Ordinary differential equations | Matrices
In mathematics, and in particular ordinary differential equations, a Green's matrix helps to determine a particular solution to a first-order inhomogeneous linear system of ODEs. The concept is named after George Green. For instance, consider where is a vector and is an matrix function of , which is continuous for , where is some interval. Now let be linearly independent solutions to the homogeneous equation and arrange them in columns to form a fundamental matrix: Now is an matrix solution of . This fundamental matrix will provide the homogeneous solution, and if added to a particular solution will give the general solution to the inhomogeneous equation. Let be the general solution. Now, This implies or where is an arbitrary constant vector. Now the general solution is The first term is the homogeneous solution and the second term is the particular solution. Now define the Green's matrix The particular solution can now be written (Wikipedia).
Calculus 3: Green's Theorem (8 of 21) Graphical Representation of a Vector Field
Visit http://ilectureonline.com for more math and science lectures! In this video I will show and explain a graphical representation of a conservative and NON-conservative vector field. Next video in the series can be seen at: https://youtu.be/7GpCErcgV4I
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM
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From playlist Introduction to Green Chemistry with Paul Anastas, Module 1
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From playlist Introduction to Green Chemistry
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From playlist Introduction to Green Chemistry
Calculus 3: Green's Theorem (12 of 21) With a NON-Conservative Vector Field: Ex. 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the work done in a NON-conservative vector field by integrating along the path x^2+y^2= a^2. Ex. 3 Next video in the series can be seen at: https://youtu.be/WUuiHQN4FmQ
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM
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From playlist Calculus 3 (Full Length Videos)
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From playlist Chapter 6 - The Matrix
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Lec 3 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
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From playlist MIT Nonlinear Finite Element Analysis
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Calculus 3: Green's Theorem (6 of 21) With a Conservative Vector Field
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain Green's Theorem with a conservative vector field. Next video in the series can be seen at:
From playlist CALCULUS 3 CH 7 GREEN'S THEOREM