Math 260: Honors Calculus II |
Spring 2012 |
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Faculty: Jerry L. Kazdan

Telephone: (215) 898-5109

email:kazdan AT math.upenn.edu

Office Hours: Wed. 10:30-11:30 (and also by appointment) in DRL 4E15TA: Jacob Robins

Telephone: (215) 573-6255

email:robinsj AT math.upenn.edu

Office Hours: TuTh 1:30-3 (and by appointment) in DRL 3C11This is an honors version of Math 240. It will cover the material in greater depth than that course, with more challenging problems and more attention to definitions and to the reasons behind the results. The course assumes familiarity with the material in Math 116. The precise sequence of topics within each semester will differ somewhat between the Math 114-240 sequence and the Math 116-260 sequence; but over the course of the two semesters, the honors sequence will cover the usual material and more.

Students who wish to take further mathematics courses beyond Math 116 and 260 will be prepared to take either of two sequences in analysis/advanced calculus (Math 360-361 or Math 508-509), and either of two sequences in abstract and linear algebra (Math 370-371 or Math 502-503).

Text:

Math 21 Lecture Notes (PDF). These are old notes from a course I have taught often. They were recently retyped in a computer format and certainly contain new typos -- which we will correct regularly (please give me your list). Thus I suggest that you make a printed copyonlyof what you really need immediately.

[In case you prefer, here is a .pdf version in smaller type printed two pages on one sheet: Math 21 2-up (PDF).]

Marsden, J, & Tromba, A.,Vector Calculus6^{th}Edition (2012), W.H. Freeman

Content:The heart of this course is to achieve some real understanding of linear maps and calculus of several variables, to see the fundamental role that

- Linear algebra: vectors, inner product, matrices, linear maps, systems of linear equations, eigenvalues and eigenvectors.

- Ordinary differential equations: linear differential equations, systems of differential equations, some nonlinear equations.

- Calculus of scalar and vector fields: functions of several variables, applications of differential calculus, line integrals, multiple integrals, surface integrals with application to the wave, heat and Laplace equations.
linearityplays. The emphesis will be on mathematical and physical insight and ideas, not complicated formulas.

Prerequisites & Review Material:Math 116 or equivalent.

Some References:books, articles, web pages

Notes:

Matrices as Maps and Symmetries

Linear maps from R^{2}to R^{3}are just linear equations.

Some Maple Examples

inner products & least squares,

Example: Fourier Series, and Fourier Series for f(x)=x

An example: u_{x}+ 3u_{y}=0

Intuition

Area of n-Sphere

Classical Examples of PDE's

Isoperimetric Inequality

Homework Assignments:

- Set 0 (This will not be collected.)
- Set 1 Due: Thurs., Jan. 19 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 2 Due: Thurs., Jan. 26 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 3 Due: Thurs., Feb. 2 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 4 Due: Never

[Exam 1 is on Thurs. Feb. 9 in class]- Set 5 Due: Thurs., Feb. 16 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 6 Due: Thurs., Feb. 23 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 7 Due: Thurs., Mar. 1 in class [Late papers will be accepted until 1:00 PM Friday.]
- Set 8 Due: Never See also Help on #7 and 11

[Exam 2 is on Tuesday March 13 in class.]- Set 9 Due: Thurs., Mar. 22 in class [Late papers will be accepted until 1:00 PM Friday.] (solutions)
- Set 10 Due: Thurs., Mar. 29 in class [Late papers will be accepted until 1:00 PM Friday.] (solutions)
- Set 11 Due: Thurs., April 5 in class [Late papers will be accepted until 1:00 PM Friday.] (solutions)
- Set 12 Due: never (solutions).

[Exam 3 is on Thursday April 12 in class.]- Set 13 Due: 1:00 PM Thurs., April 26

Exams:You may always use one 3"×5" card withhandwrittennotes on both sides

- There will be three in-class exams, from 12:00-1:20 on:

Exam. 1, Feb. 9 (solutions)

Exam. 2, March 13 (solutions)

Exam. 3, April 12 (solutions)- Final Exam, May 2, 2012 (solutions)
- List of Exam Scores