Lectures related to Center of Gravity and Variable Change

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

Explains multiple integration using spherical coordinates to calculate volumes of spheres and ellipsoids.

Series covers spherical coordinates, harmonics, Legendre polynomials, and angular momentum.

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Explores the intersection between a sphere and a cone using spherical and cylindrical coordinates.

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

Explores continuous functions and integrability through practical examples.

Covers the statement of the Bernoulli's Hospital Rule and its application.

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

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

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

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

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

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

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

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.