# MATH 408D-AP-Honors: Differential and Integral Calculus II

## Fall 2012 (Sections 55185, 55190, 55185)

### General Information

```      Instructor: Dave Rusin (rusin@math.utexas.edu)
Office hrs: MWF 9-10:30 and by appointment, in RLM 9.140

Teaching asst: Rongting Zhang (rzhang@math.utexas.edu)
Office hrs: MW 3:30-5:00pm in RLM 11.134

Text: Calculus (7th Edition, "Early Transcendentals" version) by
James Stewart. You may also use the all-electronic version of
that same book, or the "special UT edition" at the bookstore.

Lecture: RLM 4.102, MWF 8:00 a.m. -- 9:00 a.m.
Discussions on T & Th: 8:00-9:00am CBA 4.330 (55185), 4:00-5:00pm CHANGEDRLM 5.122 (55190), 5:00-6:00pm CHANGEDRLM 5.120 (55195)
```

Course webpage: http://www.ma.utexas.edu/~rusin/408D-AP/

NEW! I have been given the location of our final exam; it is in ART 1.102.

NEW! There is a write-up available which discusses the (Cauchy) Principal Value for your reading pleasure... And there's another one showing an example of a series which you can prove to be conditionally convergent without using the Alternating Series Test.

NEW! Here's a "cheat sheet" giving a thumbnail description of how to carry out some calculus-like tasks in polar coordinates.

### Description

This course is a continuation of M408C and covers a variety of topics in the theory of functions of one or more variables: indeterminate limits, improper integrals, infinite sequences, power and Taylor series, parametric curves, and derivatives and integrals of vector and multivariable functions with applications. Its objective is to provide students with practical mathematical skills necessary for advanced studies in all areas of science and engineering.

Please note that "mathematical skills" here refers to more than algebraic manipulation (although you will be expected to do that kind of thing quickly and accurately). It is an explicit goal of this course to develop your mathematical intuition: many of the problems you will be asked to solve will require much more thought than symbol-moving. I also take it as an important step in your mathematical training that you learn to communicate mathematics well: what you write must hang together logically, and be presented with enough words to make the presentation comprehensible.

### Pre-requisites

This section of Math 408D is limited to first-year students who have a score of 5 on the Calculus BC Advanced Placement exam, or a similar qualification. Generally speaking, we will cover the same material in this section that the other sections of Math 408D cover, but we will discuss the material more deeply, including some of the underlying theory. Your test questions will reflect this -- your questions will be more probing. I have always found that a more challenging class is more fun and I learned more from such classes; I hope you have the same perspective!

Your semester grade will be based on a number of components. This structure is designed to encourage you to stay actively involved in the course all the way through the semester. Any adjustments to the schedules or policies will be announced multiple times in lecture and on Blackboard and on the course website shown above.

Homeworks: these are done online using the Quest system, located at https://quest.cns.utexas.edu/. This will enable you to get constant feedback on how well you are understanding the material. The homework must be completed online by the date posted, typically about one week after it becomes available. You will accumulate points during the semester, and your "Homework score" will be the number of points earned divided by the possible number of points you could have earned, times 100.

Quizzes: There will be a quiz (almost) every week. As with the homeworks, this will give you a semester "Quiz score" of up to 100 points.

Exams: There will be 3 mid-term exams, to be held during the usual class period. Each is worth 100 points. I expect the dates to be September 21, October 26, and Wednesday, November 21 -- the day before the Thanksgiving holiday. The final exam will be Monday, December 17 2012 from 9am until noon, ART 1.102; it is worth 200 points. Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams.

Your semester grade is based only on the number of points accumulated from this mix of 700 possible points. Your grade will be no lower than what is indicated from this table:
 Point total Semester grade 650-700 A 630-649 A- 610-629 B+ 580-609 B 560-579 B- 540-559 C+ 510-539 C 490-509 C- 470-489 D+ 440-469 D 420-439 D- 0-419 F
I reserve the right to award more generous letter grades but it will be done uniformly: student X cannot have a higher letter grade than student Y unless student X has more points than student Y.

### Policies

Make-ups: it is in general not possible to make up missing quizzes or homework assignments after the due date. If you believe you will have to miss a graded event, please notify me in advance; I will try to arrange for you to complete the work early.

