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.

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Discusses conditions for functions to be strictly increasing or decreasing based on the derivative.

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Covers primitive functions, infinite primitives, the theorem on primitives, and examples of indefinite integrals.

Explores inflection points in functions, emphasizing the role of the second derivative.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Covers differentiability, derivatives, composite functions, linear approximation, and partial derivatives.

Covers the derivative of the reciprocal function and its properties.