Examples: Function Spaces

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Covers the definitions of continuous functions and derivatives, emphasizing the concept of functions being continuous at a point and the notion of derivatives.

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Differential Calculus: Introduction and Summary

Introduces and summarizes differential calculus, covering continuous functions, limits, differentiability, and tangent planes.

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Continuity and Galerkin Method

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Differential Equations: Solutions and Derivatives

Explores differential equations solutions, derivatives, differentiability, composite functions, and continuous functions.

Function Spaces: Review and Compact Operators

Covers the review of function spaces and explores the concept of compact operators.

Linear Applications and Matrix Derivatives

Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.