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No Slide Title

... 3. Translate to a system of equations and solve: Alfa Rent-a-Car rents compact cars at daily rate of $23.95 plus 20¢ per kilometer. Giant Rent-a-Car rents compact cars at daily rate of $22.95 plus 22¢ per kilometer. For what kilometer is cost will be same? ...


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... (1) is solvable in integers if and only if (a, b)|n [ 1, p. 54]. In view of these results and the general conditions imposed on (1), L e e , the solutions and parameters are to be non-negative integers, there is no loss of generality by assuming (a, b) = 1„ If (XpYi) is a solution of (1) in integers ...
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Partial differential equation



In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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