MIT 18.100B Real Analysis, Spring 2025
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What you'll learn
This course includes
- 32.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 25 lessons • 32.5 hours of video
MIT 18.100B Real Analysis, Spring 2025
25 lessons
• 32.5 hours
MIT 18.100B Real Analysis, Spring 2025
25 lessons
• 32.5 hours
- Lecture 1: Introduction to Real Numbers 01:05:56
- Lecture 2: Introduction to Real Numbers (cont.) 01:15:32
- Lecture 3: How to Write a Proof; Archimedean Property 01:19:48
- Lecture 4: Sequences; Convergence 01:18:52
- Lecture 5: Monotone Convergence Theorem 01:18:31
- Lecture 6: Cauchy Convergence Theorem 01:17:08
- Lecture 7: Bolzano–Weierstrass Theorem; Cauchy Sequences; Series 01:23:04
- Lecture 8: Convergence Tests for Series; Power Series 01:21:14
- Lecture 9: Limsup and Liminf; Power Series; Continuous Functions; Exponential Function 01:21:56
- Lecture 10: Continuous Functions; Exponential Function (cont.) 01:22:48
- Lecture 11: Extreme and Intermediate Value Theorem; Metric Spaces 01:21:49
- Review for 18.100B Real Analysis Midterm 01:16:25
- Lecture 12: Convergence in Metric Spaces; Operations on Sets 01:21:27
- Lecture 13: Open and Closed Sets; Coverings; Compactness 01:19:51
- Lecture 14: Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space 01:23:31
- Lecture 15: Derivatives; Laws for Differentiation 01:19:41
- Lecture 16: Rolle’s Theorem; Mean Theorem; L’Hôpital’s Rule; Taylor Expansion 01:18:10
- Lecture 17: Taylor Polynomials; Remainder Term; Riemann Integrals 01:21:48
- Lecture 18: Integrable Functions 01:19:53
- Lecture 19: Fundamental Theorem of Calculus 01:20:28
- Lecture 20: Pointwise Convergence; Uniform Convergence 01:18:11
- Lecture 21: Integrals and Derivatives under Uniform Convergence 01:20:07
- Lecture 22: Differentiating and Integrating Power Series; Ordinary Differential Equations (ODEs) 01:21:03
- Lecture 23: Existence & Uniqueness for ODEs: Picard–Lindelöf Theorem 01:22:00
- Review for the 18.100B Real Analysis Final Exam 01:06:51
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