Math 360: Advanced Calculus (Spring 2009)

(Approximate) Lecture Schedule

Unless otherwise stated, all sections are from Principles of Mathematical Analysis by Rudin
(*ed sections will only be covered if we have time)
Week Tuesday Thursday
Week 1:
January 15, 2009
Ordered Sets
Fields
Week 2:
January 20, 2009
The Real Field
The Extended Real Numbers
Euclidean Spaces
January 22, 2009
The Complex Field
Week 3:
January 27, 2009
Metric Spaces
January 29, 2009
Compact Sets
Connected Sets
Week 4:
February 3, 2009
Convergent Sequences
Subsequences
Cauchy Sequences
February 5, 2009
Upper and Lower Limits
*Some Special Sequences
Week 5:
February 10, 2009
Series
*Series of Nonnegative Terms
*The Number e
February 12, 2009
The Ratio and Root Tests
Power Series
Week 6:
February 17, 2009
*Summation by Parts
Absolute Convergence
February 19, 2009
Addition and Multiplication of Seies
*Rearrangements
Week 7:
February 24, 2009
Limits of Functions
Continuous Functions
February 26, 2009
Continuity and Compactness
Continuity and Connectedness
Week 8:
March 3, 2009
Discontinuities
*Monotonic Functions
March 5, 2009
Infinite Limits and Limits at Infinity
Week 9:
March 17, 2009
The Derivative of a Real Function
March 19, 2009
The Mean Value Theorem
Continuity of Derivatives
Week 10:
March 24, 2009
L'Hospital's Rule
Derivatives of Higher Order
March 26, 2009
Taylor's Theorem
*Differentiation of Vector-valued Functions
Week 11:
March 31, 2009
Definition and Existence of the Integral
April 2, 2009
Properties of the Integral
Week 12:
April 7, 2009
Integration and Differentiation
April 9, 2009
*Integration of Vector-valued Functions
*Rectifiable Curves
Week 13:
April 14, 2009
*Discussion of the Mean Value Theorem
Uniform Convergence
April 16, 2009
Uniform Convergence and Continuity
Uniform Convergence and Integration
Uniform Convergence and Differentiation
Week 13:
April 21, 2009
Equivontinuous Families of Functions
April 23, 2009
The Stone-Weierstrass Theorem
Week 14:
April 28, 2009
Misc

This page was created by Nate Ackerman, and last revised on September 2, 2007.