Name: APM3701 Assignment 02 FULL ANSWERS AND CALCULATIONS SHOWN (08 AUGUST 2025) - StudyPass
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APM3701 Assignment 02 FULL ANSWERS AND CALCULATIONS SHOWN (08 AUGUST 2025)

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This assignment covers key concepts in partial differential equations, including heat and wave equations. It includes real-world applications like vibrating strings, heat transfer in cylindrical objects, and membrane motion. Each question is solved step by step with clear explanations using methods from the study guide and prescribed textbook.

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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.