Tuesday |
Thursday |
| Jan. 27 Lecture #1: Introduction to RAII Introduction to the integral Compact Sets |
Jan. 29 Lecture #2: Definition of the Integral Homework Due: Homework #1: C Problems |
| Feb. 3 Lecture #3: Linearity of the Integral Thomae's function Cauchy Criterion Homework Due: Homework #2: C Problems |
Feb. 5 Quiz 1 Lecture #4: Cauchy Criteria for Integrals Squeeze Theorem Step Functions Homework Due: Homework #3: C Problems |
| Feb. 10 Lecture #5: Continuity Implies Riemann Integrable Additively Theorem Homework Due: Homework #4: C Problems |
Feb. 12 Lecture #6: Fundamental Theorem of Calculus (First Form) Lipschitz Continuity Homework Due: Homework #5: C Problems |
| Feb. 17 Lecture #7: Fundamental Theorem of Calculus (2nd Form) Theorem X Absolute value and Squares Homework Due: Homework #6: C Problems |
Feb. 19 Quiz 2 Lecture #8: Integration by Substitution Integration by Parts Homework Due: Homework #7: C Problems |
| Feb. 24 Lecture #9: Taylor Polynomials Pointwise Convergence Uniform Norm Homework Due: Homework #8: C Problems |
Feb. 26 Quiz 3 Lecture #10: Uniform convergence and Continuity Uniform convergence and Integrals Homework Due: Homework #9: C Problems |
| March 3 Lecture #11: Cauchy Sequences of Functions Uniform Convergence and Derivatives Homework Due: Homework #10: C Problems |
March 5 Quiz 4 Lecture #12: S and C functions Homework Due: Homework #11: C Problems |
| March 10 Lecture #13: Properties of the S and C functions Sin and Cosine Homework Due: Homework #12: C Problems |
March 12 Quiz 5 Lecture #14: More Geometry Derivative of Sine Homework Due: Homework #13: C Problems |
| March 17 Lecture #15: Ratio Comparison Test Absolute Convergence Questions for Exam Homework Due: Homework #14: C Problems (Due Friday, Sorry I forgot to uncomment it) |
March 19 Exam #1 Topics: Through sin and cos |
| March 24 Lecture #16: Power Series Radius of Convergence Power Series and Integrals Homework Due: Homework #15: C Problems |
March 26 Lecture #17: Power Series and Derivatives Length and Distance Homework Due: Homework #16: C Problems |
| March 31 Spring Break |
April 2 Spring Break |
| April 7 Lecture #18: Metric Spaces and Continuity Normed Vector Spaces Examples of Norms Homework Due: Homework #17: C Problems |
April 9 Lecture #19: More Examples of Norms Inner Product Spaces Cauchy-Schwartz Homework Due: Homework #18: C Problems |
| April 14 Quiz 6 Lecture #20: Linear Operators and Continuity Bounded Linear Operators Homework Due: Homework #19: C Problems |
April 16 Lecture #21: R^{m x n} Homework Due: Sorry no Homework |
| April 21 Lecture #22: EigenValues Singular Values X* Homework Due: Homework #20: C Problems |
April 23 Quiz 7 Lecture #23: X** Axiom of Choice and its consiquences Hahn-Banach Theorem Homework Due: Homework #21: C Problems |
| April 28 Lecture #24: e is irrational Proof that X is isometrically embedded in X** Homework Due: Work on your projects |
April 30 Lecture #25: Alternating Series Test Leibniz formula for π Proof of Hahn Bananch (Part I) Homework Due: Homework #22: Moved to Tuesday |
| May 5 Lecture #26: Alternating Series Test (Take II) Theorem X Set of Invertible Matrices is open Proof of Hahn Bananch (Zorn's Lemma) Homework Due: Homework #23: C Problems |
May 7 Lecture #27: Questions for the Final Homework Due: Homework #24: NC Problems |