Tuesday |
Thursday |
| Jan. 29 Lecture #1: Compact Sets Integration Idea Tagged partitions of [a,b] |
Jan. 31 Lecture #2: Definition of the Riemann Integral Examples using definition Homework Due: Homework #1: C Problems |
| Feb. 5 Lecture #3: Linearity of the Integral Thomae's function Cauchy Criterion Homework Due: Homework #2: C Problems |
Feb. 7 Lecture #4: Integrability of Continuous and Monotone functions Homework Due: Homework #3: C Problems |
| Feb. 12 Lecture #5: Additive Theorem Fundamental Theorem of Calculus (First Form) Homework Due: Homework #4: C Problems |
Feb. 14 Lecture #6: Lipschitz Continuity Fundamental Theorem of Calculus (2nd Form) Homework Due: Homework #5: C Problems |
| Feb. 19 Lecture #7: Integration by Substitution Integration by Parts Mean Value Theorem (Integral Form) Taylor's Theorem (Integral Form) Homework Due: Homework #6: C Problems |
Feb. 21 Lecture #8: Taylor expansion of ln Convergence of Functions Uniform Convergence Homework Due: Homework #7: C Problems |
| Feb. 26 Lecture #9: Uniform convergence and Continuity Uniform convergence and Integrals Homework Due: Homework #8: C Problems |
Feb. 28 Lecture #10: Cauchy Sequences of Functions Uniform Convergence and Derivatives Homework Due: Homework #9: C Problems |
| March 5 Quiz 1 Lecture #11: Uniform Convergence and Derivatives Proof S and C functions Homework Due: Homework #10: C Problems |
March 7 Lecture #12: Properties of S and C Homework Due: Homework #11: C Problems |
| March 12 Lecture #13: Pi Periodicity of S function Homework Due: Homework #12: C Problems |
March 14 Midterm |
| March 19 Lecture #14: Geometry and Sin and Cosine Homework Due: Homework #13: C Problems |
March 21 Lecture #15: Derivative of Sin Series Ratio Test Homework Due: Homework #14: C Problems |
| March 26 Spring Break |
March 28 Spring Break |
| April 2 Lecture #16: Root Test Power Series Radius of Convergence Homework Due: Homework #15: C Problems |
April 4 Lecture #17: Uniform convergence and power series Power Series and integrals Homework Due: Homework #16: C Problems |
| April 9 Lecture #18: Power Series and derivatives Length and Distance Homework Due: Homework #17: C Problems |
April 11 Lecture #19: Normed Vector Spaces Examples of Norms Homework Due: Homework #18: C Problems |
| April 16 Quiz 2 Lecture #20: L^p spaces Inner Product spaces Homework Due: Homework #19: C Problems |
April 18 Lecture #21: Completeness Banach and Hilbert Space Homework Due: Homework #20: C Problems |
| April 23 Lecture #22: Bounded Functions to a Banach Space Linear Transformations Homework Due: Homework #21: C Problems |
April 25 Lecture #23: Bounded Linear Functions Homework Due: C Continue to Work on Your Projects! |
| April 30 Quiz 3 Lecture #24: norms on the derivative 2-norm on R^mxn Homework Due: Homework #22: C Problems |
May 2 Lecture #25: e is irrational (Nick) Continuity and Bounded |
| May 7 Lecture #26: Alternating Series Axiom of Choice Homework Due: Homework #23: (If you did not get it last time) C Problems |
May 9 Lecture #27: l^2 spaces Hanh-Banach Homework (Not to be turned in): C Final Review |