Monday |
Wednesday |
Friday |
| Jan. 27 |
Jan. 29 |
Jan. 31 Lecture #1: Introduction to Math361 Real Numbers |
| Feb. 3 Lecture #2: Compact Sets Continuous Functions Riemann Integration Homework Due: Homework #1: Problems |
Feb. 5 Lecture #3: Showing functions are Integrable |
Feb. 7 Lecture #4: Changing finitely many points Linearity of the Integral Homework Due: Homework #2: Problems |
| Feb. 10 Lecture #5: Cauchy Criterion for Integrals Homework Due: Homework #3: Problems |
Feb. 12 Lecture #6: Thomae Function Squeeze Theorem |
Feb. 14 Quiz #1 Lecture #7: Indicator Functions Step Functions Uniform Continuity Homework Due: Homework #4: Problems |
| Feb. 17 Lecture #8: Continuity and Integrability Monotone functions Homework Due: Homework #5: Problems |
Feb. 19 Lecture #9: Additive Theorem |
Feb. 21 Quiz #2 Lecture #10: Extended Additive Theorem Mean Value Theorem for Derivatives Homework Due: Homework #6: Problems |
| Feb. 24 Lecture #11: Fundamental Theorem of Calculus (First Form) Homework Due: Homework #7: Problems |
Feb. 26 Lecture #12: Fundamental Theorem of Calculus (Second Form) Natural Log |
Feb. 28 Quiz #3 Lecture #13: Darboux Theorem X Homework Due: Homework #8: Problems |
| March 3 Lecture #14: MVT for Integrals Substitution Integration by Parts Homework Due: Homework #9: Problems |
March 5 Lecture #15: Taylor Series Remainder Convergence |
March 7 Quiz #4 Lecture #16: Irrational Exponents Power Rule Homework Due: Homework #10: Problems |
| March 10 Spring Break |
March 12 Spring Break |
March 14 Spring Break |
| March 17 Lecture #17: Taylor series for exp(x) Pointwise vs uniform convergence Homework Due: Homework #11: Problems |
March 19 Lecture #18: Uniform convergence and continuity |
March 21 Quiz #5 Lecture #19: Uniform convergence and integrals Cauchy w.r.t. uniform norm Completeness w.r.t. uniform norm Homework Due: Homework #12: Problems |
| March 24 Lecture #20: Completeness of b(A) Weierstrass function Homework Due: Homework #13: Problems |
March 26 Lecture #21: Uniform Convergence and the derivative |
March 28 Midterm Through Completeness w.r.t uniform norm Study Work on Practice problems |
| March 31 Lecture #22: Complete proof of derivatives Intro to S and C functions Homework Due: Homework #14: Problems |
April 2 Lecture #23: Uniqueness of C and S Properties of C and S |
April 4 Lecture #24: Roots of C and S π! Period of C and S Homework Due: Homework #15: Problems |
| April 7 Lecture #25: Ratio Comparison Test Absolute Convergence Homework Due: Homework #16: Problems |
April 9 Quiz #6 Lecture #26: Ratio Test Power Series |
April 11 Lecture #27: Very interesting result! Fun Day Homework Due: Homework #17: Problems |
| April 14 Lecture #28: Power Series and Uniform Convergence Homework Due: Homework #18: Problems |
April 16 Quiz #7 Lecture #29: Derivatives of Power series |
April 18 Easter Break |
| April 21 Easter Break |
April 23 Lecture #30: Abstraction in Analysis Topological Spaces |
April 25 Lecture #31: Metric Spaces Homework Due: Homework #19: Problems |
| April 28 Lecture #32: Discrete metric spaces Totally Bounded Homework Due: Homework #20: Problems |
April 30 Lecture #33: Normed Vector Spaces |
May 2 Quiz #8 Lecture #34: Inner Product Spaces Homework Due: Homework #21: Problems |
| May 5 Lecture #35: Bounded linear functions Homework Due: Homework #22: Problems |
May 7 Lecture #36: Bounded Linear Operators R^{m x n} |
May 9 Lecture #37: Singular Values When L(X,Y) is Banach X* Homework Due: Homework #23: Problems |
| May 12 Lecture #38: Chain Rule X** Homework Due: Homework #24: Problems |
May 14 Lecture #39: Darboux's theorem √2 Isometric Embedding |
May 16 Lecture #40: e is irrational products are continuous Hahn-Banach Prep for Final Not to be turned it Problems |