1 Answer
#### **Solution:**
- A **Partial Differential Equation (PDE)** is a type of differential equation that contains **partial derivatives** (derivatives with respect to more than one variable).
- PDEs are used in physics, engineering, and applied sciences to describe systems involving multiple changing variables.
#### **Example:**
- The heat equation, which describes the flow of heat in a material, is a PDE:
\[
\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}
\]
where:
- \( u(x,t) \) is the temperature at position \( x \) and time \( t \).
- \( k \) is a constant.
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- A **Partial Differential Equation (PDE)** is a type of differential equation that contains **partial derivatives** (derivatives with respect to more than one variable).
- PDEs are used in physics, engineering, and applied sciences to describe systems involving multiple changing variables.
#### **Example:**
- The heat equation, which describes the flow of heat in a material, is a PDE:
\[
\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}
\]
where:
- \( u(x,t) \) is the temperature at position \( x \) and time \( t \).
- \( k \) is a constant.
---