Math 408C, Spring Semester 2011
Differential and Integral Calculus
Unique Numbers 55405, 55410, and 55415.
Instructor: Thomas Chen
Office: RLM 12.138.
Office hours: Thursdays 12:45 - 2:30 PM.
Email: t c A_T m a t h . u t e x a s . e d u
Lectures: TTH 11:00 AM - 12:30 PM.
Location:
CPE 2.214.
Teaching Assistant: Ivy Girao
Office: TBA.
Office hours: Mondays 2 - 3 PM, Wednesdays 1 - 3 PM.
Email: i v y g i r a o A_T y a h o o . c o m . b r
Problem sessions:
COURSE DESCRIPTION AND PREREQUISITES
M408C introduces basic topics in the theory of real-valued functions of a real variable: Limits, continuity, derivatives, maxima and minima, integration, area under a curve, volumes of revolution, trigonometric, logarithmic and exponential functions and techniques of integration. M408C classes meet three hours per week for lectures and two hours per week for problem sessions.
The prerequisite for this course is a score of at least 80 on the Aleks placement exam.
This website will be updated frequently. Please check regularly.
SYLLABUS
Textbook:
Stewart Calculus
6th Edition, John Wiley and Sons.
Ivy Girao has kindly offered to scan and post the class notes on
Blackboard.
Below, the numbering corresponds to chapters in the textbook. This schedule is tentative, and
may change for didactical reasons.
It is your responsibility to keep track of any changes as the semester progresses.
- 1. Functions and Models (Self-reading until January 21)
- 2. Limits and Rates of Change (Three Lectures: January 18, 20, 25)
- 2.1 The Tangent and Velocity Problems
- 2.2 The Limit of a Function
- 2.3 Calculating Limits Using the Limit Laws
- 2.4 The Precise Definition of a Limit
- 2.5 Continuity
- 3. Derivatives (Five Lectures: January 27. February 1, 3, 8, 10)
- 3.1 Derivatives and Rates of Change
- 3.2 The Derivative as a Function
- 3.2 Differentiation Formulas
- 3.4 Derivatives of Trigonometric Functions
- 3.5 The Chain Rule
- 3.6 Implicit Differentiation
- 3.8 Related Rates
- 3.9 Linear Approximations and Differentials
- 4. Applications of Differentiation (Four Lectures: February 15, 17, 22, 24)
- 4.1 Maximum and Minimum Values
- 4.2 The Mean Value Theorem
- 4.3 How Derivatives Affect the Shape of a Graph
- 4.4 Limits at Infinity; Horizontal Asymptotes
- 4.5 Summary of Curve Sketching
- 4.7 Optimization Problems
- 4.9 Antiderivatives
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MIDTERM I on March 1
- 5. Integrals (Four Lectures: March 3, 8, 10, 22)
- 5.1 Areas and Distances
- 5.2 The Definite Integral
- 5.3 The Fundamental Theorem of Calculus
- 5.4 Indefinite Integrals and the Net Change Theorem
- 5.5 The Substitution Rule
- 6. Applications of Integration (Two Lectures: March 24, 29)
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MIDTERM II on April 5
- 7. Inverse Functions: Exp Log and Inverse Trig (Five Lectures: March 31. April 7, 12, 14, 19)
- 7.1 Inverse Functions
- 7.2 Exponential Functions Their Derivatives
- 7.3 Logarithmic Functions
- 7.4 Derivatives of Logarithmic Functions
- 7.5 Exponential Growth and Decay
- 7.6 Inverse Trigonometric Functions
- 8. Techniques of Integration (Five Lectures: April 21, 26, 28. May 3, May 5)
- 8.1 Integration by Parts
- 8.2 Trigonometric Integrals
- 8.3 Trigonometric Substitution
- 8.4 Integration of Rational Functions by Partial Fractions
- 8.5 Strategy for Integration
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FINAL EXAM on May 12
HOMEWORK
There will be weekly homework assignments posted on
Quest.
To solve them, you can print them out and work on them anywhere you like.
To submit, you must enter your answers in Quest.
The usual format will be multiple choice.
Quest will immediately tell you if your answer
is correct or not. You are allowed multiple tries, with a reduction of points after each
unsuccessful attempt.
Please note that on Quest, the unique number # 55405 is
affiliated with this course for all students.
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HW 0 self-reading of Chapter 1 in the book until January 21.
Some problems for this chapter are contained in HW 1.
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HW 1 due on Wednesday, January 26, until 11:59 PM on
Quest.
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HW 2 due on Wednesday, February 2, until 11:59 PM on
Quest.
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HW 3 due on Wednesday, February 9, until 11:59 PM on
Quest.
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HW 4 due on Wednesday, February 16, until 11:59 PM on
Quest.
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HW 5 due on Wednesday, February 23, until 11:59 PM on
Quest.
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HW 6 due on Wednesday, March 9, until 11:59 PM on
Quest.
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HW 7 due on Wednesday, March 23, until 11:59 PM on
Quest.
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HW 8 due on Wednesday, March 30, until 11:59 PM on
Quest.
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HW 9 due on Wednesday, April 13, until 11:59 PM on
Quest.
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HW 10 due on Wednesday, April 20, until 11:59 PM on
Quest.
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HW 11 due on Wednesday, April 27, until 11:59 PM on
Quest.
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HW 12 due on Friday, May 6, until 11:59 PM on
Quest.
There will be absolutely no acceptance of any late submissions.
The deadlines posted on Quest are definite, and sharp to the minute.
Usually, the homework will be due at 11:59 PM (one minute before midnight) on Wednesdays.
EXAMS
There will be 2 Midterm Exams on the following dates, during regular class hours:
MIDTERM I on March 1, 2011.
MIDTERM II on April 5, 2011.
Please save these dates, there will absolutely be no make-up exams !
Should you miss a midterm exam, your grade for the final exam will be used for it. However, this policy does not apply retroactively (the final does not replace a midterm that you did submit).
The final exam is scheduled as follows (location TBA):
FINAL EXAM on Thursday, May 12, 2:00-5:00 pm.
Location:
ART 1.102
It is implicit in your registration for this class that, barring some unforeseen calamity,
you affirm to be present to take the final examination at this time.
GRADING
The class grade will be determined as follows:
Homework: 10 percent
Exam 1: 25 percent
Exam 2: 25 percent
Final: 40 percent
The letter grades are distributed as follows:
92 - 100 points: Grade A
90 - 92 points: Grade A-
88 - 89 points: Grade B+
80 - 87 points: Grade B
78 - 79 points: Grade B-
76 - 77 points: Grade C+
68 - 75 points: Grade C
66 - 67 points: Grade C-
64 - 65 points: Grade D+
56 - 63 points: Grade D
51 - 55 points: Grade D
0 - 50 points: Grade F
TUTORING
The UT Learning Center offers tutoring services to calculus students. Some resources are posted online on their
webpage.
UTLC also offers Drop-In Tutoring, a free, walk-in study environment supported by mathematics tutors.
Additionally, they offer appointment tutoring, consisting of one hour, individualizing tutoring sessions for a fee.
For detailed information, please see
here.
COMMENTS AND OPINIONS
In addition to the course evaluation at the end of the semester, you will be able to anonymously share your thoughts and constructive criticism
with your course instructor and TA via
You will be notified by email several times during
the semester about online course surveys made ready for you,
which you may fill out in a given time window.
The University of Texas at Austin provides upon request appropriate academic accommodations
for qualified students with disabilities.
For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.