Lectures related to Taylor's approximation: Analysis & Applications

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

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

Explores functions, limits, continuity, differentiability, and important notions of limits and divergence.

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

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

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

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

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

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

Explores the limit of the quotient for sequences and the periodicity of functions.

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

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

Explores Taylor expansion, convex functions, and Lipschitz continuity with illustrative examples.

Covers the integration of limit expansions and continuous functions by pieces.

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.