Lectures related to Composition of Taylor Expansions

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

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

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.

Covers the definitions and examples of hyperbolic tangent and cotangent functions.

Explains the Taylor series expansion of order 4 for the cosine function.

Covers the interpretation of Taylor's formula through an example, focusing on developing limited series for sin(x) around a=0.

Explores algebraic operations on Taylor expansions and the development of various functions.

Presents the solution to finding the second-order Taylor polynomial of a function.

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

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.

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

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Covers hyperbolic functions, including definitions, properties, and derivatives, explained with detailed examples and derivations.

Introduces the basics of trigonometric functions, their properties, and practical applications in geometry and physics.

Explores functions, series, and critical points in mathematics, including maximum, minimum, supremum, and infimum concepts.

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

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

Explores power series, Taylor series, convergence criteria, and applications in mathematics.