Math 361: Advanced Calculua II |
Fall 2015 |
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Faculty: Jerry L. KazdanTelephone: (215) 898-5109

email:kazdan AT math.upenn.eduOffice Hours: Wed. 10:30-11:30 (and by appointment) in DRL 4E15TA: Soumyashant NayakTelephone: (215) 898-5975

email:home pagensoum AT math.upenn.eduOffice Hours: Wed. 1:00-3:00 (and by appointment) in DRL 3N2B

Text:Recommended -- butnotrequired: Jerrold E. Marsden, Michael J. Hoffman,Elementary Classical Analysis, 2nd edition, W. H. Freeman, 1993

ISBN-13: 9780716721055

errata

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: noneYou may always use one 3"x5" card withhandwrittennotes on both sides.

Exam Scores

Some References:books, articles, web pagesNote that a Canvas site has been arranged for the course. You may find it useful for communication.

Step one is to sign-up.

Notes:

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 isfree. 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 limitContracting 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

Remark: The Homework Assignments:difficultyof an exercise is not at all the same as theamount 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.

- Set 0 [Rust Remover] Due: Never -- but you will be expected to know this material.
- Set 1 Due: Thurs., Sept. 3. Late papers: accepted (without penalty) until 1:00 PM Friday

[LaTeX source]- Set 2 [LaTeX source] Due: Thurs., Sept. 10. Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 3 [LaTeX source] Due: Thurs., Sept. 17. Late papers: accepted (without penalty) until 1:00 PM Friday

[Scan of the Homework Set 3 problems in Marsden-Hoffman]- Set 4 [LaTeX source] Due: Thurs., Sept. 24. Late papers: accepted (without penalty) until 1:00 PM Monday
- Set 5 [LaTeX source] Due: Thurs., Oct. 15 Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 6 [LaTeX source] Due: Thurs., Oct. 22 Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 7 [LaTeX source] Due: Thurs., Oct. 29 Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 8 [LaTeX source] Due: Thurs., Nov. 5 Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 9 [LaTeX source] Due: Thurs., Nov. 19 Late papers: accepted (without penalty) until 1:00 PM Friday
- Set 10 [LaTeX source] Due: Thurs., Dec. 3 Late papers: accepted (without penalty) until 1:00 PM Friday