Lectures related to Modular Forms: Properties and Applications

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

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

Explores the properties and transformations of theta functions, including modular forms and lattice levels.

Covers Fourier series, periodic functions, and Fourier transforms.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Covers functions, including even and odd functions, periodicity, and function operations.

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

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

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

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.

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

Covers mathematical concepts from number theory to probability and statistics.

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

Explores the application of Fourier series and the challenges of using multiple methods to solve problems.

Covers classical harmonic analysis on the circle, Fourier series convergence, and applications in PDEs.

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

Covers fundamental programming concepts and highlights the importance of modular code design.

Covers the definition and properties of convolution of two functions and explores radioactive material decay rates.

Covers the theory of polynomials, including definitions, properties, and applications.