Lectures related to Integral Techniques: Change of Variable

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

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

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

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

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

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

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Covers the derivative of the composition of two functions and its applications.

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

Explains partial derivatives, Hessienne matrix, and their properties.

Covers the fundamental theorem of calculus, immediate integration, and properties of derivatives, with examples of integration by substitution.

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

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

Covers smooth piecewise arcs integration and the importance of closed paths.

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

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

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

Explores differentiability, tangent lines, and graph interpretation.

Explores the derivative of composite functions and their application in changing variables.