Solution of Laplace’s Equation

Solution of Laplace’s Equation
In this lecture we discuss the solution of Laplace’s equation by using the method of separation of variables. The Laplace equation is written as:
The following examples explain how to find the solution.
Solution of Laplace’s Equation
In this lecture we discuss the solution of Laplace’s equation by using the method of separation of variables. The Laplace equation is written as:
The following examples explain how to find the solution.
Example 1: Solve the Laplace’s equation by the method of separation of variables

Solution : Assume the solution is


Solution of Laplace’s Equation
In this lecture we discuss the solution of Laplace’s equation by using the method of separation of variables. The Laplace equation is written as:
The following examples explain how to find the solution.
Example 1: Solve the Laplace’s equation by the method of separation of variables

Solution : Assume the solution is







Either








Example 2: Solve the Laplace’s equation by the method of separation of variables

Solution :





















Example 3: Solve the Laplace’s equation by the method of separation of variables

Solution :
















H.W: Apply the method of separation of variables to solve Laplace’s equation