Lectures related to Linear Response for Chaotic Systems

Derivative of a Function: Tangent Equation

Explores finding tangent equations and slopes through derivatives.

Provides solutions to an Analysis I exam, covering various topics.

Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.

Jacobian Matrix: Derivative of Composite Functions

Explains the Jacobian matrix and derivative of composite functions with examples.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

Taylor Series: Convergence and Applications

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

Theorem of Generalized Mean Value: Study of Functions

Explores the conditions for continuity and differentiability of functions on a closed interval.

Chaos Theory: Discrete Dynamical Systems

Explores Chaos Theory through Discrete Dynamical Systems and the Arnold's Cat Map.