Lectures related to Advanced Analysis I - Finite Differences

Covers the theorem of finite increments in derivative functions.

Discusses the error between f'(x0) and its approximation using a backward finite difference formula.

Covers the demonstration of the chain rule and the theorem of Rolle.

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.

Explores the theorems of continuity and derivative numbers, including strict monotonicity and the Newton ratio.

Covers the definition of derivative, examples, Newton's quotient, and continuity.

Explores the conditions for a function to be continuous and differentiable.

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

Explores derivability, continuity, and composite functions with illustrative examples.

Explores finding the equation of the tangent line to a function's graph at a point.