Lectures related to Differentiable Functions: Derivatives and Approximations

Explores differentiable functions, Taylor approximations, and directional derivatives in open sets.

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

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

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Covers differentiable functions, derivatives, and tangent planes in mathematics.

Covers implicit functions, Taylor polynomials, and tangent equations.

Covers Taylor polynomials for function approximation and their properties, with examples.

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

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Explores Taylor polynomials, including order, development, limits, and algebraic operations.

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Covers Taylor polynomials and their role in approximating functions in multiple variables.

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

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Explores algebraic operations for derivatives, including addition, multiplication, and composition of functions on an interval.

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

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