MATH 408C: Differential and Integral Calculus

Course Unique Numbers: 52395, 52400

General Information

Instructor: David Clark (clark@math.utexas.edu)

Lectures: Monday, Wednesday, Friday 4pm-4:50pm in RLP 0.126

Office hours: Monday 9am-10am, Wednesday 10am-11am, Friday 11am-noon, or by appointment; in room PMA(RLM) 13.164 or by telephone 512-471-6410 (only during office hours).

Teaching Assistant: Teddy Weisman (weisman@math.utexas.edu).

Discussion Sections: Tuesday, Thursday 10:00am-10:50am in BUR 212 (52395). Tuesday, Thursday 12:30pm-1:20pm in CPE 2.220 (52400).

TA Office hours: Tuesday, Thursday 1:45pm-3:15pm, or by appointment; in room PMA(RLM) 9.116

Text: Calculus, Early Transcendentals, 8th Ed., by Stewart, ISBN 9781305394063.

Final exam date: Friday, December 13, 7:00pm-10:00pm, location will be announced later.

Course webpage: http://www.ma.utexas.edu/users/clark/Courses/2019/Fall/408C/.

Course Description

This is the standard first-year calculus course. It is directed at students in engineering and the natural and social sciences. The emphasis in this course is on problem solving, not on the presentation of theory. Topics include trigonometric, logarithmic and exponential functions, limits, continuity, derivatives, maxima and minima, integration, volumes of revolution, techniques of integration.

This course carries the Quantitative Reasoning flag. Quantitative Reasoning courses are designed to equip you with the 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.

This course may be used to fulfill the mathematics component of the university core curriculum and addresses the following three core objectives established by the Texas Higher Education Coordinating Board: communication skills, critical thinking skills, and empirical and quantitative skills.

Prerequisites

The prerequisite is a sufficiently high score on the Aleks placement exam.

Grading for this Course

Homework: There will be homework assigned after each lecture and done online using the Quest system, located at https://quest.cns.utexas.edu/. The homework must be completed online by the date posted, typically about three days after it becomes available. Note that Quest will subtract points for wrong answers, so think carefully before you answer or you could end up with a negative score.

Exams: There will be three midterm exams, to be held during the usual class period, and a comprehensive final exam. The midterms are tentatively scheduled for September 23, October 23, and November 25. The final exam is scheduled for Friday, December 13, 7:00pm-10:00pm, location to be announced later. Please mark on your calendars now the time and date of the exams. Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams.

Grading Scheme: The final grade will be the maximum determined under these two grade weighting schemes:

Activity Scheme 1 Scheme 2

Homework 20%

Midterm Exams 45%

Final Exam 35% 100%

Letter Grades

The grading convention, 90.00-100% A, 86.67-90.00% A-, 83.33-86.67% B+, 80-83.33% B, 76.67%-80.00% B-, 73.33-76.67% C+, 70.00-73.33% C, 66.67%-70.00% C-, 63.33-66.67% D+, 60.00-63.33% D,56.67%-60.00% D-, less than 56.67% F, will be followed. If for some reason there is a deviation from this scale it will be applied uniformly to the whole class. Changes to the scale will only make the scale more generous.

Class Resources

Quest: 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.

CalcLab: The CalcLab is staffed by current mathematics graduate students (including your calculus TA), as well as advanced undergraduate Learning Assistants. It is located in PMA(RLM) 8.136.

CalcLab webpage: http://www.ma.utexas.edu/academics/undergraduate/calclab/.

Sanger Learning Center: The Sanger Learning Center offers drop-in tutoring and limited one-on-one tutoring.

Sanger Learning Center webpage: http://ugs.utexas.edu/slc/.

University Policies

University Code of Conduct: The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Student Honor Code: "As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity."

Academic Integrity: A fundamental principle for any educational institution, academic integrity is highly valued and seriously regarded at The University of Texas at Austin. More specifically, you and other students are expected to maintain absolute integrity and a high standard of individual honor in scholastic work undertaken at the University. This is a very basic expectation that is further reinforced by the University's Honor Code. At a minimum, you should complete any assignments, exams, and other scholastic endeavors with the utmost honesty which requires you to:

acknowledge the contributions of other sources to your scholastic efforts;
complete your assignments independently unless expressly authorized to seek or obtain assistance in preparing them;
follow instructions for assignments and exams, and observe the standards of your academic discipline; and
avoid engaging in any form of academic dishonesty on behalf of yourself or another student.

