Mathematics 2411       Honors Calculus III       Course Description

Spring, 2013 (TTh 3:05 in the Clough Undergraduate Learning Commons, room 102, with recitations MW in Skiles 270 )

Instructor: Evans Harrell, Office Skiles 218D, 894 3300, harrell at math.gatech.edu
Instructor's office periods: Monday 11:00-12:00 and Thursday 11:30-12:30 at Skiles 218D. Ordinarily I will also be available for 20 minutes after each class.
Recitation:

### Class web page

The class will be coordinated through T-Square, but you can also consult the Class web page directly. It is your responsibility to consult T-Square or the web page regularly for information about the class, such as homework assignments. You will also be in e-mail contact with the instructor and the teaching assistant, and we will do our best to respond to your questions.

### Required texts and materials

We will use Marsden and Tromba, Vector Calculus, and on-line materials, which may be linked to from the class website or T-Square. You are also required to have a clicker for classroom use.

Description: Calculus is not only essential in engineering; it is one of mankind's greatest intellectual achievements. After thousands of years of confusion on the part of philosophers, Newton, Leibniz, and Euler created effective conceptual tools for understanding the infinite and the infinitesimal. In the third term of calculus we learn about derivatives and integrals in three (or even more) dimensions and their uses.

### Grading and requirements

There will be tests in the recitations on
1. Wednesday, 23 January,
2. Wednesday, 13 February,
3. Wednesday, 13 March,
4. Wednesday, 10 April,

There will also be a final exam, of course. Homework will be collected on Tuesdays, and there will be regular clicker quizzes. Your homework-quiz average will incorporate at least two drops. In addition, Prof. Harrell may announce occasional contests, and the winner of a contest will receive a small number of extra-credit points.

Students' grades will depend on the following quantity:

```    (T1  + T2  + T3  + T4 + HQ  + F  - min(T1..T4,F) )    + E + F/2
```
where the components of this formula correspond to the ingredients mentioned above, after scaling so that all of them except E = extra credit total have a common median of 70. The drop in the formula is the mechanism for coping with personal events such as illness and family emergencies. There will be no opportunities for make-up tests after the fact. In the event of an absence due to travel representing Georgia Tech, such as an intercollegiate sports competition, you must notify the professor at least two weeks in advance to arrange an early test or other alternative. Otherwise, such absences will be treated as personal.

### Calculators and tests

No restrictions will be placed on the use of calculators that do elementary mathematics on the tests. Calculators that can do calculus symbolically shall not be brought to tests. No credit will be given on tests for a correct answer without the intermediate steps.

The schedule of reading will be posted on the 2411 assignments page and on T-Square. The subject matter covered will be roughly the following:
Parametrized paths, velocity and acceleration, curvature and arclength
Continuity, etc. for functions of several variables. Graphs and contour plots
Partial derivatives and the chain rule. Taylor's theorem in several variables
The gradient, tangent planes, best linear approximation and best quadratic approximation
Optimization, types of critical points
Lagrange multipliers, Newton's method in several variables
Double integrals, iterated integrals. Applications: area, center of mass, and volume by Pappus's Theorem
Area integrals in polar coordinates, general coordinates and the Jacobian in the plane
Triple integrals, spherical and cylindrical coordinates
Jacobian in three variables. Improper multiple integrals and applications
Vector fields and line integrals, work and flux
Green's theorem in the plane for both work and flux integrals. Exact vector fields
Parameterized surfaces and surface integrals
Gauss's Theorem and Stokes's Theorem
Applications

### On-line materials

This course will benefit from occasional on-line materials, which may require the software in the student software suite, especially Netscape, Maple, and Acrobat. There is a home page for the class at http://www.math.gatech.edu/~harrell/2411S13/.

Scientists and Engineers today do mathematics differently than in the past. Complicated calculations can be done with software such as Maple, Mathematica, or Matlab, and there are many powerful items on the World Wide Web to help you both to learn mathematics and to do it effectively. We hope that you will use software and the Internet to help with calculations and learning, but always remember that real understanding requires you to exercise your mind as well as your fingers.

### Learning Disabilities

It is the right of any student with a certified learning disability to request necessary accommodation. Such requests must be made well in advance of the time that the accommodation is required and a letter of documentation from the ADAPTS office must be presented at the time of any request.

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