Penn Math Math 260: Honors Calculus II Spring 2012

Faculty: Jerry L. Kazdan
    Telephone: (215) 898-5109
    email: kazdan AT
    Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15
TA: Jacob Robins
    Telephone: (215) 573-6255
    email: robinsj AT
    Office Hours: TuTh 1:30-3 (and by appointment) in DRL 3C11

This 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).

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 copy only of 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 Calculus 6th Edition (2012), W.H. Freeman


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 linearity plays. The emphesis will be on mathematical and physical insight and ideas, not complicated formulas.

Prerequisites & Review Material: Math 116 or equivalent.

Course and Homework Grading

Some References: books, articles, web pages

Matrices as Maps and Symmetries
Linear maps from R2 to R3 are just linear equations.
Some Maple Examples
inner products & least squares,
Example: Fourier Series, and Fourier Series for f(x)=x
An example: ux + 3uy=0
Area of n-Sphere
Classical Examples of PDE's
Isoperimetric Inequality

Homework Assignments:

Exams: You may always use one 3"×5" card with handwritten notes on both sides