Solution of Linear Equations

S. P. Venkateshan () and Prasanna Swaminathan ()
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S. P. Venkateshan: Indian Institute of Technology Madras, Department of Mechanical Engineering
Prasanna Swaminathan: Universite Sorbonne Paris Nord, Charge de recherche 2

Chapter Chapter 2 in Computational Methods in Engineering, 2023, pp 19-109 from Springer

Abstract: Abstract Linear equations are encountered in all branches of engineering and hence have received much attention. Geometric applications include the determination of the equation of a plane that passes through three non-collinear points, determination of the point of intersection of three non-parallel planes. Engineering applications are to be found in di verse areas such as analysis of electrical networks, conduction of heat in solids, solution of partial differential equations by finite difference and finite element methods. When the number of equations is small solution may be obtained by elementary methods. For example, two or three equations may be solved easily by the use of Cramer’s rule. When the number of equations become larger Cramer’s rule is cumbersome and one of several alternate methods may be used. The present chapter considers some elementary cases amenable to traditional methods followed by more complex applications that require advanced techniques.

Date: 2023
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DOI: 10.1007/978-3-031-08226-9_2

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