Partial Diff Qn: Int Double Integral of u w.r.t x & y

Thread starter fredrick08
Start date May 21, 2009
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In summary, a partial differential equation (PDE) is a mathematical equation involving multiple independent variables and their partial derivatives, used to describe physical systems that vary in space and time. A double integral is a mathematical operation involving integrating a function of two variables over a specific region in the xy-plane, used to calculate volume or area. The main difference between an ordinary differential equation (ODE) and a PDE is the number of independent variables. Solving a PDE using a double integral allows for finding a general solution that satisfies the equation for all values of independent variables. To evaluate a double integral, limits of integration for each variable are determined and integration techniques are used to solve the integral.

May 21, 2009

fredrick08

Homework Statement

latex(int(int(u, x), y));

Homework Equations

The Attempt at a Solution

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May 22, 2009

Mark44

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fredrick08 said:

Homework Statement

latex(int(int(u, x), y));

Homework Equations

The Attempt at a Solution

You don't give us much to go on...

1. What is a partial differential equation (PDE)?

A partial differential equation is a type of mathematical equation that involves multiple independent variables and their partial derivatives. It is used to describe physical systems that vary in space and time, such as heat transfer, fluid mechanics, and quantum mechanics.

2. What is a double integral?

A double integral is a type of mathematical operation that involves integrating a function of two variables over a specific region in the xy-plane. It is represented by the symbol ∫∫ and is used to calculate the volume under a surface or the area of a region in two-dimensional space.

3. What is the difference between an ordinary differential equation (ODE) and a PDE?

The main difference between an ODE and a PDE is the number of independent variables. ODEs involve only one independent variable, while PDEs involve multiple independent variables. Additionally, the derivatives in ODEs are ordinary derivatives, while the derivatives in PDEs are partial derivatives.

4. What is the purpose of solving a partial differential equation using a double integral?

Solving a PDE using a double integral allows us to find a general solution that satisfies the equation for all values of the independent variables. This is useful in physics and engineering, where we want to model and predict the behavior of a system over a range of values.

5. How is a double integral of a function over a region evaluated?

To evaluate a double integral, we first need to determine the limits of integration for each variable. Then, we use integration techniques to solve the integral, such as substitution or integration by parts. Finally, we plug in the limits of integration and solve the resulting expression to obtain the numerical value of the integral.