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 Office of the Dean of Students at 471-6259, 471-4641 TTY.

Drop dates: Sept 14 is the last day to drop the course for a possible refund; Nov 6 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. 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/12-13/

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 \$25 charge per student for its use, which 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. You have the option to wait up to 30 days to pay while still continuing to use Quest for your assignments. If you are taking more than one course using Quest, you will not be charged more than \$50/semester. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email quest.billing@cns.utexas.edu.

Bennett exam: The Bennett contest exam is a competition held at The University of Texas Mathematics Department at the end of every regular semester. (This semester that will be Sunday, Dec. 9.) Participation is limited to students who are finishing the Calculus sequence that semester. That includes you! The questions are based on the topics covered in the Calculus courses, but require more than the usual amount of persistence and cleverness. There are cash prizes for the top scorers. Please plan to participate!

### Assistance with course work

In addition to visiting the instructor or the teaching assistant during office hours, you might want to make use the services of the Sanger Learning and Career Center. The Sanger Center offers several forms of tutoring to students throughout the semester (for students in select math courses, including M408D):
• Drop-In Tutoring -- A free, walk-in study environment supported by Sanger's mathematics tutors
• Appointment Tutoring -- Individualized one-hour meetings with one of the mathematics tutors
• Final exam review
This semester, Sanger is also offering a brief Calculus Refresher for M408D on 9/4 – 9/6 (T, W, Th) from 6:00 to 7:30.pm A further description of the Sanger Learning and Career Center services can be found here: http://lifelearning.utexas.edu/ Students can now enroll in refresher classes and register for tutoring support by going directly to the Student Login portion of the Sanger website. Another service, offered free to students with majors in the College of Natural Sciences, is RHSG, the Residential Halls Study Groups. These are tutoring groups that meet weekday evenings at Jester and Kinsolving dorms. I encourage you to participate if you are looking for additional resources to succeed in this course.

### Schedule

This semester we will cover most of chapters 10-15 of the text, following this pattern (subject to minor variation):

• 4.4 Indeterminate Forms and L'Hospital's Rule (Review)
• 7.8 Improper Integrals (one day)
• 11 Infinite Sequences and Series (twelve days)
• 11.1 Sequences
• 11.2 Series
• 11.3 The Integral Test and Estimates of Sums
• 11.4 The Comparison Tests
• 11.5 Alternating Series
• 11.6 Absolute Convergence and the Ratio and Root Tests
• 11.7 Strategy for Testing Series
• 11.8 Power Series
• 11.9 Representations of Functions as Power Series
• 11.10 Taylor and Maclaurin Series
• 11.11 Applications of Taylor Polynomials
• 10 Parametric Equations and Polar Coordinates (four days)
• 10.1 Curves Defined by Parametric Equations
• 10.2 Calculus with Parametric Curves
• 10.3 Polar Coordinates
• 10.4 Areas and Lengths in Polar Coordinates
• 12 Vectors and the Geometry of Space (six days)
• 12.1 Three-Dimensional Coordinate Systems
• 12.2 Vectors
• 12.3 The Dot Product
• 12.4 The Cross Product
• 12.5 Equations of Lines and Planes
• 12.6 Cylinders and Quadric Surfaces
• 13 Vector Functions (two days)
• 13.1 Vector Functions and Space Curves
• 13.2 Derivatives and Integrals of Vector Functions
• 14 Partial Derivatives (seven days)
• 14.1 Functions of Several Variables
• 14.2 Limits and Continuity
• 14.3 Partial Derivatives
• 14.4 Tangent Planes and Linear Approximations
• 14.5 The Chain Rule
• 14.6 Directional Derivatives and the Gradient Vector
• 14.7 Maximum and Minimum Values
• 14.8 Lagrange Multipliers
• 15 Multiple Integrals (seven days)
• 15.1 Double Integrals over Rectangles
• 15.2 Iterated Integrals
• 15.3 Double Integrals over General Regions
• 15.4 Double Integrals in Polar Coordinates
• 15.5 Applications of Double Integrals (optional)
• 15.10 Change of Variables in Multiple Integrals (if time permits)