Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


2.003J Dynamics and Control I and 18.075 Advanced Calculus for Engineers

Course Description

This course discusses theoretical concepts and analysis of wave problems in science and engineering. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics, blood flow, nondestructive evaluation, and other applications.

Topics Covered

  1. Sample wave problems and elementary concepts
    • Taut string, elastic rod
    • Shallow-water waves, acoustic waves in a pipe
    • Traffic flow, blood flow in arteries
    • Exponential notation, frequency, wave number, phase velocity, etc.
  2. One-dimensional propagation
    • The wave equation: transient responses, characteristics
    • Dispersion: rod on elastic foundation, flexural waves in a beam
    • Group velocity: dispersion of transient waves, stationary phase
    • Group velocity and energy transport
    • Scattering of harmonic waves, radiation condition
  3. Two-dimensional propagation
    • Plane waves, sound in homogeneous fluids
    • Nearly plane waves, geometrical acoustics
    • P, SV and SH waves in elastic solids
    • Rayleigh waves in half space, Love waves in a layered medium
    • Reflection and refraction from a plane interface, mode conversion
    • Scattering of elastic waves, diffraction, parabolic approximation
    • Waves in an elastic layer
  4. Free-surface and internal gravity waves in fluids
    • Free-surface waves: dispersion relation, group velocity, phase velocity
    • Waves in a current, ship waves
    • Transients due to impulsive forcing
    • Internal waves in a stratified fluid, anisotropic wave propagation
    • Modes in a stratified fluid layer
  5. Waves in periodic media
    • Bloch–Floquet theory
    • Stop bands, pass bands
    • Bragg resonance


The subject is based on the material presented in the lectures. There is no official textbook.


There were 5 problem sets when the course was taught on MIT campus. They are not available here.


There are two quizzes: a mid-term quiz and a final quiz. Both quizzes are take-home. There is no final exam.

Grading Policy

Homework 1/3
Midterm Quiz 1/3
Final Quiz 1/3