Calculus of variations | Partial differential equations
The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle. It is deeply related to the study of minimal surfaces and the capacity of a set in potential theory as well. Applications include the study of fluid filtration in porous media, constrained heating, elasto-plasticity, optimal control, and financial mathematics. The mathematical formulation of the problem is to seek minimizers of the Dirichlet energy functional, in some domain where the functions represent the vertical displacement of the membrane. In addition to satisfying Dirichlet boundary conditions corresponding to the fixed boundary of the membrane, the functions are in addition constrained to be greater than some given obstacle function . The solution breaks down into a region where the solution is equal to the obstacle function, known as the contact set, and a region where the solution is above the obstacle. The interface between the two regions is the free boundary. In general, the solution is continuous and possesses Lipschitz continuous first derivatives, but that the solution is generally discontinuous in the second derivatives across the free boundary. The free boundary is characterized as a Hölder continuous surface except at certain singular points, which reside on a smooth manifold. (Wikipedia).
C49 Example problem solving a system of linear DEs Part 1
Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.
From playlist Differential Equations
B06 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
B04 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
B07 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
B09 Example problem with a linear equation
Solving a linear differential equation
From playlist Differential Equations
C56 Continuation of previous problem
Adding a bit more depth to the previous problem.
From playlist Differential Equations
B05 Example problem with separable variables
Solving a differential equation by separating the variables.
From playlist Differential Equations
C50 Example problem solving a system of linear DEs Part 2
Part 2 of the prvious example problem, solving a system of linear differential equations, where one of the equations is non-homogeneous.
From playlist Differential Equations
The singular set in the fully nonlinear obstacle problem - Ovidiu Savin
Analysis Seminar Topic: The singular set in the fully nonlinear obstacle problem Speaker: Ovidiu Savin Affiliation: Columbia University Date: November 18, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Yuliy Baryshnikov (1/19/20): Linear Obstacles in Linear Systems and Ways to Avoid Them
Topology of the spaces of obstacle-avoiding directed paths emerged as a research topic in theoretical computer science. In this talk I will show how a similar class of spaces arises in control theory, and how to describe the cohomology rings of those spaces in some simplest situations, rel
From playlist AATRN 2022
8ECM EMS Prize Lecture: Joaquim Serra
From playlist 8ECM EMS Prize Lectures
A06 Example problem including the Wronskian
Example problem solving a system of linear differential equations, including a look at the Wronskian so make sure that the solutions are not constant multiples of each other.
From playlist A Second Course in Differential Equations
Somil Bansal: "Scaling Hamilton-Jacobi Reachability Analysis for Robotics"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "Scaling Hamilton-Jacobi Reachability Analysis for Robotics: Multi-agent Systems to Real-time Computation" Somil Bansal - University of California, Berkeley A
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
game programming patterns part 1 - creating the infinite runner
I created an infinite runner in P5.js in preparation for learning proper game programming design patterns. Code: [https://github.com/brooks-builds/learning_game_design_patterns](https://github.com/brooks-builds/learning_game_design_patterns) Game Design book: [http://gameprogrammingp
From playlist Game Programming Patterns Book
Game Programming Patterns part 7.8 - (Rust) Observer Pattern
I use the observer pattern to have the player send an event to the game state that the player got hit by an obstacle. This closes out the implementation of the observation pattern. Links code - https://github.com/brooks-builds/learning_game_design_patterns twitter - https://twitter.com/b
From playlist Game Programming Patterns Book
How To Make A Game In Unity Using C# | Creating A Game In Unity For Beginners | Simplilearn
This video on How To Make A Game In Unity Using C# will acquaint you with a clear understanding of the fundamentals of Creating A Game In Unity For Beginners. In this C# Unity Tutorial on How To Make A Game In Unity Using C#, you will get better understanding on Creating A Game In Unity Fo
From playlist C++ Tutorial Videos
Game Programming Patterns part 4.5 - (Rust) Obstacles
We begin creating obstacles that the player will have to jump over. Links code - https://github.com/brooks-builds/learning_game_design_patterns twitter - https://twitter.com/brooks_patton -- Watch live at https://www.twitch.tv/brookzerker
From playlist Game Programming Patterns Book
Higher Regularity of the Singular Set in the Thin Obstacle Problem - Yash Jhaveri
Analysis Seminar Topic: Higher Regularity of the Singular Set in the Thin Obstacle Problem. Speaker: Yash Jhaveri Affiliation: Member, School of Mathematics Date: April 4, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
C51 Example problem of a system of linear DEs
Example problem solving a system of linear differential equations.
From playlist Differential Equations
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture IV
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools