentials, product rule (3.1,3.2) Lecture 07-1 Lecture 07-2
Sep. 22 (T) Quotient rule, derivatives of trig functions (3.2,3.3) Lecture 08-1 Lecture 08-2
Sep. 24 (Th) Chain rule (3.4), implicit differentiation (3.5) Lecture 09-1 Lecture 09-2
Sep. 29 (T) Exam 1
Oct. 1 (Th) Implicit differentiation, derivatives of logs (3.5,3.6) Lecture 10-1
Oct. 6 (T) Exponential growth and decay, related rates (3.9) Lecture 11-1 Lecture 11-2
Oct. 8 (Th) Linear approximations (3.10) Lecture 12-1 Lecture 12-2
Oct. 13 (T) Hyperbolic functions (3.11), maximum and minimum values (4.1) Lecture 13-1 Lecture 13-2
Oct. 15 (Th) Mean value theorem, graphing using derivatives (4.2,4.3) Lecture 14-1 Lecture 14-2
Oct. 20 (T) Indeterminate forms and L'Hospital's rule (4.4) Lecture 15-1 Lecture 15-2
Oct. 22 (Th) Summary of curve sketching, optimization (4.5,4.7)
Oct. 27 (T) Optimization, antiderivatives (4.7,4.9) Lecture 17-1 Lecture 17-2
Oct. 29 (Th) Exam 2
Nov. 3 (T) Areas and distances, the definite integral (5.1,5.2) Lecture 18-1 Lecture 18-2
Nov. 5 (Th) Fundamental theorem of calculus (5.3) Lecture 19-1 Lecture 19-2
Nov. 10 (T) Indefinite integrals and net change theorem (5.4) Lecture 20-1 Lecture 20-2
Nov. 12 (Th) Substitution (5.5) Lecture 21-1 Lecture 21-2
Nov. 17 (T) Areas between curves (6.1) Lecture 22-1 Lecture 22-2
Nov. 19 (Th) Volumes (6.2) Lecture 23-1 Lecture 23-2
Nov. 24 (T) Work, average values (6.4-6.5) Lecture 24-1 Lecture 24-2
Dec. 1 (T) Exam 3
Dec. 3 (Th) Extra stuff Lecture 25-1 Lecture 25-2


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 $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 final exam will be offered only at the time and date 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.

Discussion sessions

The teaching assistants 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 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 will be open M 11-7, Tu-W-Th 2-7, F 2-5 in WEL 2.228, beginning on Monday, August 31. 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.

Another resource which may be of use 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; see www.cmhc.utexas.edu for more information.

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