MATH 311 Advanced Calculus - Winter 2018

Instructor: Yevgeniy Kovchegov
e-mail: kovchegy @math.
Office: Kidder 368C
Office Phone No: 7-1379
Office Hours: MW 1:30 pm - 2:30 pm, in MLC

Homework 30%
Short quizzes 10%
Midterm 25%
Final 35%

Place and time: MWF 11:00 am - 11:50 am in BEXL 320, and W 10:00 am - 10:50 am in BEXL 328

Textbook: Patrick M. Fitzpatrick, Advanced Calculus (Second Edition)

Goals and expectations: The goal of the course is to promote understanding, expertise and experience in the area of first term advanced calculus. In particular, the successful student will be able to prove basic results about properties of the real numbers, limits, continuity, and differentiation as presented in the first four chapters of the text.

Prerequisites: MATH 254 or instructor's approval.

Course Material: This is a course in Advanced Calculus. During the term, we will be covering most of the material in chapters 1,2,3,4 and 6. You should not expect to follow everything in lecture as it is being presented. However, after working through your lecture notes and reading the corresponding sections in the text, you should understand the material. If you have any questions about anything that is presented, let me know.

We will follow the text rather closely. The mathematical content is in a careful development of single variable calculus. In an initial study of calculus, the emphasis is on technique. This course is different from most previous mathematics courses. You are going to learn to speak and write mathematical language.

We will spend a lot of time examining how theorems are stated and proved. You will practice constructing examples to help you understand definitions and theorems, and you will get practice in building your own proofs. It is very important for you to keep up with the course work, and the weekly homework assignments are the way in which you can tell how you are doing. Start the problem sets early, and present a well written product to turn in. We expect to have seven or eight homework sets assigned in the course of the quarter: one will be due almost every week.

There are two sections of this course, and they will be coordinated so that we cover pretty much the same material, but you should attend your own class.

Syllabus:  .pdf

Homework: There will be eight homework assignments.

Homework #1 (due Wednesday, January 24):  HW1 (PDF)

Midterm: The midterm exam is scheduled for Wednesday of the 6th week (February 14th). The material covered will include sections 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, and 9.1 in the book.

Final Exam: TBA

Monday, January 8  Overview. Field Axioms. Fields. Real numbers. Mathematics induction. Exercises and examples. Sections: Preliminaries and 1.1
Wednesday, January 10  Field Axioms. Fields. Real numbers. Positivity Axioms. Sections: Appendix A.
Friday, January 12  Positivity Axioms. Completeness Axiom. Supremum and infimum. Sections: Appendix A and 1.1.
Friday, January 19  Completeness Axiom. Archimedean Property. The set of rational numbers is dense in R. Exercises and examples. Sections: 1.2