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Created by:
Last updated:
September 21, 2023
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
18.100A Real Analysis (Fall 2020, MIT OCW). Instructor: Dr. Casey Rodriguez. This course covers the fundamentals of mathematical analysis
Convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts through a study of real numbers, and teaches an understanding and construction of proofs. (from ocw.mit.edu)
Course Curriculum
- Lecture 01 – Sets, Set Operations and Mathematical Induction Unlimited
- Lecture 02 – Cantor’s Theory of Cardinality (Size) Unlimited
- Lecture 03 – Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least … Unlimited
- Lecture 04 – The Characterization of the Real Numbers Unlimited
- Lecture 05 – The Archimedean Property, Density of the Rotations, and Absolute Value Unlimited
- Lecture 06 – The Uncountability of the Real Numbers Unlimited
- Lecture 07 – Convergent Sequences of Real Numbers Unlimited
- Lecture 08 – The Squeeze Theorem and Operations Involving Convergent Sequences Unlimited
- Lecture 09 – Limsup, Liminf, and the Bolzano-Weierstrass Theorem Unlimited
- Lecture 10 – The Completeness of the Real Numbers and Basic Properties of Infinite Series Unlimited
- Lecture 11 – Absolute Convergence and the Comparison Test for Series Unlimited
- Lecture 12 – The Ratio, Root, and Alternating Series Tests Unlimited
- Lecture 14 – Limits of Functions in terms of Sequences and Continuity Unlimited
- Lecture 15 – The Continuity of Sine and Cosine and the Many Discontinuities of … Unlimited
- Lecture 16 – The Min/Max Theorem and Bolzano’s Intermediate Value Theorem Unlimited
- Lecture 17 – Uniform Continuity and the Definition of the Derivative Unlimited
- Lecture 18 – Weierstrass’ Example of a Continuous and Nowhere Differentiable Function Unlimited
- Lecture 19 – Differentiation Rules, Rolle’s Theorem, and the Mean Value Theorem Unlimited
- Lecture 20 – Taylor’s Theorem and the Definition of Riemann Sums Unlimited
- Lecture 21 – The Riemann Integral of a Continuous Function Unlimited
- Lecture 22 – Fundamental Theorem of Calculus, Integration by Parts, and … Unlimited
- Lecture 23 – Pointwise and Uniform Convergence of Sequences of Functions Unlimited
- Lecture 24 – Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits Unlimited
- Lecture 25 – Power Series and the Weierstrass Approximation Theorem Unlimited
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