#### Description

A rigorous analysis of functions of one variable.

#### Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and minimum grade of C- in MATH310

Level of Rigor

Advanced

Sample Textbooks

Advanced Calculus, by P.M. Fitzpatrick

Working Analysis, by J. Cooper

Applications

Chemistry, computer science, economics, engineering, physics, astronomy, mathematics

If you like this course, you might also consider the following courses

MATH 411, MATH 437, MATH464

Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should strongly consider this course

#### Topics: Chapters 1-4 and 6-9 from Advanced Calculus, by P.M. Fitzpatrick:

1. Axioms and properties of real numbers

2. Convergent and divergent sequences. Closed and compact sets.

3. Continuous and uniformly continuous functions

4. Differentiation

6. Integration (Darboux integral): Two Fundamental Theorems

7. Integration by parts and substitution (Sections 7.2) and Approximation of integrals: Trapezoidal, Simpson's Rules (section 7.4)

8. Approximation by Taylor polynomials (not including 8.7: Weierstrass Approximation Theorem)

9. Sequences and Series of Functions.