G12MAN - Mathematical Analysis

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. 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

Lecture 10a - Proof of the Sequence Criterion for Closedness

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Workshop 01 - Mathematical Analysis Module: The Nature of the Module
Revision Quiz
Lecture 01 - A Revision of Notation: Sets, Subsets, Intersections and Unions
Lecture 2a - Properties of the Euclidian Norm
Lecture 2b - Open Balls and Closed Balls
Workshop 02 - Why do We Do Proofs?
Lecture 03 - Bounded Sets
Lecture 4a - Examples of Bounded and Unbounded d-cells
Lecture 4b - Bounded and Unbounded d-cells (cont.)
Workshop 03 - Examples Class 1
Lecture 05 - Interior and Non-interior Points
Lecture 06 - Interior Points/ Non-interior Points
How do We Do Proofs? Part I
Lecture 07 - Topology of d-dimensional Euclidian Space
Lecture 8a - Open Sets and Closed Sets
Lecture 8b - Sequences in d-dimensional Euclidian Space
Lecture 09 - Absorption of Sequences by Sets
Workshop 05 - Examples Class 2
Lecture 10a - Proof of the Sequence Criterion for Closedness
Lecture 10b - Subsequences and Sequential Compactness
How do We Do Proofs? Part II
Lecture 11 - Subsequences of Sequences: Bolzano-Weierstrass and Heine-Borel Theorems
Lecture 12a - Proof of Bolzano-Weierstrass Theorem
Lecture 12b - Functions, Limits and Continuity
Lecture 13a - Functions, Limits and Continuity (cont.)
Lecture 13b - Continuous Functions
Lecture 14a - Sequence Definition of Continuity
Lecture 14b - Further Theory of Function Limits and Continuity
Workshop 08 - Examples Class 4
Lecture 15 - Sandwich Theorem for Real-valued Function Limits
Lecture 16 - Application of the Sandwich Theorem
Lecture 17a - The Boundedness Theorem for Continuous Real-valued Functions
Lecture 17b - Pointwise Convergence: Definition and Examples
Lecture 18 - Sequences of Functions
Lecture 19a - Uniform Convergence
Lecture 19b - Rigorous Differential Calculus
Lecture 20 - Fermat's Theorem, Rolle's Theorem and the Mean Value Theorem
Lecture 21 - An Introduction to Riemann Integration