Lectures related to Mathematics: Functions and Series

Explores real functions, covering parity, periodicity, and polynomial functions.

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

Covers Fourier series, periodic functions, and Fourier transforms.

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

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

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Introduces real numbers, their properties, and their significance in analysis.

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

Discusses local extrema of functions in two variables around the point (0,0).

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

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

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

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

Covers the properties of functions, including symmetry, continuity, and limits.

Covers Morse theory, focusing on critical points and non-degeneracy.

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

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

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

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

Covers the basics of real analysis, including functions, limits, and max/min functions.