Penn Math Math 361: Advanced Calculua II Fall 2015

Faculty: Jerry L. Kazdan
Telephone: (215) 898-5109
email: kazdan AT
Office Hours: Wed. 10:30-11:30   (and by appointment) in DRL 4E15
TA: Soumyashant Nayak
Telephone: (215) 898-5975
email: nsoum AT   home page
Office Hours: Wed. 1:00-3:00   (and by appointment) in DRL 3N2B

Text: Recommended -- but not required: Jerrold E. Marsden, Michael J. Hoffman, Elementary Classical Analysis, 2nd edition, W. H. Freeman, 1993
ISBN-13: 9780716721055

Syllabus: We will "roughly" follow the Marsden-Hoffman text and assume you already know the material in Chapters 1-5, although we will review this, particularly Chapter 5.
We will begin with the theory of the derivative and integral of functions of one variable (end of Chapter 5) and continue with the subsequent chapters. However, I strongly recommend that you look at other references (listed below), particularly G. H. Hardy, A Course of Pure Mathematics.

Prerequisites & Review Material

Exams: There will be three in-class exams, from 10:30-11:50
Exam 1: * Thurs. Oct. 1 pdf, condensed, solutions
Exam 2: * Tues, Nov. 10 pdf, condensed, solutions
Exam 3: * Tues. Dec. 8 pdf, condensed, solutions
Final Exam: none
You may always use one 3"x5" card with handwritten notes on both sides.
Exam Scores

Course and Homework Grading

Some References: books, articles, web pages

Note that a Canvas site has been arranged for the course. You may find it useful for communication. Step one is to sign-up.

LaTeX: If you will be writing many documents that contain equations, it is wise to learn (and use) LaTeX. It is available on Windows, Macs, and Linux -- and is free. See TeX Stuff.
For some students, this might be the most useful item you learn in this course.

A Collection of Analysis Problems
Compactness and Uniform Continuity   [ LaTeX Source]
Taylor's Theorem: Integral Remainder   [LaTeX Source]   [large]
Differentiation of a limit
Contracting Maps: Contracting Mappings (K-F),   Existence: u'=Au + f,   The Magic of Iteration,   The Cobweb Model in Economics
Notes on Convolution   [large]
Linear Maps: F
Taylor's Theorem - Integral version   [Large print]
Max-Min Notes
Is there a smooth function f(x,y) on the plane with exactly two critical points, both non-degenerate local min?   Example: 2 Local Min

Homework Assignments:
Remark: The difficulty of an exercise is not at all the same as the amount of work it involves. A long series of straightforward manipulations can have a low level of difficulty, but involve a lot of work. In this course the majority of problems will have short solutions -- although it may take real time to think them through.