To develop a unified mathematical theory of oscillations and waves in physical systems.
Simple and Damped Simple Harmonic Oscillation:
Mass-Spring System, Simple Harmonic Oscillator Equation, Complex Number Notation, LC Circuit, Simple Pendulum, Quality Factor, LCR Circuit.
Forced Damped Harmonic Oscillation:
Steady-State Behavior, Driven LCR Circuit, Transient Oscillator Response, Resonance.
Two Spring-Coupled Masses, Two Coupled LC Circuits, Three Spring Coupled Masses, Normal Modes, Atomic and Lattice Vibrations.
Transverse Standing Waves, Normal Modes, General Time Evolution of a Uniform String, Phase velocity, Group Velocity.
Spring Coupled Masses, Sound Waves in an Elastic Solid, Sound Waves in an Ideal Gas.
Standing Waves in a Finite Continuous Medium, Traveling Waves in an Infinite Continuous Medium, Energy Conservation, Transmission Lines, Reflection and Transmission at Boundaries, Electromagnetic Waves.
Fourier Series and Fourier Transforms, Bandwidth, Heisenberg’s Uncertainty Principle.
Plane Waves, Three-Dimensional Wave Equation, Laws of Geometric Optics, Waveguides, Cylindrical Waves.
Interference and Diffraction of Waves:
Double-Slit Interference, Single-Slit Diffraction.