Advanced Calculus II
Revised: November 2006
Course Description
Integration; series of points and functions; topology of the real line. Prerequisite: Math 422. Three semester hours.
Objectives
To continue the objectives of Math 422.
Text
Gordon. Real Analysis, A First Course. Addison-Wesley, 1997.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
-
Chapter 6: Integration (11 days)
The Riemann Integral and the Fundamental Theorem of Calculus -
Chapter 7: Infinite Series (11 days)
Convergence and tests for convergence -
Chapter 8: Sequences and Series of Functions (12 days)
Point-wise and uniform convergence; power series, Taylor series, and other series of functions. -
Chapter 9: Point-Set Topology (11 days)
Open, closed, and compact sets; limit points, Heine-Borel, and continuous functions. - Times include review and testing.