Students who violate university rules regarding academic integrity are subject to disciplinary penalties, including the possibility of failure in the course and/or dismissal from the university. Policies on scholastic honesty will be strictly enforced. This includes but is not limited to: writing another student’s name on an in-class activity, or otherwise taking or giving credit for work that is not one’s own. This is viewed as a form of cheating by The University of Texas and will be treated as such in this class as well. You are responsible for understanding UT’s Academic Honesty and the University Honor Code which can be found at the following web address: http://deanofstudents.utexas.edu/sjs/acint_student.php

Excused Absences: For an absence to be excused you must provide legitimate documentation prior to or no later than one week after your absence. Excused absences include:

Illness (must have a signed note from your physician on their letterhead; generic “no excuse” form letters from University Health Services will not be accepted)
Critical family events (e.g., weddings or funerals)
Official UT events (e.g., games if you’re an athlete, concerts if you’re a band member)
Religious Holy Days

If you have an excused absence, you will have one week to complete whatever in-class work you missed (quiz, exam, etc.). If your excused absence occurred on a day when a quiz or an exam was given, it is your responsibility to arrange to take a make-up quiz or exam. It is also your responsibility to leave the classroom if the quiz or exam is being discussed before you take the make-up version. Failure to do so will result in forfeiting your opportunity to take the make-up.

Drop dates: September 3 is the last day to drop without approval of the department chair; September 13 is the last day to drop the course for a possible refund; October 31 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class, referred to as Q drop, except for urgent and substantiated, nonacademic reasons. Under Texas law, you are only allowed six Q drops while you are in college at any public Texas institution. For more information, see: http://www.utexas.edu/ugs/csacc/academic/adddrop/qdrop. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, http://registrar.utexas.edu/calendars/18-19/.

University Resources for Students

Your success in the class is important to me. If there are aspects of this course that prevent you from learning or exclude you, pleas let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

Personal or Family Emergencies: If you you experience a personal or family emergency (death in the family, protracted sickness, serious mental health issues) you should contact Student Emergency Services in the Office of the Dean of Students. Student Emergency Services supports students by providing the most comprehensive outreach, assistance, intervention, and referrals. They will also work with you to communicate with me and your other professors and let them know of your situation. http://deanofstudents.utexas.edu/emergency/index.php BeVocal:BeVocal is a university-wide initiative to promote the idea that individual Longhorns have the power to prevent high-risk behavior and harm. At UT Austin all Longhorns have the power to intervene and reduce harm. To learn more about BeVocal and how you can help to build a culture of care on campus, go to http://wellnessnetwork.utexas.edu/BeVocal

Title IX Reporting: Title IX is a federal law that protects against sex and gender-based discrimination, sexual harassment, sexual assault, sexual misconduct, dating/domestic violence and stalking at federally-funded educational institutions. UT Austin is committed to fostering a learning and working environment free from discrimination in all its forms. When sexual misconduct occurs in our community, the university can:

Intervene to prevent harmful behavior from continuing or escalating.
Provide support and remedies to students and employees who have experienced harm or have become involved in a Title IX investigation.
Investigate and discipline violations of the university's relevant policies.

Faculty members and certain staff members are considered "Responsible Employees" or "Mandatory Reporters," which means that they are required to report violations of Title IX to the Title IX Coordinator. I am a Responsible Employee and must report any Title IX related incidents that are disclosed in writing, discussion, or one-on-one. Before talking with me, or with any faculty or staff member about a Title IX related incident, be sure to ask whether they are a responsible employee. If you want to speak with someone for support or remedies without making an official report to the university, email advocate@austin.utexas.edu For more information about reporting options and resources visit http://titleix.utexas.edu or contact the Title IX Office at titleix@austin.utexas.edu.

Services for Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice) or 232-2937 (video phone) or http://ddce.utexas.edu/disability/

Behavior Concerns Advice Line (BCAL): If you are worried about someone who is acting differently, you may use the Behavior Concerns Advice Line to discuss by phone your concerns about another individual’s behavior. This service is provided through a partnership among the Office of the Dean of Students, the Counseling and Mental Health Center (CMHC), the Employee Assistance Program (EAP), and The University of Texas Police Department (UTPD). Call 512-232-5050 or visit http://www.utexas.edu/safety/bcal

Campus Safety and Security: In case of an emergency evacuation, please be aware of the following recommendations the Office of Campus Safety and Security has outlined to keep you and others safe. Additional information may be available at 512-471-5767 or http://www.utexas.edu/safety/.

Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside.
Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building.
Students requiring assistance in evacuation shall inform their instructor in writing during the first week of class.
In the event of an evacuation, follow the instruction of faculty or class instructors.
Do not re-enter a building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office.
Information regarding emergency evacuation routes and emergency procedures can be found at: http://www.utexas.edu/emergency

Counseling and Mental Health Center: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. The Counseling and Mental Health Center (CMHC) provides counseling, psychiatric consultation, and prevention services that facilitate students' academic and life goals and enhance their personal growth and well-being. Counseling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. Tel. 512-471-3515 (appointments), 512-471-CALL (crisis line), or www.cmhc.utexas.edu

Student Rights and Responsibilities

You have a right to a learning environment that supports mental and physical wellness.
You have a right to respect.
You have a right to be assessed and graded fairly.
You have a right to freedom of opinion and expression.
You have a right to privacy and confidentiality.
You have a rihgt to meaningful and equal participation.
You have a right to learn in an environment that is welcoming to all people.

