Ordinary Differential Equations - Principles and Applications

TAILLE DU FICHIER: 8,61 MB

AUTEUR: A-K Nandakumaran

ISBN: 9781108416412

NOM DE FICHIER: Ordinary Differential Equations - Principles and Applications.pdf

DATE DE PUBLICATION: 2017-Dec-01

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Many important real-life problems in mathematics, physics, chemistry, biology, engineering, economics, sociology and psychology are modelled using the tools and techniques of ordinary differential equations (ODEs). This book on ODE discusses relevant topics including first and second order linear equations, initial value problems and qualitative theory. The text covers two-point boundary value problems for second order linear and nonlinear equations. Using two linearly independent solutions, a Green's function is also constructed for given boundary conditions. The authors emphasize the use of calculus concepts in justification and analysis of equations to get solutions in explicit form. 'While discussing first order linear systems, tools from linear algebra are used and the importance of these tools is clearly explained. Real-life applications are interspersed throughout. Additionally readers can find the methods and tricks to solve numerous mathematical problems with sufficient derivations and explanations. The first few chapters can be used for an undergraduate course on ODE, and later chapters can be used at graduate level.
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Ordinary Differential Equations by A. K. Nandakumaran

In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common, therefore differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations ...

PDF Handbook of Ordinary Differential Equations

When a differential equation involves a single independent variable, we refer to the equation as an ordinary differential equation (ode). Example 1.0.2. If there are several dependent variables and a single independent variable, we might have equations such as dy dx = x2y xy2 +z, dz dx = z ycos x.