Description
This assignment for APM3701 explores various physical problems modeled using partial differential equations. Question 1 deals with the heat equation in a rod with changing boundary conditions, focusing on formulating the problem and proving uniqueness and comparison principles. Question 2 explores the motion of a semi-infinite vibrating string, using the method of odd extension and d’Alembert’s formula. Question 3 models heat flow in a cylinder using the radial form of the heat equation in cylindrical coordinates, solved using separation of variables and Bessel functions. Question 4 discusses the wave equation on a circular membrane, applying separation of variables in polar coordinates, leading to solutions involving Bessel functions and trigonometric modes. The assignment emphasizes practical applications, mathematical formulation, and solution techniques using foundational PDE methods.
Reviews
There are no reviews yet.