Lectures related to Automorphic Kernels: Heat Equation Solutions

Differential Equations: Speed Variation Analysis

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

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Advanced Analysis II: Differential Equations and Timers

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

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Complex Analysis: Laplace and Fourier Transforms

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.

Complex Analysis: Residue Theorem and Fourier Transforms

Discusses complex analysis, focusing on the residue theorem and Fourier transforms, with practical exercises and applications in solving differential equations.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Differential Equations and Heat Diffusion

Covers differential equations, heat diffusion, and advanced analysis for engineers.

Multi-injection microreactors: Modeling and Heat Transfer Analysis

Explores modeling and heat transfer in multi-injection microreactors, analyzing temperature, concentration, and reactor length.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Transport of Pollutants: Numerical Analysis and Equations

Discusses the numerical analysis of pollutant transport equations and their applications in environmental modeling.

Cauchy-Euler Equations

Covers the definition and solution of Cauchy-Euler equations, which are second-order differential equations with specific form and solutions.

Differential Equations: Solution Methods

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Harmonic Forms: Main Theorem

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