Nonlinear is Essential, Linearization is Not Enough, Visualization is Absolutely Necessary

2013 ◽  
pp. 89-112
Author(s):  
Beverly West
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Real World ◽  
Linear Differential Equations ◽  
World Systems ◽  
Undergraduate Level ◽  
Linear Differential

Linear differential equations have been well understood for some time and are an important tool for studying the nonlinear systems that most frequently arise in mathematical models of real world systems. Nonlinear systems do not usually have formula solutions, but with graphics, we can see the behaviors of the solutions and thereby “understand” the differential equations. Dynamic and interactive presentations provide students with a streamlined route to understanding these behaviors, resulting in immense power and efficiency that was not previously available at the undergraduate level.

scholarly journals MATHEMATICAL MODELING OF THE PREVENTION OF MAN-MADE DISASTERS

2021 ◽  
Vol 6 (2(52)) ◽  
pp. 70-75
Author(s):  
M.V. Makarova
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Mathematical Models ◽  
Spectral Power ◽  
Linear Differential Equations ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Power Densities

In the article explores objects whose mathematical models are linear differential equations with constant coefficients. These facilities are subject to indignant forces, which are random. Their correlational functions and spectral power densities are known. An algorithm is given to build a guarantee control that ensures the reliability of the objects in question.

scholarly journals Boundary value problem for a singularly perturbed system of linear differential equations with impulses

1988 ◽  
Vol 31 (1) ◽  
pp. 107-126 ◽  
Author(s):  
D. D. Bainov ◽  
M. A. Hekimova ◽  
V. M. Veliov
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Automatic Control ◽  
Linear Differential Equations ◽  
Singularly Perturbed ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Linear Differential ◽  
Short Time

In connection with the analysis of mathematical models of real processes undergoing short time perturbations, in the last years the interest in the differential equations with impulses remarkably increased. Going back to the papers of Mil'man and Myshkis [4, 5] the investigations of this subject are now extended to different directions concerning applications in physics, biology, electronics, automatic control etc.

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