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Review of Basic Laws and Equations
Published in Pradip Majumdar, Computational Methods for Heat and Mass Transfer, 2005
All problems and improvements discussed for the Gauss elimination method are applicable to the Gauss-Jordan method. So, the method of pivoting is applicable to the Gauss-Jordan method to avoid zero division and to reduce round-off error. It can be mentioned here that the Gauss-Jordan method usually takes more operations than Gauss-elimination. Therefore, the Gauss-elimination method is usually the method of choice for obtaining the exact solutions of a system of linear equations. The Gauss-Jordan method is preferred for obtaining a matrix inverse A−1 that provides a convenient way of evaluating a set of simultaneous equations with multiple right-hand side force vectors, {c}.
Solving simultaneous equations
Published in John Bird, Bird's Engineering Mathematics, 2021
Simultaneous equations arise a great deal in engineering and science, some applications including theory of structures, data analysis, electrical circuit analysis and air traffic control. Systems that consist of a small number of equations can be solved analytically using standard methods from algebra (as explained in this chapter). Systems of large numbers of equations require the use of numerical methods and computers. Matrices are generally used to solve simultaneous equations (as explained in chapter 59). Solving simultaneous equations is an important skill required in all aspects of engineering.
Kinematic Analysis of Planar Mechanisms
Published in Kevin Russell, Qiong Shen, Raj S. Sodhi, Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®, 2018
Kevin Russell, Qiong Shen, Raj S. Sodhi
The displacement equations presented in this chapter form sets of two nonlinear simultaneous equations. Unlike linear simultaneous equations, nonlinear simultaneous equations cannot be solved algebraically. Using a root-finding method, such equation sets can be solved numerically. The Newton–Raphson method is one of the most common root-finding methods. In the Appendix B.1 and B.3 through B.6 MATLAB files, the displacement, velocity, and acceleration equations for the planar four-bar, slider-crank, geared five-bar, Watt II, and Stephenson III mechanisms, respectively, are solved numerically.
Measurement and analysis of clothes dryer air leakage
Published in Drying Technology, 2021
Philip Boudreaux, Kyle R. Gluesenkamp, Viral K. Patel, Bo Shen
This system of equations can be solved with simultaneous equation-solving software such as Engineering Equation Solver.[15] The pressure drop between each component is calculated using the measured in situ differential pressure between the duct and ambient. These data, along with the calculated CvLs, are used as inputs to the simultaneous equation solver, which will solve for the leakage flow rates.