This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Advanced Calculus I -- Fall 2016

### From Mathematics Is A Science

**MTH 427/527 - 3 - Advanced Calculus I.** The number system, limits, sequences, partial differentiation with applications, maxima and minima of functions of several variables. Theory of definite integrals, multiple integrals, line and surface integrals, improper integrals, infinite series. PR: MTH231 and MTH300. CR: MTH331.

**MTH 428/528 - 3 - Advanced Calculus II.** A rigorous development of algebra and topology of Euclidean spaces, differentiability and integrability of functions of several variables. PR: MTH427. 3 Credit Hours

- Time and Place: TR 2:00-3:15 at 437 Smith Hall
- Instructor: Peter Saveliev (call me Peter)
- Office: Smith Hall 713
- Office Hours: MW 2:30 - 5:00, or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Class Web-Page: math03.com
- Prerequisites: linear algebra (proofs based)
- Text: A First Course in Real Analysis by Protter and Morrey (Chapters 2-5,9)
- Goals: good familiarity with the foundations of Calculus and beginning of mathematical analysis, ability to work in the definition-theorem-proof format.
- Grade Breakdown:
- homework and quizzes: 30%
- midterm: 30%
- final exam: 40%

- Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60

See also Course policy and Student's guide to proof writing.

## 1 Lectures

They will appear here as the course progresses.

HW: Suppose $f,g\in C[0,1]$. Prove that the following is a compact set: $$A=\{tf+(1-t)g:0\le t\le 1\}.$$

## 2 Exams

- Advanced Calculus I -- Fall 2016 -- midterm: Tuesday October 25
- Advanced Calculus I -- Fall 2016 -- final exam: Thursday, Dec. 15, 12:45-2:45 (same place)
- Advanced Calculus II -- Spring 2017 -- midterm: March
- Advanced Calculus II -- Spring 2017 -- final exam: Thursday, May 4, 12:45-2:45 (same place)

Old exams, part I:

Old exams, part II: