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This course covers the fundamentals of mathematical analysis:
FREE
This course includes
Hours of videos
694 years, 4 months
Units & Quizzes
25
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
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
Course Currilcum
- Sets, set Operations and Mathematical Induction Unlimited
- Cantor’s Theory of Cardinality (size) Unlimited
- Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least Upper Bound Property Unlimited
- The Characterization of the Real Numbers Unlimited
- The Archimedian Propert Density of the Rationals and Absolute value Unlimited
- The Uncountabality of the Real Numbers Unlimited
- Convergent Sequences of Real Numbers Unlimited
- The Sequeeze Theorem and Operations Involving Convergent Sequences Unlimited
- Limsup, Liminf, and the Bolzano-Weierstrass Theorem Unlimited
- The Completness Of the real Numbers and Basic Properties Of Infinite Series Unlimited
- Abolute Convergence and the Comparison Test for Series Unlimited
- The Ratio, Root, and Alternating Series Tests Unlimited
- Limits of Function Unlimited
- Limits Of Functions In terms Of Sequences and Continuity Unlimited
- The Continuity of Sine and and the many Discontinuities of Dirichlet’s Functions Unlimited
- The Min/Max Theorem and Bolzano’s Intermediate Value Theorem Unlimited
- Uniform Continuity and The Definition of The Derivativeva Unlimited
- Weierstrass’s Example of a Continuous and Nowhere Differnetiable Function Unlimited
- Differentiation Rules, Role’s Theorem, and The Mean Value Theorem Unlimited
- Taylor’s Theorem and the Definition of Riemann Sums Unlimited
- The Riemann Integral of a Continuous Function Unlimited
- Fundamental theorem of Calculus, Integration By Parts, and Change of Variable Formula Unlimited
- Pointwise and Uniform Convergence of Sequences of Function Unlimited
- Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits Unlimited
- Power Series and the Weierstrass Approximation Theorem Unlimited
