M 408C (Differential and Integral Calculus), Fall 2018

This is the course page for the fall 2018 iteration of M 408C, unique numbers 53510, 53515.

Vital information

Andrew Neitzke
Email: neitzke@math.utexas.edu
Office: RLM 9.134
Office hours: Monday 2-3pm, Wednesday 3:30-4:30pm
Teaching Assistant
Hannah Turner
Email: hannahturner@math.utexas.edu
Web page: https://sites.google.com/view/hturner/
MWF 10:00 am-10:50 am in ETC 2.108
Discussion sessions
53510: TTh 11:00-12:00 am in CPE 2.216
53515: TTh 4:00-5:00 pm in CPE 2.206
Calculus: Early Transcendentals, 8th Edition by James Stewart
There are two kinds of homework assignments in this course. Regular homework assignments will be due every Tuesday morning at 3am. There are also "learning modules" loosely based on chapters of the text: we will have one of these due at midnight the night before most of our regular in-class meetings. The Quest system will be used to assign and submit the homework.
Midterm exams
Oct. 1 (in class)
Nov. 2 (in class)
Dec. 7 (in class)
Final exam
Dec. 17, 9am-noon, ETC 2.108
Grade weights
Homework (lowest 3 dropped)12%
Learning modules (lowest 5 dropped)3%
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 42 full-class meetings in all, 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 full-class meetings will also be posted here.

Aug. 29 (W) Generalities on functions (1.5) Lecture 01
Aug. 31 (F) Generalities on functions; exponentials (1.5); composition of functions (1.6) Lecture 02
Sep. 5 (W) Inverse functions; logarithms (1.6) Lecture 03
Sep. 7 (F) Tangents and velocities; limits (2.1-2.3) Lecture 04
Sep. 10 (M) Limit laws (2.4) Lecture 05
Sep. 12 (W) Continuity (2.5) Lecture 06
Sep. 14 (F) Limits at infinity (2.6) Lecture 07
Sep. 17 (M) Derivatives (2.7,2.8) Lecture 08
Sep. 19 (W) Derivatives (2.7,2.8) Lecture 09
Sep. 21 (F) Derivatives of polynomials and exponentials (3.1), product rule (3.2) Lecture 10
Sep. 24 (M) Quotient rule (3.2), derivatives of trig functions (3.3) Lecture 11
Sep. 26 (W) Chain rule (3.4) Lecture 12
Sep. 28 (F) Implicit differentiation (3.5) Lecture 13
Oct. 1 (M) Midterm exam 1
Oct. 3 (W) Implicit differentiation, derivatives of logs and inverse trig (3.5,3.6) Lecture 14
Oct. 5 (F) Exponential growth and decay, related rates (3.9) Lecture 15
Oct. 8 (M) Related rates, linear approximation (3.9-3.10) Lecture 16
Oct. 10 (W) More linear approximation (3.10) Lecture 17
Oct. 12 (F) Compound interest (3.9), hyperbolic functions (3.11) Lecture 18
Oct. 15 (M) Maximum and minimum values (4.1) Lecture 19
Oct. 17 (W) Graphing using derivatives (4.2,4.3) Lecture 20
Oct. 19 (F) Mean value theorem and more graphing with derivatives (4.2,4.3) Lecture 21
Oct. 22 (M) Graphing with derivatives, indeterminate forms and L'Hospital's rule (4.3,4.4)
Oct. 24 (W) Indeterminate forms and L'Hospital's rule (4.3,4.4) Lecture 23
Oct. 26 (F) Curve sketching summary (4.5), optimization (4.7) Lecture 24
Oct. 29 (M) Optimization (4.7), Newton's method (4.8) Lecture 25
Oct. 31 (W) Newton's method (4.8), Antiderivatives (4.9), review on related rates Lecture 26 last class before drop deadline
Nov. 2 (F) Midterm exam 2
Nov. 5 (M) Antiderivatives, area under curves (4.9, 5.1) Lecture 27
Nov. 7 (W) Area under curves, definite integrals (5.1, 5.2) Lecture 28
Nov. 9 (F) Definite integrals (5.2) Lecture 29
Nov. 12 (M) Fundamental theorem of calculus (5.3) Lecture 30
Nov. 14 (W) Indefinite integrals, net change (5.4) Lecture 31
Nov. 16 (F) Net change (5.4), substitution (5.5) Lecture 32
Nov. 19 (M) Substitution (5.5) Lecture 33
Nov. 26 (M) Area between curves (6.1) Lecture 34
Nov. 28 (W) Area between curves (6.1), volumes (6.2) Lecture 35
Nov. 30 (F) Volumes (6.2) Lecture 36
Dec. 3 (M) Average values (6.3) Lecture 37
Dec. 5 (W) Work (6.3), midterm review Lecture 38
Dec. 7 (F) Midterm exam 3
Dec. 10 (M)


Weekly homework assignments will be posted on Quest, and you will submit your homework using the same website. The homework contributes 12% to the final grade. The 3 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 3 lowest scores are dropped, you can miss several assignments without penalty.

Learning modules

Learning modules will also be posted and submitted on Quest. The purpose of the learning modules is to give you some exposure to the course material before our class meeting, and to help you identify which points are particularly difficult. The learning modules contribute 3% to the final grade. The 5 lowest learning module scores are dropped when computing the final grade.

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 requires a $30 charge per student per course, 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. For payment questions, email quest.billing@cns.utexas.edu.


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

One of the midterm exam scores may be dropped and replaced with the final exam exam score, assuming that doing so would result in a higher grade. Because of this, you may miss one midterm exam without necessarily incurring any penalty. This policy is intended to cover cases of illness, required attendance of university sanctioned events, and other situations.

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 Tuesday and Thursday. 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, 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.

There is an online version of the textbook available. My understanding is that you can get a semester's worth of access for $30, and there is a 14-day free trial. The interface to the textbook is through Canvas. Here are instructions for access.

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 for: Mondays 2-7pm, Tuesdays 2-7pm, Wednesdays 3-6pm, Thursdays 3-6pm, Fridays 2-5pm, in RLM 8.136. This is a joint TA session for all calculus classes taught at UT. 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