You should do a first reading of the correspondig textbook sections and lecture notes before watching each lecture. When you watch a lecture have paper and pen at hand and a printout of the lecture notes. Take notes. Write down any questions you have. Stop the video and think periodically. Then carefully read the textbook - over and over.
Week 1 Lecture 1: Introduction. Algebraic Systems. text video (17 min, 38 sec) [Ignore hwk assignments - they are old. See main page.] Lecture 2: Chapter 1, Section 2, Dedekind Cuts. text video (42 min, 48 sec) Lecture 3: Chapter 1, Section 2, Dedekind Cuts. '' video (42 min, 2 sec) Week 2 Lecture 4: Chapter 2, Section 1, Metric Spaces. text video (17 min, 24 sec) Lecture 5: Chapter 2, Section 2, Continuity. text video (11 min, 9 sec) Lecture 6: Chapter 2, Section 3, Topology. text video (18 min, 16 sec) Week 3 Lecture 7: Chapter 2, Section 3, More Continuity. text video ( 7 min, 38 sec) Lecture 8: Chapter 2, Section 3, Closure, etc. text video (10 min, 18 sec) Lecture 9: Chapter 2, Section 3, Subspaces. text video ( 9 min, 10 sec) Week 4 Lecture 10: Chapter 2, Section 3, Prod's & complete text video ( 9 min, 55 sec) Lecture 11: Supplement, The Open Subsets of R. text video (16 min, 42 sec) Lecture 12: Chapter 2, Section 4: Compactness. text video (24 min, 45 sec) Correction!!! Lecture 13: Chapter 2, Section 4: Compactness. '' video (17 min, 7 sec) Week 5 Lecture 14: Chapter 2, Section 5: Connectedness. text video (36 min, 35 sec) Lecture 15: Chapter 2, Section 6: Other stuff. text video (16 min, 39 sec) Lecture 16: Chapter 2, Section 6: Other stuff. '' video ( 1 min, 17 sec) Lecture 17: Chapter 2, Section 7: Coverings. text video (29 min, 7 sec) Week 6 Lecture 18: Chapter 2, Section 8: Cantor Sets. text video (41 min, 6 sec) Lecture 19: Chapter 2, Section 9: Cantor Sets. '' video (10 min, 15 sec) Lecture 20: Supplement, Fractals. text video (10 min, 26 sec) Week 7 Lecture 21: Chapter 2, Section 10a: Completion. text video (19 min, 40 sec) Lecture 22: Chapter 2, Section 10b: Q --> R. text video (16 min, 46 sec) Lecture 23: Chapter 3, Section 1: Differentiation. text video (15 min, 48 sec) Week 8 Midterm: Three hours. Date and time to be scheduled. Lecture 24: Chapter 3, Section 1: Differentiation. '' video (18 min, 40 sec) Lecture 25: Supplement, e is irrational. text video ( 5 min, 45 sec) Lecture 26: Chapter 3, Section 2: Riemann Integration. text video (25 min, 37 sec) Week 9 Lecture 27: Chapter 3, Section 2: Riemann Integration. '' video (18 min, 28 sec) Lecture 28: Chapter 3, Section 2: Riemann Integration. '' video (19 min, 29 sec) Lecture 29: Chapter 3, Section 2: Riemann Integration. '' video (22 min, 24 sec) Lecture 30: Chapter 3, Section 2: Riemann Integration. '' video ( 3 min, 41 sec) Week 10 Lecture 31: Supplement, Riemann-Stieltjes integration. text video (10 min, 42 sec) Lecture 32: Chapter 3, Section 3: Series. text video (11 min, 44 sec) Lecture 33: Chapter 3, Section 3: Series. '' video (12 min, 42 sec) Week 11 Lecture 34: Chapter 4, Section 1: Uniform Convergence. text video (14 min, 37 sec) Lecture 35: Chapter 4, Section 1: Uniform Convergence. '' video (14 min, 20 sec) Lecture 36: Chapter 4, Section 2: Power Series. text video ( 3 min, 29 sec) Week 12 Lecture 37: Chapter 4, Section 3: Equicontinuity. text video (15 min, 22 sec) Lecture 38: Chapter 4, Section 3: Equicontinuity. '' video ( 9 min, 49 sec) Pop Quiz Lecture 39: Chapter 4, Section 4: Uniform Approximation. text video (26 min, 18 sec) Lecture 40: Chapter 4, Section 4: Uniform Approximation. '' video (28 min, 49 sec) Week 13 Lecture 41: Chapter 4, Section 5: Contractions & ODEs. text video (26 min, 53 sec) Added note Lecture 42: Chapter 4, Section 6: Analytic Functions. text video (28 min, 4 sec) Lecture 43: Chapter 4, Section 6: Analytic Functions. '' video ( 7 min, 30 sec) Lecture 44: Chapter 4, Section 6: Analytic Functions. '' video (10 min, 10 sec) Week 14 Lecture 45: Chapter 4, Section 7: Continuous nowhere text video (12 min, 15 sec) Lecture 46: Chapter 4, Section 7: diff'able functions '' video (10 min, 11 sec) Lecture 47: Chapter 4, Section 7: are everywhere! '' video (16 min, 32 sec) Week 15 Lecture 48: Intro to Lebesgue Integration text video ( min, sec) Lecture 49: Intro to Ergodic Theory text video ( min, sec) Week 16 Final Exam: Three hours. Date and time to be scheduled.