M408K: Differential Calculus (Unique
numbers 59430,
59435, 59440)
Instructor Information:
- Lexing Ying, lexing@math.utexas.edu (preferred),
471-3149, RLM 10.164.
- Lecture hour: TTh 2-3:30pm, WEL 2.246
- Office hour: TTh 5-6:30pm
Teaching Assistant Information:
- Phillip Schmitz, pschmitz@math.utexas.edu,
475-9136, RLM 9.132.
- Discussion time and Location:
- 59430 -> MW 8-9 RLM 5.122
- 59435 -> MW 2-3 RLM 6.114
- 59440 -> MW 4-5 RLM 6.120
- Office hour: W 3-4pm, F 2-5pm
Announcements:
- (Nov 27) Homework 15 is available on the homework website. It will be due at
3am on Dec 4.
- (Nov 20) Homework 14 is available on the homework website. It will be due at
3am on Nov 28.
- (Nov 14) Homework 13 is available on the homework website. It will be due at
3am on Nov 21.
- (Nov 6) Homework 12 is available on the homework website. It will be due at
3am on Nov 14.
- (Oct 30) TA's review session for the second exam
will be held on Thursday Nov 2nd 6-8pm at in ESB 223.
- (Oct 30) Homework 11 is available on the homework website. It will be due at
3am on Nov 7.
- (Oct 24) Homework 10 is available on the homework website. It will be due at
3am on Oct 31.
- (Oct 16) Homework 9 is available on the homework website. It will be due at
3am on Oct 24.
- (Oct 11) Homework 8 is available on the homework website. It will be due at
3am on Oct 17.
- (Oct 3) TA's review session for the first exam
will be held on Thursday 5th October 6-8pm at CPE 2.208.
- (Oct 3) Homework 7 is available on the homework website. It will be due at
3am on Oct 10.
- (Sept 26) Homework 6 is available on the homework website. It will be due at
3am on Oct 3.
- (Sept 18) Homework 5 is available on the homework website. It will be due at
3am on Sept 26.
- (Sept 11) Homework 4 is available on the homework website. It will be due at
3am on Sept 19.
- (Sept 6) Students interested in taking Putnam
exam will meet Tuesdays 4-5pm in RLM 10.176. First meeting will be on
9/12. Students can sign up at one of these sessions or by contacting
Charles Friedman (Office: RLM 11.146, office hour TTH 2:30-3:30) or
Lorenzo Sadun (Office: RLM 9.114.)
- (Sept 6) Study
strategies
workshop offered at UT Learning center. See handout.
- (Sept 5) Schedule added.
- (Sept 5) Homework 3 is available on the homework website. It will be due at
3am on Sept 12.
- (Sept 5) Instructor office hour updated (TTh
5-6:30pm).
- (Sept 5) TA office hour updated (W 3-4pm, F 2-5pm).
- (Aug 29) The first and second homeworks are on
the homework website. The first
homework
(pre-calculus material) is due at 3am on Sept 15 and the second
homework is due at 3am on Sept 5.
- (Aug 29) Appendixes A-D and
Sections 1.1-1.3 are assigned as reading.
Schedule:
- Here is the schedule we will follow in the
course. If possible, please read the relevant sections before the
lecture.
Week starting on
|
T
|
Th
|
8/27
|
|
2.1
|
9/3
|
2.2
|
2.3
|
9/10
|
2.5
|
2.6
|
| 9/17 |
3.1
|
3.2
|
| 9/24 |
3.3
|
3.4
|
10/1
|
3.5, 3.6
|
3.6, 3.7
|
10/8
|
Review, 3.8
|
3.8, 3.9
|
10/15
|
3.10, 4.1
|
4.1, 4.2
|
10/22
|
4.3
|
4.4, 4.5
|
10/29
|
4.5, 4.7
|
4.7, 4.8
|
11/5
|
Review
|
4.10
|
11/12
|
7.1, 7.2
|
7.2, 7.3
|
11/19
|
7.4
|
no class
|
11/26
|
7.5
|
7.7
|
12/3
|
Review
|
Review
|
Notes:
Syllabus:
- Prerequisite and degree relevance:
Either four years of high school mathematics and a
Mathematics Level I or IC Test score of at least 520, or M
305G with a grade of at least C. Note: Students who score
less than 600/580 on the Mathematics Level I or IC Test are
advised to take the M408KLM sequence rather than M408CD. Only one of
the follwing may be counted: M 403K, 408C, 408K. Calculus is offered in
two equivalent sequences: a
two-semester sequence, M 408C/408D, which is recommended
only for students who score at least 600 on the mathematics
Level I or IC Test, and a three-semester sequence, M
408K/408L/408M. For some degrees, the two-semester sequence M 408K/408L
satisfies the calculus requirement . This sequence is also a
valid prerequisite for some upper-division mathematics
courses, including M325K, 427K, 340L, and 362K. M408C and M408D (or the
equivalent sequence M408K, M408L,
M408M) are required for mathematics majors, and mathematics
majors are required to make grades of C or better in these
courses.
- Course description:
M408K is one of two first-year calculus courses. It is
directed at students in the natural and social sciences and
at engineering students. In comparison with M408C, it covers
fewer chapters of the text. However, some material is
covered in greater depth, and extra time is devoted the
development of skills in algebra and problem solving. This
is not a course in the theory of calculus. The syllabus for M408K
covers differential calculus: limits,
continuity, derivatives, maxima and minima, trigonometric,
logarithmic and exponential functions.
- Timing and Optional Sections
A 'typical' semester has 43 MWF days; a day or so will be
lost to course-instructor evaluations, etc. The syllabus
contains material for 40 days; you cannot afford to lose
class periods. Those teaching on TTh should adjust the
syllabus; a MWF lecture lasts 50 min; a TTh therefore 75
min.
- Forty Class Days As:
- Appendixes (assigned as reading and reference)
- A Numbers, Inequalities, and Absolute
Values
- B Coordinate Geometry and Lines
- C Graphs of Second-Degree Equations
- D Trigonometry
- 1 Functions and Models (assigned as reading and
reference)
- 1.1 Four Ways to Represent a Function
- 1.2 Mathematical Models: A Catalog of
Essential Functions
- 1.3 New Functions from Old Functions
- 2 Limits and Rates of Change (seven days)
- 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
- 2.6 Tangents, Velocities, and Other Rates
of Change
- 3 Derivatives (eleven days)
- 3.1 Derivatives
- 3.2 The Derivative as a Function
- 3.2 Differentiation Formulas
- 3.4 Rates of Change in the Natural and
Social Sciences
- 3.5 Derivatives of Trigonometric Functions
- 3.6 The Chain Rule
- 3.7 Implicit Differentiation
- 3.8 Higher Derivatives
- 3.9 Related Rates
- 3.10 Linear Approximations and
Differentials
- 4 Applications of Differentiation (eleven days)
- 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
- 4.8 Applications to Business and Economics
- 4.9 Newton's Method (optional)
- 4.10 Antiderivatives (light)
- 7 Exponential Logarithmic and Inverse
Trigonometric
Functions (eight days)
- 7.1 Inverse Functions
- 7.2 Exponential Functions Their Derivatives
- 7.3 Logarithmic Functions
- 7.4 Derivatives of Logarithmic Functions
- 7.5 Inverse Trigonometric Functions (skip
material with integration)
- 7.7 Indeterminate Forms and L'Hospital's
Rule