Mechanical Engineering Analysis

This section features assignments/projects from the ME 564 and ME 565 sequence at the University of Washington under Professor Steve Brunton. These projects combine powerful computational techniques and engineering analysis within the realm of fluid mechanics, elasticity and vibrations, weather and climate systems, epidemiology, space mission design, and applications in control.

Chaos Dynamics.pdf

Chaos Dynamics

The significance of these problems lies in their application to real-life scenarios. Understanding the stability and behavior of dynamical systems, such as the Lorenz system and the Van der Pol oscillator, is crucial in fields like physics, engineering, and biology, as it allows for predicting and controlling the behavior of complex systems. Additionally, numerical methods for solving differential equations, such as the Runge-Kutta method and derivative approximation, are essential tools for simulating and analyzing real-world phenomena when analytical solutions are not available or practical to obtain.

Software Used: MATLAB

Assignment 2.pdf

Real World Applications of Differential Equations

These problems involve solving second-order differential equations, analyzing long-term system behavior, transforming equations into different forms, and exploring the dynamics of coupled systems. These exercises are significant as they provide practical applications in fields like physics and engineering, where understanding differential equations and their solutions is essential for stability analysis, control systems, vibrations, and simplifying complex systems. The optional recreational problem of boat pursuit demonstrates the use of differential equations in solving real-world scenarios and developing problem-solving skills.

Software Used: MATLAB