Results 291 to 300 of about 756,333 (330)

Differential Equations: Partial

2000
We have been studying nonlinear oscillatory processes, starting with the simplest autonomous case, and later incorporating forcing. The modelling was in terms of ordinary differential equations (ODE), and the most important tool used was the phase diagram.
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Partial Differential Equations

1988
In this chapter, procedures will be developed for classifying partial differential equations as elliptic, parabolic or hyperbolic. The different types of partial differential equations will be examined from both a mathematical and a physical viewpoint to indicate their key features and the flow categories for which they occur.
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Partial Differential Equations

2002
An ordinary differential equation (ODE) of order n has a general solution (excluding singular solutions) which depends on n arbitrary constants of integration. In the case of partial differential equations (PDE) the situation is more complicated. The general solution of a PDE does not depend on arbitrary constants, but on arbitrary functions.
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Partial Differential Equations

1978
As an example to show how the Laplace transform may be applied to the solution of partial differential equations, we consider the diffusion of heat in an isotropic solid body.
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Partial Differential Equations

2019
The field of partial differential equations is arguably the workhorse of applied mathematics. While the field is steeped with a rich and fruitful history supporting volumes of research, our modest goal is to present a couple of the standard models and to show how to solve them with introductory methods.
Allen Holder, Joseph Eichholz
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Partial Differential Equations

2012
In this chapter we study some classes of partial differential equations, including the heat equation, the Laplace equation, and the wave equation. In particular, based on the study of Fourier series, we find solutions for several equations and several types of boundary conditions. We mainly use the method of separation of variables. In contrast to what
Luis Barreira, Claudia Valls
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Partial Differential Equations and Difference Equations

Proceedings of the American Mathematical Society, 1965
(1. 1) Pi(alax)y = ? (1 _ i _ m) where x = (x1, * , xn), a/ax = (a/ax1, *, O/0xn). The Pi's are assumed to be homogeneous polynomials with real coefficients. The term solution is used to include the generalized solutions. A generalized solution is any function continuous on R which is a uniform limit on compact subsets of CX solutions (see [2, p. 65]).
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Applications to Partial Differential Equations

1971
Publisher Summary The applications of integral equations are not restricted to ordinary differential equations. The most important applications of integral equations arise in finding the solutions of boundary value problems in the theory of partial differential equations of the second order.
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Partial Differential Equations [PDF]

, 2018
Ronald B. Guenther, A. Kharab
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Linear Partial Differential Equations

1957
Although we shall mainly be concerned in this Part with differential equations, the methods we use here for their discussion and solution are intimately connected with the geometry of the rest of the volume. In particular, the results obtained depend to a great extent on the theory of modules and the intersections of a set of algebraic varieties ...
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