Regularization by Noise - Lecture 4
Dive into regularization by noise in fluid dynamics, exploring advanced mathematical concepts and their applications to Euler and Navier-Stokes equations in this in-depth lecture.
Wavelet-inspired Nash's Iteration - Lecture 3
Dive into wavelet-inspired Nash's iteration techniques for analyzing Euler and Navier-Stokes equations in fluid mechanics, exploring advanced mathematical concepts and recent breakthroughs in the field.
Regularization by Noise - Lecture 3
Dive into regularization by noise in fluid dynamics, exploring advanced mathematical concepts and their applications to Euler and Navier-Stokes equations in this in-depth lecture.
Statistical Solutions of Fluids and Their Computation
Explore statistical solutions of fluid dynamics and computational methods. Gain insights into Euler and Navier-Stokes equations, Onsager's conjecture, and recent breakthroughs in fluid mechanics research.
Regularization by Noise - Lecture 1
Dive into regularization by noise in fluid dynamics, exploring advanced mathematical concepts and their applications to Euler and Navier-Stokes equations in this comprehensive lecture.
Generalizations of the Bernstein Problem
Dive into Otis Chodosh's exploration of the Bernstein Problem's generalizations, examining minimal surface equations and their connections to higher dimensions.
Nonlinear Harmonic Maps and the Energy Identity
Dive into nonlinear harmonic maps, exploring singularity formation and defect measures. Gain insights into the Energy Identity conjecture and its recent proof in this advanced mathematics lecture.
The Landscape Law and Wave Localization
Explore the landscape function's role in predicting wave localization patterns and eigenfunction behavior in complex systems with Svitlana Mayboroda's mathematical insights.
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.
Multivariable Calculus
Comprehensive exploration of advanced calculus concepts, covering vector analysis, partial differentiation, complex analysis, and multivariable integration with practical examples and solutions.
Special Functions - Bessels and Legendre
Comprehensive exploration of Bessel's functions and Legendre polynomials, covering recurrence relations, proofs, and applications in partial differential equations.
Differential Equation
Comprehensive exploration of differential equations, covering first-order, higher-order, and partial differential equations, with various solution methods and applications in mathematical analysis.
Partial Differentiation
Comprehensive exploration of partial differentiation techniques, covering Euler's theorem, Jacobians, envelopes, and evolutes. Includes examples, solutions, and applications in multivariable calculus.
Partial Differential Equation - CF & PI
Explore homogeneous and non-homogeneous partial differential equations, focusing on complementary functions and particular integrals. Learn general methods and rules for solving PDEs.
Deriving the Wave Equation
Comprehensive derivation of the Wave Equation, exploring its applications in physics and engineering, with examples from guitar strings to illustrate key concepts.
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.
Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization
Exploring SINDy algorithm for developing efficient nonlinear models in complex fluid flows, with applications in various fields including bluff body wakes, thermal convection, and magnetohydrodynamics.
Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2
Explore center manifolds in Hamiltonian systems and PDEs, including Lorenz system bifurcation, unstable directions, and applications to flame front evolution and celestial mechanics.
Hamiltonian Normal Forms, Lie Series Method for Transformations - Infinite-Dimensional Hamiltonians
Explore Hamiltonian normal forms, Lie series transformations, and infinite-dimensional systems. Learn to simplify complex dynamics and analyze PDEs like shallow water equations.