# Linear elliptical Differential equation

## in one dimension

1D Elasticity at steady state 1D Mass diffusion at steady state 1D Heat conduction at steady state

# The differential equation:

• $$\dfrac{d\sigma}{dx} + f(x) = 0$$ in $$(0, L)$$

# Introduction

• A method to solve Engineering Problems
• A approximate method

• Strong form
• Weak form

# Video 4

The differential equation:

$$\frac{d\sigma}{dx} + f(x) = 0 \quad in \quad (0, L)$$

• Open interval: Domain between $$x=0 \quad \& \quad x=L$$, excluding endpoints $$x=0 \quad \& \quad x=L$$ themseleves.
• Here boundary conditions either on $$u(x)$$ or on $$u_{,x}$$ at boundary points.