Finite element method | Multilinear algebra
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs and finite element meshes. DEC methods have proved to be very powerful in improving and analyzing finite element methods: for instance, DEC-based methods allow the use of highly non-uniform meshes to obtain accurate results. Non-uniform meshes are advantageous because they allow the use of large elements where the process to be simulated is relatively simple, as opposed to a fine resolution where the process may be complicated (e.g., near an obstruction to a fluid flow), while using less computational power than if a uniformly fine mesh were used. (Wikipedia).
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
11_3_5 When is a multivariable function continuous
Determining where is multivariable function is continuous.
From playlist Advanced Calculus / Multivariable Calculus
Introduction to Discrete and Continuous Functions
This video defines and provides examples of discrete and continuous functions.
From playlist Introduction to Functions: Function Basics
11_3_6 Continuity and Differentiablility
Prerequisites for continuity. What criteria need to be fulfilled to call a multivariable function continuous.
From playlist Advanced Calculus / Multivariable Calculus
Prerequisites of a smooth function.
From playlist Advanced Calculus / Multivariable Calculus
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS
We introduce the concept of injective functions, surjective functions, bijective functions, and inverse functions. #DiscreteMath #Mathematics #Functions Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--P
From playlist Discrete Math 1
Lecture 3: Exterior Algebra (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
DSI | Diagrammatic Differential Equations in Physics Modeling and Simulation
Abstract: I’ll discuss some results from a recent paper on applying categories of diagrams for specifying multiphysics models for PDE-based simulations. We developed a graphical formalism inspired by the graphical approach to physics pioneered by the late Enzo Tonti. We will discuss the gr
From playlist DSI Virtual Seminar Series
Lecture 8: Discrete Differential Forms (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 7: Integration (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 14: Discrete Surfaces (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 1: Overview (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 13: Smooth Surfaces II (Discrete Differential Geometry)
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From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 5: Differential Forms (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
11_2_1 The Geomtery of a Multivariable Function
Understanding the real-life 3D meaning of a multivariable function.
From playlist Advanced Calculus / Multivariable Calculus