A rigorous analysis of functions of one variable. 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 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.
Description
Prerequisites
Topics: Chapters 1-4 and 6-9 from Advanced Calculus, by P.M. Fitzpatrick: