Advanced Analysis I: March 14

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Related lectures (29)

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Differentiation: Continuity vs Differentiability

Explores the relationship between continuity and differentiability of functions, highlighting examples where functions exhibit different properties at specific points.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Derivability and Composition

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Solutions to QCM Questions

Covers the solutions to multiple-choice questions related to functions and derivatives.

Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Functions and Coordinate Changes

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Advanced Analysis II: Differentiability and Continuity

Explores differentiability and continuity in advanced analysis, emphasizing the importance of continuity and demonstrating key concepts.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.