Differential and Integral Calculus (M408C #55417-55419)
First Day of Class Handout
This class meets on MWF 2-2:50pm in ECJ 1.202.
The discussion section 55417 meets on TTh 8:30-9:20am in RLM 5.118.
The discussion section 55418 meets on TTh 2-2:50pm
in ECJ 1.202.
The discussion section 55419 meets on TTh 4:4:50pm
in ECJ 1.202.
Instructor: Gerard Brunick
Office: RLM 11.166
Email: [email protected]
Office Hours: M 3-4pm, W 4-6pm and by appointment
TA: Zhihui Xie
Office: RLM 11.134
Email: [email protected]
Office Hours: TTh 9:30-11:00 and by appointment
Course Website: http://www.math.utexas.edu/users/gbrunick/teaching.html
All course materials will be posted on this website. Homework assignments, announcements, and grades will be posted using the Quest system.
Text: Calculus, 6th Edition. James Stewart, 2008.
Prerequisites: The minimum required score on the Aleks placement exam. 408C may
not be counted by students with credit for Mathematics 403K, 408K, 408N, or 408L.
M408C and M408D (or the equivalent sequence M408K, M408L, M408M; M408N,
M408S, M408M) are required for mathematics majors, and mathematics majors are
required to make grades of C- or better in these courses.
M408C and M408D (or one of the equivalent sequence M408K, M408L, M408M;
M408N, M408S, M408M) are required for mathematics majors, and mathematics majors are required to make grades of C or better in these courses.
Course Material: This course is the accelerated first-semester calculus course. We will
cover most of the 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.
Grading Scheme: There will be weekly homeworks, three tests, and a final exam. Plus
and minus grades will not be given. A third of your grade will be determined by your
performance on the homework and the remaining two thirds of your grade will be
determined by your performance on the tests.
To determine the homework portion of your grade, the two lowest homework scores will
be removed and the remaining scores will be averaged. To determine the test portion
of your final grade, the scores on the tests and final exam will be averaged with the
final exam counting as two tests.
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Class Schedule:
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Date
Jan. 19
Jan. 21
Jan. 24
Jan. 26
Jan. 28
Jan. 31
Feb. 2
Feb. 4
Feb. 7
Feb. 9
Feb. 11
Feb. 14
Feb. 16
Feb. 18
Feb. 21
Feb. 23
Feb. 25
Feb. 28
Mar. 2
Mar. 4
Mar. 7
Mar. 9
Mar. 11
Mar. 21
Mar. 23
Mar. 25
Mar. 28
Mar. 30
Apr. 1
Apr. 4
Apr. 6
Apr. 8
Apr. 11
Apr. 13
Apr. 15
Apr. 18
Apr. 20
Apr. 22
Apr. 25
Apr. 27
Apr. 29
May 2
May 4
May 6
May 13
Topic
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
3.1 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
3.7 Rates of Change in the Sciences
3.9 Linear Approximations and Differentials
Catch-up and Review
Test 1 Ch. 2-3
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
5.1 Areas and Distances
5.2 The Definite Integral
Spring Break
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
Catch-up and Review
Test 2 Ch. 4-5
6.1 Areas between Curves
6.2 Volumes
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 (optional)
7.6 Inverse Trigonometric Functions
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
More on strategies for integration
Catch-up and Review
Test 3 Ch 6-8
Final exam
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HW1 Posted
HW2 Posted
HW1 Soln Posted
HW3 Posted
HW2 Soln Posted
HW4 Posted
HW3 Soln Posted
HW4 Soln Posted
HW5 Posted
HW6 Posted
HW5 Soln Posted
HW7 Posted
HW6 Soln Posted
HW7 Soln Posted
HW8 Posted
HW9 Posted
HW8 Soln Posted
HW10 Posted
HW9 Posted
HW11 Posted
HW10 Soln Posted
HW12 Posted
HW11 Soln Posted
HW12 Soln Posted
Homework Assignments: Homework will be assigned weekly using the Quest system and
is due the day before the solutions are posted. Late homework will not be accepted
after the solutions have been posted, and this will occur very early on Friday morning.
You are allowed to discuss homework problems with each other; however, you must
submit your own answers online. You will have an opportunity to ask questions about
the homework in the discussion section; however, the amount of time that is available
is limited. I encourage you to work on the assignments before the discussion sections
so that you have a chance to determine which questions you find the most challenging.
Tests and Final: Tests will be given on the dates Mon. Feb. 21st, Wen. Mar. 30th,
and Fri. May 6th. If you must miss a test for a legitimate reason, and you notify
me beforehand, then the missed test will simply be omitted when your test average is
computed. In particular, there will be no make-up tests. The final exam for this class
is on Friday, May 13, 2:00-5:00 pm. If you cannot attend this exam time, then you
should enroll in a different section of this class.
If you take all the tests, and your final grade in the class is at least 95% prior taking
the final, then you will receive an A in the class and you do not have to take the final
exam. Do not make travel plans under the assumption that you will not have to take
the final.
Additional Information: 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, 471-6441 TTY.
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