Problem Solving: Difference between revisions
No edit summary |
No edit summary |
||
| Line 12: | Line 12: | ||
The incidence matrix, A, is a matrix of dimensions m x n, where m is the number of edges and n is the number of nodes. If x is the vector that contains all the nodes in order, A satisfies: <math>A\vec{x}_{edge} = x_{end} - x_{start}</math> Thus, the resulting matrix will have zeros in every element of each row, except for the start and the end nodes, which will be -1 and 1 respectively: | The incidence matrix, A, is a matrix of dimensions m x n, where m is the number of edges and n is the number of nodes. If x is the vector that contains all the nodes in order, A satisfies: <math>A\vec{x}_{edge} = x_{end} - x_{start}</math> Thus, the resulting matrix will have zeros in every element of each row, except for the start and the end nodes, which will be -1 and 1 respectively: | ||
[[File:Incidence_matrix.jpg|350px|thumb|center|Incidence matrix of a sample graph.<ref>{{Citation|last=Strang|first=Gilbert|date=July 19, | [[File:Incidence_matrix.jpg|350px|thumb|center|Incidence matrix of a sample graph.<ref>{{Citation|last=Strang|first=Gilbert|date=July 19, 2016|title=Introduction to Linear Algebra|publisher=Wellesley-Cambridge Press|edition=5th|isbn=978-0-9802327-7-6}}</ref> | ||
]] | ]] | ||
Revision as of 18:31, 29 November 2017
Linear algebra can be used to solve large ohmic circuits. This page explains how to define the circuit problem in terms of a linear system that can be solved with computational methods like matlab or python.
The Main Idea
We can describe an electrical circuit as a graph where the nodes represent specific points and the edges represent the components connecting them. E.g:
Incidence Matrix
The incidence matrix, A, is a matrix of dimensions m x n, where m is the number of edges and n is the number of nodes. If x is the vector that contains all the nodes in order, A satisfies: [math]\displaystyle{ A\vec{x}_{edge} = x_{end} - x_{start} }[/math] Thus, the resulting matrix will have zeros in every element of each row, except for the start and the end nodes, which will be -1 and 1 respectively:
Loop Rule
Kirchhoff's Current Law
A Mathematical Model
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Middling
Difficult
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading
Books, Articles or other print media on this topic
External links
Internet resources on this topic
References
This section contains the the references you used while writing this page