Laplace Transform Solutions to PDEs
Explore Laplace transform techniques for solving partial differential equations, enhancing your understanding of advanced mathematical methods in engineering applications.
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.
Numerical Integration and Numerical Solutions to ODEs
Explore numerical methods for integration and solving ordinary differential equations, enhancing your computational skills in engineering mathematics.
ODEs with External Forcing and the Convolution Integral
Explore inhomogeneous ODEs and convolution integrals, learning to solve differential equations with external forcing for advanced engineering applications.
ODEs with External Forcing - Inhomogeneous ODEs
Explore inhomogeneous ODEs and external forcing in engineering mathematics, covering key concepts and applications for solving complex differential equations.
2x2 Systems of ODEs - With Eigenvalues and Eigenvectors, Phase Portraits
Explore 2x2 systems of ODEs, eigenvalues, eigenvectors, and phase portraits in engineering mathematics. Learn to analyze and visualize complex dynamical systems.
Linearization of Nonlinear ODEs, 2x2 Systems, Phase Portraits
Explore linearization techniques for nonlinear ODEs, analyze 2x2 systems, and visualize phase portraits in this advanced engineering mathematics lecture.
Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs
Explore higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations in engineering mathematics, with accompanying notes and MATLAB code.
Taylor Series and Solutions to First and Second Order Linear ODEs
Explore Taylor series and solutions to linear ODEs, enhancing your understanding of engineering mathematics with practical applications and MATLAB code examples.
Analytical Aspects of Emergent Dynamics in Systems of Collective Behavior
Explore analytical aspects of emergent dynamics in collective behavior systems, focusing on alignment dynamics in disconnected flocks and new approaches using topological fractional diffusion and random fluctuations.
Gaussian Lower Bounds for the Boltzmann Equation Without Cut-off - SIAM PDE Seminar
Explore Gaussian lower bounds for the Boltzmann equation, examining particle density evolution in gases and conditional estimates for solving global well-posedness challenges in fluid dynamics.
Optimal Transport of Matrix-Valued Measures - SIAM PDE Seminar
Explore optimal transport of matrix-valued measures, inspired by incompressible Euler equations. Discover a matricial analogue of Hellinger-Kantorovich metric spaces in this advanced mathematical seminar.
Parametric Polynomial Systems and Biochemical Reaction Networks
Explore parametric polynomial systems in biochemical reaction networks, focusing on multistationarity and the dual futile cycle. Gain insights into steady state analysis and parameter region determination.
Optimal Transport for Inverse Problems and Implicit Regularization
Exploring optimal transport theory for inverse problems, addressing nonconvexity and noise sensitivity in least-squares methods, with applications in industry and broader data-fitting challenges.
How Much Math Do You Need to Know to Solve an Initial Value Problem - SIAM PDE Seminar
Explore mathematical techniques for solving nonlinear Schrödinger equations, from harmonic analysis to dynamical systems, focusing on long-time dynamics and energy transfer in initial value problems.
Ginzburg-Landau Model in Superconductivity - Old and New Results
Explore Ginzburg-Landau model of superconductivity, analyzing vortex patterns in 2D and 3D, energy minimizers, and vortex dynamics with expert Sylvia Serfaty from NYU's Courant Institute.
Auxiliary Functionals - A Path to Solving the Problem of Turbulence
Explore innovative approaches to solving turbulence in fluid dynamics using auxiliary functionals and sum-of-squares polynomial optimization, with applications to Kuramoto-Sivashinsky and Navier-Stokes equations.
Finite Dimensional Approximations of Hamilton-Jacobi-Bellman Equations in Probability Measure Spaces - SIAM PDE Seminar
Explore finite dimensional approximations of Hamilton-Jacobi-Bellman equations in probability measure spaces, focusing on convergence of viscosity solutions and representation formulas for limiting equations.
The Calderon Problem: 40 Years Later - Seminar in the Analysis and Methods of PDE
Explore Calderon's inverse problem, its applications in medical imaging and geophysics, recent developments, and open questions with expert Gunther Uhlmann in this insightful seminar.