PurdueX: Mathematics of Waves: Visualized with Neural Networks

PurdueX: Mathematics of Waves: Visualized with Neural Networks

by Purdue University

Waves and Oscillatory Systems: A Neural Network Approach

Course Description

Welcome to an innovative and groundbreaking course that will revolutionize your understanding of waves and oscillatory systems! This intermediate-level engineering course, offered by PurdueX, takes a unique approach to studying waves by unifying various physical phenomena through the lens of neural networks. Over two intensive weeks, you'll explore the fascinating world of oscillators and waves, gaining insights that bridge the gap between seemingly disparate fields of physics.

What Students Will Learn

  • A unified perspective on diverse oscillatory systems, from mechanical springs to quantum spins
  • How to visualize complex mathematical structures using neural network-like representations
  • The formation and behavior of wave systems through coupled oscillators
  • Concepts of dispersion relation and group velocity in wave propagation
  • Quantitative calculation techniques for waves generated by various sources
  • Applications of wave theory in acoustic, quantum, and electromagnetic systems

Prerequisites

To fully benefit from this course, students should have a solid foundation in:

  • Elementary linear algebra
  • Differential equations

Additionally, a basic understanding of physics concepts would be advantageous.

Course Content

Week 1: Oscillators

  • Mathematical and conceptual framework for oscillatory systems
  • Exponential and oscillatory responses
  • Various oscillator examples (mechanical, electrical, ferromagnets, quantum spins)
  • Impulse response and sinusoidal excitation

Week 2: Waves

  • Transition from oscillators to waves
  • Normal modes in wave systems
  • Applications in transmission lines and musical instruments
  • Electromagnetic waves and dipole antennas

Who This Course Is For

  • Engineering students looking to deepen their understanding of wave phenomena
  • Physics enthusiasts interested in a unified approach to oscillatory systems
  • Professionals in fields such as acoustics, electronics, or quantum mechanics seeking a fresh perspective
  • Anyone curious about the underlying connections between different types of waves in nature

Real-World Applications

  • Acoustic engineering for improved sound systems and noise control
  • Antenna design for better wireless communication systems
  • Quantum computing and information processing
  • Seismology and geophysics for earthquake prediction and analysis
  • Medical imaging technologies utilizing wave properties
  • Optical systems and photonics engineering
  • Materials science and nanotechnology

Detailed Syllabus

Week 1: Oscillators

  1. Math and the Physical World
  2. Exponential Response
  3. Oscillatory Response
  4. More Oscillator Examples
  5. Impulse Response
  6. Sinusoidal Excitation

Week 2: Waves

  1. Oscillators to Waves
  2. Normal Modes
  3. Tx Lines and Guitars
  4. Dipole Antenna

Join us on this exciting journey to uncover the hidden unity behind the waves that shape our world!

Similar Courses
Course Page   PurdueX: Mathematics of Waves: Visualized with Neural Networks