Introduction to Electromagnetism
This course introduces students to handling electromagnetic theory using vector calculus. This enables students to handle problems that are more complicated than they are used to from their school days.
Electromagnetic Theory
Comprehensive exploration of electromagnetic theory, covering fields, potentials, Maxwell's equations, waves, and applications in waveguides and radiation. Ideal for advanced physics students.
Partial Differential Equations
Explore partial differential equations through various methods, including characteristic, coordinate, and transform approaches. Learn to solve wave and heat equations using advanced techniques.
Partial Differential Equations
Explore advanced mathematical concepts including Laplace equations, convolution, polar coordinates, and more. Master techniques for solving complex differential equations and their applications.
Introduction to CFD
Explore computational fluid dynamics fundamentals, from numerical methods to advanced techniques like multigrid and parallel computing, with practical demonstrations and applications.
PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation
Explore the powerful Separation of Variables technique for solving PDEs, focusing on Laplace's equation in 2D for steady-state heat distribution, with applications in physics and engineering.
Viscosity Solutions Approach to Variational Problems - Daniela De Silva
Explore viscosity solutions for variational problems with Daniela De Silva. Learn about Laplace's equation, Harnack inequality, and discrete equations in this advanced mathematics lecture.
Canonical Linear PDEs- Wave Equation, Heat Equation, and Laplace's Equation
Explore fundamental linear PDEs: wave, heat, and Laplace's equations. Gain insights into their properties, applications, and mathematical foundations in engineering and physics.
Heat Equation- Derivation and Equilibrium Solution in 1D - Laplace's Equation
Explore the derivation and equilibrium solution of the heat equation in 1D, including Laplace's equation, boundary conditions, and practical applications in engineering mathematics.
Potential Flow and Laplace's Equation
Explore potential flow and Laplace's equation in engineering mathematics, covering vector fields, heat conduction, and practical applications in fluid dynamics and thermodynamics.
The Regularity Problem for the Laplace Equation in Rough Domains
Explores recent advances in Boundary Value Problems for the Laplace operator in rough domains, focusing on the equivalence between Dirichlet and regularity problem solvability.
Complex Analysis - Analytic Functions Solve Laplace's Equation
Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.
Numerical Solution to Laplace's Equation in Matlab - Intro to Fourier Series
Explore numerical solutions to Laplace's Equation using MATLAB and get introduced to Fourier Series in this engineering mathematics lecture, with practical code examples and comprehensive notes provided.
Heat Equation in 2D and 3D - 2D Laplace Equation on Rectangle
Explore multidimensional heat equations and the 2D Laplace equation on rectangles, advancing your understanding of engineering mathematics and partial differential equations.
Analytic Solution to Laplace's Equation in 2D - On Rectangle
Explore the analytic solution to Laplace's equation in 2D on a rectangle, enhancing your understanding of engineering mathematics and partial differential equations.
The Laplace Equation in Spherical Coordinates: Illustrative Examples - Lecture 72
Explore illustrative examples of the Laplace Equation in spherical coordinates, enhancing understanding of this fundamental concept in mathematical physics.
The Laplace Equation in Spherical Coordinates: Solution - Lecture 71
Solve the Laplace equation in spherical coordinates, exploring methods and techniques for finding solutions to this fundamental partial differential equation.
Recovering Bicomplex Holomorphic Functions Without Cauchy-Riemann Equations
Explore advanced techniques for recovering bicomplex holomorphic functions without using Cauchy-Riemann equations, focusing on complex harmonic functions and their applications in hypercomplex analysis.
The Laplace Equation: Dirichlet and Neumann Boundary Conditions - Lecture 67
Explore Dirichlet and Neumann boundary conditions for the Laplace Equation, enhancing understanding of partial differential equations and their applications.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
Potential Flow, Stream Functions, and Examples
Explore potential flow, stream functions, and Laplace's equation with practical examples in fluid dynamics. Gain insights into fundamental concepts and their applications.