Advanced Calculus

(15-Math-6002)

real number field, completeness axiom, limit superior and inferior, subsequences, Bolzano-Weierstrass and Heine-Borel theorems, continuity and differentiability, the Chain Rule, the Intermediate and Mean Value theorems, Taylor series and theorem, Weierstrass M-test, the Riemann integral

Department of

Mathematical

Sciences

This page is a work in progress! (Last revised 7 Jan 2013)

Instructor Prof David A Herron
4514 French Hall West, 556-4075 		My Office Hours
Mon 2:30-3:00, Wed 11:30-12:00, 2:30-3:00,
Th 1:30-2:30, Fri 11:30-12:00, and by appt 		E-mail me at David's e-address
My web page is at David's w-address		 Problem Session
Thur during class time (except exam days)

Basic Course Information

Textbooks There are scores of Advanced Calculus/Introduction to Analysis texts available in the Geo-Math-Physics Library. Below I list just a few of the many many such texts. I will use Wade's book to generate my lectures, and most if not all HW problems will come from Wade. Sometimes it can be a good idea to look at more than one book, because often some author will say things in just the 'right' way. Also, do not overlook the web as a resource.

The last book, by Trench, is free and available here. The book by Rudin is somewhat more sophisticated than the rest, but it's a great reference.

W Wade An Introduction to Analysis
A Apostol Mathematical Analysis
DD Dence & Dence Advanced Calculus: A Transition to Analysis
F Folland Advanced Calculus
Ro Rosenlicht Introduction to Analysis
Ru Rudin Principles of Mathematical Analysis
T Trench Introduction to Real Analysis

General Syllabus Chapters: and 10-14 in Wade's book.

Course Goals First and foremost, this is a course geared towards teaching you to think, act, and problem solve like a mathematician. Of particular importance, to me, is your acquiring the ability to communicate mathematical ideas effectively. This means learning how to read, and especially to write, mathematical proofs. In addition, you should come to understand that different environments lend to different communication requirements.

We shall study elementary analysis. A subgoal, at least for some of you, is preparation for the graduate program Qualifying Exam; I will have (much) more to say about this in the spring (at which time I may run a practice problem session). Here is a list of the Qualifying Exam topics and some practice problems.

Exams and Important Dates

Grades

Your final course grade will be determined from your performance on two in class exams, a comprehensive final exam, your homework scores on written assignments, and your classroom and problem session participation. Here is a precise breakdown:

The Final Exam is scheduled for Tuesday 23 April at 12:00-2:00pm. The in-class hour exams are (tentatively) scheduled for Thursday February 14 and Thursday March 28.

You should be sure to work all of the exercises as well as the problems in the text. I may use some of these on the exams and quizzes.

I will ask you write up and hand in solutions to certain exercises from the textbook (aka, Homework); these will be graded and returned to you. I'll say more about this in class. Please be sure to check out my guidelines for writing up your HW solutions.

Here are some links to some interesting *things* such as videos, power point files, etc. I will add to this list as the year progresses.

Writing Mathematics

Class Stuff

Unless I explicitly indicate otherwise, you should read everything in Wade's book and work all of the exercises that you find as you read. Any of these exercises, as well as all of the "fill in the details" that I mention during lectures, are fair game as "easy" exam questions.