**Math 254 , Wi 2010**

**Instructor**:
*Rodica D. Costin*

This web page is updated after each lecture. It contains the topics covered and other announcements (written homework due, interesting web resources, bonus problems, exam review guide, etc.).

The general course policy, as seen in the hand-out, is found at General Information (page which will not be changed).

Do take advantage of the **Tutoring offered at MSLC.**

**M Jan. 4** Sec. 14.1.

**W Jan. 6 ** Sec. 14.2

**F Jan. 8 **Sec. 14.3 part 1 (partial derivatives, geometric interpretation, implicit differentiation).

**M**: Sec. 14.3 part 2: derivatives for functions of more variables, higher derivatives, partial differential equations. Besides examples like the ones in the textbook we solved problem 71 and 67.

**W** **Jan. 13**: Sec. 14.4

**F** **Jan. 15 **Sec. 14.5

**W Jan. 20** Sec. 14.5 continued (higher order derivatives with the chain rule, the implicit function theorem)

**F** **Jan. 22** Sec. 14.6

Review problems for Exam 1 Please look over the problems by Monday. The solutions will be discussed in lecture**.**

**M Jan 25** Review

**W** **Jan 27 **First midterm exam

**F Jan 29** Sec. 14.7

**M Feb. 1** Sec. 14.7 continued (absolute extrema) and start Sec.14.8

**W Feb. 3** Sec. 14.8

**F Feb 5** Sec. 15.1.

**M Feb 8 **Sec. 15.2

**W Feb 10 **Sec. 15.3

**F Feb 12 ** Sec. 15.3 problems 9, we discuss symmetry, 25, and started 28

**M Feb 15 **Sec. 15.3 problems 28, 27,45, 15

**W Feb 17 ** Sec. 15.4, and problems 12, 19, 22, Also look over 32 and the examples in the textbook.

Plan:

**F Feb 19 **Sec. 15.5: density and mass, moments, center of mass, improper integrals (definition of the integral on the full plane, the calculation of the integral on the real line of exp(-x^2)). [Please read moments of inertia and probability]. Sec. 15.6

**M Feb 22** Sec. 15.6, 15.7

**W Feb 24 ** Sec. 15.7

**Review problems for Exam 2** Please solve thse problems by Friday. Thes solutions will be discussed in lecture.

**F Feb 26** Review of Sec. 14.7 to 15.7

**Midterm 2 - Monday, March 1 in Pomerene Hall 306 Note the place for the midterm!**

**W March 3** 15.8

F March 5 16.1, 16.2 (up to Example 3)

plan:

M 16.2

W 16.3 only: Theorems 2 and 5, the fact that the integral of a conservative field is independent of path, and its integral over a closed curve is zero,calculation of the potential of a conservative field.

F 16.4

**Final exam information:**

Tu March 16 at 11:30 in **Pomerene Hall 306 **

You are allowed to **bring and use a page (written on both sides) with your own notes.**

**A few review problems** (Note: in problem 1: solve first 1b and then 1a with the solution of 1a being: since F is conservative then the integral is path-independent.)

I am grateful to Siva for supplying corrections to *calculation errors in the solutions* to the review problems (and to Jillian for pointing them out). Here they are: 1c. 1+1+3-0=5 and not 3; 2. sqrt(10) should be sqrt(11). 3. cos(theta) was mis-copied below as cos(phi) so the final answer should be zero (Why does zero make sense?) 6b. df/dy should be replaced by its correct value. 6c. the answer is like in the midterm and midterm review problems. As I said in class, these are my notes containing problems to go over in class, and I was not thorough or careful in writing up the solutions, and they do NOT represent a model of how your solutions should look like when written up

**Research opportunities at OSU: ****MBI Summer Undergraduate Program**

June 21 - July 2, 2010 Location: Mathematical Biosciences Institute, The Ohio State University

This program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (6 weeks to be followed immediately after the 2 weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences. The summer long research experience for undergrads (REU) will begin July 5, and the presentations will be August 13, 2010.

Application: http://www.mbi.osu.edu/forms/applyundergrad.html

More information: http://www.mbi.osu.edu/eduprograms/undergrad2010.html

Flyer: http://www.mbi.osu.edu/eduprograms/flyers/2010undergrad.pdf