MIT 18.100A Real Analysis, Fall 2020
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What you'll learn
This course includes
- 29.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 25 lessons • 29.5 hours of video
MIT 18.100A Real Analysis, Fall 2020
25 lessons
• 29.5 hours
MIT 18.100A Real Analysis, Fall 2020
25 lessons
• 29.5 hours
- Lecture 1: Sets, Set Operations and Mathematical Induction 01:14:22
- Lecture 2: Cantor's Theory of Cardinality (Size) 01:25:07
- Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property 01:18:40
- Lecture 4: The Characterization of the Real Numbers 01:22:04
- Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value 01:18:13
- Lecture 6: The Uncountabality of the Real Numbers 01:21:41
- Lecture 7: Convergent Sequences of Real Numbers 01:00:39
- Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences 01:14:53
- Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem 01:13:43
- Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series 01:15:37
- Lecture 11: Absolute Convergence and the Comparison Test for Series 01:00:03
- Lecture 12: The Ratio, Root, and Alternating Series Tests 01:00:21
- Lecture 13: Limits of Functions 01:12:54
- Lecture 14: Limits of Functions in Terms of Sequences and Continuity 01:01:14
- Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function 01:01:58
- Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem 01:08:24
- Lecture 17: Uniform Continuity and the Definition of the Derivative 01:12:55
- Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function 01:15:36
- Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem 01:14:27
- Lecture 20: Taylor's Theorem and the Definition of Riemann Sums 52:32
- Lecture 21: The Riemann Integral of a Continuous Function 01:06:35
- Lecture 22: Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula 01:12:13
- Lecture 23: Pointwise and Uniform Convergence of Sequences of Functions 01:09:17
- Lecture 24: Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits 01:15:10
- Lecture 25: Power Series and the Weierstrass Approximation Theorem 01:16:07
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