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G12MAN - Mathematical Analysis (University of Nottingham). This is a series of video lectures taught by Dr. Joel Feinstein, introducing mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus.
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English [CC]
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Description
It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof. (from unow.nottingham.ac.uk)
Course content
- Workshop 01 – Mathematical Analysis Module: The Nature of the Module Unlimited
- Revision Quiz Unlimited
- Lecture 01 – A Revision of Notation: Sets, Subsets, Intersections and Unions Unlimited
- Lecture 2a – Properties of the Euclidian Norm Unlimited
- Lecture 2b – Open Balls and Closed Balls Unlimited
- Workshop 02 – Why do We Do Proofs? Unlimited
- Lecture 03 – Bounded Sets Unlimited
- Lecture 4a – Examples of Bounded and Unbounded d-cells Unlimited
- Lecture 4b – Bounded and Unbounded d-cells (cont.) Unlimited
- Workshop 03 – Examples Class 1 Unlimited
- Lecture 05 – Interior and Non-interior Points Unlimited
- Lecture 06 – Interior Points/ Non-interior Points Unlimited
- How do We Do Proofs? Part I Unlimited
- Lecture 07 – Topology of d-dimensional Euclidian Space Unlimited
- Lecture 8a – Open Sets and Closed Sets Unlimited
- Lecture 8b – Sequences in d-dimensional Euclidian Space Unlimited
- Lecture 09 – Absorption of Sequences by Sets Unlimited
- Workshop 05 – Examples Class 2 Unlimited
- Lecture 10a – Proof of the Sequence Criterion for Closedness Unlimited
- Lecture 10b – Subsequences and Sequential Compactness Unlimited
- How do We Do Proofs? Part II Unlimited
- Lecture 11 – Subsequences of Sequences Unlimited
- Lecture 12a – Proof of Bolzano-Weierstrass Theorem Unlimited
- Lecture 12b – Functions, Limits and Continuity Unlimited
- Lecture 13a – Functions, Limits and Continuity (cont.) Unlimited
- Lecture 13b – Continuous Functions Unlimited
- Lecture 14a – Sequence Definition of Continuity Unlimited
- Lecture 14b – Further Theory of Function Limits and Continuity Unlimited
- Workshop 08 – Examples Class 4 Unlimited
- Lecture 15 – Sandwich Theorem for Real-valued Function Limits Unlimited
- Lecture 16 – Application of the Sandwich Theorem Unlimited
- Lecture 17a – The Boundedness Theorem for Continuous Real-valued Functions Unlimited
- Lecture 17b – Pointwise Convergence: Definition and Examples Unlimited
- Lecture 18 – Sequences of Functions Unlimited
- Lecture 19a – Uniform Convergence Unlimited
- Lecture 19b – Rigorous Differential Calculus Unlimited
- Lecture 20 – Fermat’s Theorem, Rolle’s Theorem and the Mean Value Theorem Unlimited
- Lecture 21 – An Introduction to Riemann Integration Unlimited
Instructor
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