Math 362 - Advanced Calculus I

### MATH 362 - Avanced Calculus IISpring 2002

This class is listed as:

• Math 362-001 - Call # 13697 - Advanced Calculus II

Graduate students in Engineer and Statistics can register in:

• Math 551-008 - Call # 20026 - Problems

Textbook: Introduction to analysis by Maxwell Rosenlicht (required).
The way of analysis by Robert S. Strichartz (recommended). There are many other excellent introductory analysis books. Reading from other sources could be very valuable.

Course Structure: There are 3 lectures per week. The course will cover most of the material in Chapters 3 to 10 of our textbook. It is very helpful to read the material before it is discussed in class.

Course content: This course is an introduction to analysis on several variables. Some of the topics to be discussed are listed below: convergence of sequences, compactness, continuity and limits are revisited on metric spaces. Interchange of limit operations: differentiation, integration, series, power series. Fix point theorems, existence and uniqueness theorems for ODEs. Partial derivatives, implicit and inverse function theorems. Multiple integrals, change of variables.
This class is the natural continuation of Math 361. If you did not take Math 361 last Fall (or an equivalent class) you will still be able to follow this class. We will review many of the most basic concepts in the context of metric spaces, so that way we will all be on the same page. Those of you who took Math 361 last Fall will recognize all the results that we proved with lots of hard work for functions of one variable. Hopefully this second time around will give you a better insight on the proofs and will make clear why we chose the proofs we chose at the time, since they will readily generalize to the more general setting. There were some one variable topics we did not have time to cover last semester like Taylor series and integration, we will certainly discuss them in the one variable setting and then extend to more variables.

Homework: Homeworks will be assigned periodically. You are encouraged to discuss the homework with each other, but you should do the writing separately. You learn mathematics by doing, and there is no way around it. It is not enough to see your teacher or your friends solving problems, you have to try it yourself. Difficult as it may seem at the begining, if you persist, you will learn how to write a proper mathematical proof, you will learn how to read and understand other's proofs, and you will learn to appreciate and enjoy the beauty of an elegant argument.

Exams: There will be one midterm exam and a final project

Grades: The final grade will be determined by your performance on homeworks, midterm/s, and final exam. The grading policies will be discussed in class.

Prerequisites: Prerequisite: Math 361/461, and Math 321 or Math 314, or permission from the instructor.

Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.

Last updated: Jan 8, 2002