Lectures related to Fourier Series and Equations

Products and Convolution of Transforms

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

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Laplace Transform: Properties and Applications

Covers the properties and applications of the Laplace transform in solving differential equations.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Transforms of the Place

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

Laplace Transforms: Applications and Convergence Properties

Introduces Laplace transforms, their properties, and applications in solving differential equations.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Limit of the Quotient and Periodicity

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Taylor Series: Convergence and Applications

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

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

Solutions of Differential Equations

Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Harmonic Forms: Main Theorem

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

Real Functions: Definitions and Properties

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

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.