Fundamental Solutions

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Related lectures (53)

Cheeger's Inequalities Log in to Mediaspace to watch this video

Explores Cheeger's inequalities for random walks on graphs and their implications.

Weak Formulation of Elliptic PDEs Log in to Mediaspace to watch this video

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Curve Integrals of Vector Fields Log in to Mediaspace to watch this video

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Green-Riemann Formulas Log in to Mediaspace to watch this video

Covers the Green-Riemann formulas and their applications in evaluating integrals and solving differential equations.

Cauchy Problem: Initial Conditions Log in to Mediaspace to watch this video

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Transforms Properties Log in to Mediaspace to watch this video

Covers the properties of transforms and their applications in mathematics.

Convex Optimization: Gradient Descent Log in to Mediaspace to watch this video

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Boundary Value Problems in Elasticity Log in to Mediaspace to watch this video

Explores Boundary Value Problems in Elasticity, stress-strain relations, and the use of Green's function in solving elasticity problems.

Regularity in Higher Dimension Log in to Mediaspace to watch this video

Explores regularity in higher dimensions for scalar problems and discusses weak sense solutions and interior regularity.

Proof of Sylow Subgroup Properties Log in to Mediaspace to watch this video

Explores the properties of p-subgroups of Sylow in a group.

Analytical Solutions: EDO Log in to Mediaspace to watch this video

Explores the analytical solutions of ordinary differential equations, emphasizing the identification and solving process for various EDO types.

Rigorous Proof of Differential Equations Log in to Mediaspace to watch this video

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Introduction to PDES Log in to Mediaspace to watch this video

Covers harmonic functions, Laplacian operator, Dirichlet and Robin problems, and sub-harmonic functions in Partial Differential Equations.

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