With these rights come responsibilities:

You are responsible for taking care of yourself, managing your time, and communicating with the teaching team and with others if things start to feel out of control or overwhelming.
You are responsible for acting in a way that is worthy of respect and always respectful of others.
Your experience with this course is directly related to the quality of the energy that you bring to it, and your energy shapes the quality of your peers' experiences.
You are responsible for creating an inclusive environment and for speaking up when someone is excluded.
You are responsible for holding yourself accountable to these standards, holding each other to these standards, and holding the teaching team accountable as well.

Personal Names and Pronouns: Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name, unless they have added a "preferred name" with the Gender and Sexuality Center. I will gladly honor your request to address you by a name that is different from what appears on the official roster and by the gender pronoun you use. Please advise me of this early in the semester so that I may make appropriate changes to my records.

Rough Schedule

Date	Section	Learning Objectives
Aug 28	1.4	Interpret a function from an algebraic, numerical, graphical, and verbal perspective and extract information relevant to the phenomena modeled by the function.
Aug 30	1.5	Determine whether functions have inverse functions. If they do, find the inverse function.
Sep 2	Labor Day
Sep 4	2.1, 2.2	Determine whether limits exist. If they do, find the limits. Find one-sided limits.
Sep 6	2.3	Use limit laws to calculate limits. Use the Squeeze Theorem to calculate limits
Sep 9	2.4	Use the ε-δ definition of limit to calculate simple limits^*
Sep 11	2.5	Recognize continuous and discontinuous functions. Calculate limiits of continuous functions using the substitution rule. Use the Intermediate Value Theorem to locate zeros of functions.
Sep 13	2.6	Calculate limits at infinity. Determine horizontal asymptotes of functions.
Sep 16	2.7	Find the slope of the tangent line to a curve. Interpret the derivative as an instatntaneous rate of change.
Sep 18	2.8	Use the limit definition to find the derivative of a function. Understand the ways a function can fail to be differentiable.
Sep 20	Review
Sep 23	Midterm 1
Sep 25	3.1	Find derivatives using the constant rule, the power rule, the constant multiple rule, and the sum and difference rules. Differentiate polynomials and exponential functions.
Sep 27	3.2	Find derivatives using the product rule and the quotient rule.
Sep 30	3.3	Differentiate trigonometric functions.
Oct 2	3.4	Find derivatives using the chain rule.
Oct 4	3.5	Find derivatives of functions defined implicitly.
Oct 7	3.6	Differentiate logarithmic functions. Use logarithmic differentiation to determine the derivative of a function.
Oct 9	3.7	Apply differentiation and rates of change in the natural and social sciences.
Oct 11	3.8	Apply exponential growth and decay models to population growth, radioactive decay, and Newton's law of cooling.
Oct 14	3.9	Use derivatives to solve related rates problems.
Oct 16	3.10	Find a linear approximation to a function at a particular value.
Oct 18	3.11	Differentiate hyperbolic trigonometric functions.^*
Oct 21	Review
Oct 23	Midterm 2
Oct 25	4.1	Use the First Derivative Test to find the relative extrema of a function.
Oct 28	4.2	Apply Rolle's Theorem and the Mean Value Theorem to characterize the roots or the rate of change of a function.
Oct 30	4.3	Find where a function is increasing or decreasing. Find critical points, maxima and minima, and inflection points of functions. Determine the concavity of curves.
Nov 1	4.4	Evaluate indeterminate forms of limits using L'Hôpital's Rule.
Nov 4	4.5	Sketch curves identifying intercepts, horizontal and vertical asymptotes, intervals of increase and decrease, local maxima and minima, points of inflection, and concavity.
Nov 6	4.7	Solve optimization problems.
Nov 8	4.9	Find antiderivatives of functions by reversing the process of finding derivatives.
Nov 11	5.1	Find areas of regions and distances along curves as limits.
Nov 13	5.2	Interpret the definite integral as the limit of a Riemann sum. Calculate definite integras using areas and properties of definite integrals.
Nov 15	5.3	Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
Nov 18	5.4	Evaluate definite integrals using antiderivatives (Net Change Theorem).
Nov 20	5.5	Use the substitution rule to evaluate definite integrals.
Nov 22	Review
Nov 25	Midterm 3
Nov 27	Thanksgiving
Nov 29	Thanksgiving
Dec 2	6.1	Find the area between two curves as a definite integral.
Dec 4	6.2	Use the method of slicing to find the volume of a solid of revolution.
Dec 6	6.3	Use the method of cylindrical shells to find the volume of a solid of revolution.
Dec 9	Review

^*These topics may be covered by homework questions but will not be covered by examinations.

This list of learning objectives is intended as a minimal list to be mastered in order to be reasonable sure of passing the course. It is not guaranteed that particular learning objectives will occur on examinations.

Activity	Scheme 1	Scheme 2
Homework	20%
Midterm Exams	45%
Final Exam	35%	100%