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NURI SENSOY | nurisensoy.wordpress.com Reviews
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(by Nuri Şensoy)
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1 nuri sensoy
2 mathematics
3 differential equations
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6 about me
7 separable equations
8 nuri şensoy
9 yorum bırakın
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Cauchy Problem for The Heat Equation | NURI SENSOY

https://nurisensoy.wordpress.com/2013/02/21/cauchy-problem-for-the-heat-equation

Cauchy Problem for The Heat Equation. Şubat 21, 2013. Cauchy Problem for Heat Equation. I will solve the Cauchy Problem on the real line for the heat conductivity equation. Applying the Fourier Transform to (1) and (2), we obtain. Multiplying (3) by the integrating factor. Integrating (5) from 0 to. And using the initial condition (4), we have. To find the solution. We will prove two propositions. Applying polar coordinates to the double integral, we obtain. Be two functions in. Then, from (6), we obtain.

2

Heat Equation with Dirichlet Boundary Conditions | NURI SENSOY

https://nurisensoy.wordpress.com/2013/03/03/heat-equation-in-a-finite-segment

First Order Linear Ordinary Differential Equation. Heat Equation with Dirichlet Boundary Conditions. Mart 3, 2013. Heat Equation in Finite Segment. Heat Equation with Boundary Conditions. Let’s attempt a solution of the form. To seperate variables. This method is called the. Substituting this equation into the equation (1), we obtain. In this equation, the left-hand side depends only on. And the right-hand side depends only on. So, we have separated the variables. Since. This means that for some constant.

3

Separable Equations | NURI SENSOY

https://nurisensoy.wordpress.com/2013/03/27/seperable-equations

First Order Linear Ordinary Differential Equation. Mart 27, 2013. An equation of the form. Is called a separable equation. Because if it is written in the differential form. Then terms involving each variable may be placed on opposite sides of the equation. Be any antiderivative of. And equation (2) becomes. According to the chain rule,. Consequently, by using this result, we can write equation (4) as. By integrating both sides of the equation (5) with respect to. And the right-hand side with respect to.

4

First Order Linear Ordinary Differential Equation | NURI SENSOY

https://nurisensoy.wordpress.com/2013/03/18/first-order-linear-ordinary-differential-equation

Heat Equation with Dirichlet Boundary Conditions. First Order Linear Ordinary Differential Equation. Mart 18, 2013. First order linear differential equation. The general First Order Linear Ordinary Differential Equation has the form. Our aim is to multiply the equation (1) by a nonzero function. And then the resulting equation is readily integrable. Multiplying the equatin (1) by a nonzero function. Let us try to determine. So that the left hand side of the equation (2) is the derivative of the expression.

5

Young’s Inequality | NURI SENSOY

https://nurisensoy.wordpress.com/2013/02/26/youngs-inequality

Cauchy Problem for The Heat Equation. Heat Equation with Dirichlet Boundary Conditions. Şubat 26, 2013. Are nonnegative real numbers and. Are positive real numbers such that. To prove the inequality, I will firstly give a definition and a proposition. Is convex on an interval. If for any two points. Is differentiable function on. Be two points in. Then it is clear. That (1) holds. Without loss of generality, suppose that. By using the Mean Value Theorem, there exist. Rearranging the last equation, we have.

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Mart 27, 2013. An equation of the form. Is called a separable equation. Because if it is written in the differential form. Then terms involving each variable may be placed on opposite sides of the equation. Be any antiderivative of. And equation (2) becomes. According to the chain rule,. Consequently, by using this result, we can write equation (4) as. By integrating both sides of the equation (5) with respect to. And the right-hand side with respect to. Solve the given differential equation. So that the...

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