Oscillations and Waves: An Introduction

Author:            Richard Fitzpatrick

Publisher:         CRC Press, Taylor & Francis Group

Publication Date:  January 7th, 2013

ISBN:              978-1-4665-6608-8

Bridging lower-division physics survey courses with upper-division physics courses, Oscillations and Waves: An Introduction develops a unified mathematical theory of oscillations and waves in physical systems. Emphasizing physics over mathematics, the author includes many examples from discrete mechanical, optical, and quantum mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; and electromagnetic waves.
Assuming familiarity with the laws of physics and college-level mathematics, the book focuses on oscillations and waves whose governing differential equations are linear. The author covers aspects of optics that crucially depend on the wave-like nature of light, such as wave optics. He also introduces the conventional complex representation of oscillations and waves later in the text during the discussion of quantum mechanical waves. This helps students thoroughly understand how to represent oscillations and waves in terms of regular trigonometric functions before using the more convenient, but much more abstract, complex representation.
Based on the author's longstanding course at the University of Texas at Austin, this classroom-tested text helps students acquire a sound physical understanding of wave phenomena. It eases students' difficult transition between lower-division courses that mostly encompass algebraic equations and upper-division courses that rely on differential equations.

1. Simple Harmonic Oscillation. Mass on a Spring; Simple Harmonic Oscillator Equation; LC Circuits; Simple Pendula; Compound Pendula; Exercises.

2. Damped and Driven Harmonic Oscillation.. Damped Harmonic Oscillation; Quality Factor; LCR Circuits; Driven Damped Harmonic Oscillation; Driven LCR Circuits; Transient Oscillator Response; Exercises.

3. Coupled Oscillations. Two Spring-Coupled Masses; Two Coupled LC Circuits; Three Spring-Coupled Masses; Exercises.

4. Transverse Standing Waves. Normal Modes of a Beaded String; Normal Modes of a Uniform String; General Time Evolution of a Uniform String; Exercises.

5. Longitudinal Standing Waves. Spring-Coupled Masses; Longitudinal Waves on a Thin Elastic Rod; Sound Waves in an Ideal Gas; Fourier Analysis; Exercises.

6. Traveling Waves. Standing Waves in a Finite Continuous Medium; Traveling Waves in an Infinite Continuous Medium; Wave Interference; Energy Conservation; Transmission Lines; Normal Reflection and Transmission at Interfaces; Electromagnetic Waves; Doppler Effect; Wave Propagation in Inhomogeneous Media; Exercises.

7. Multi-Dimensional Waves. Plane Waves; Three-Dimensional Wave Equation; Cylindrical Waves; Spherical Waves; Oscillation of an Elastic Sheet; Polarization of Electromagnetic Waves; Laws of Geometric Optics; Fresnel Relations; Total Internal Reflection; Sound Waves in Fluids; Exercises.

8. Wave Pulses. Fourier Transforms; General Solution of 1D Wave Equation; Bandwidth; Exercises.

9. Dispersive Waves. Pulse Propagation; Electromagnetic Waves in Unmagnetized Plasmas; Faraday Rotation; Electromagnetic Wave Propagation in Conductors; Waveguides; Pulse Propagation in Two Dimensions; Gravity Waves; Wave Drag on Ships; Ship Wakes; Capillary Waves; Exercises.

10. Wave Optics. Introduction; Two-Slit Interference; Coherence; Multi-Slit Interference; Thin Film Interference; One-Dimensional Fourier Optics; Single-Slit Diffraction; Multi-Slit Diffraction; Two-Dimensional Fourier Optics; Exercises.

11. Wave Mechanics. Introduction; Photoelectric Effect; Electron Diffraction; Representation of Waves via Complex Numbers; Schrodinger's Equation; Probability Interpretation of Wavefunction; Wave Packets; Heisenberg's Uncertainty Principle; Wavefunction Collapse; Stationary States; Three-Dimensional Wave Mechanics; Particle in Finite Square Potential Well; Square Potential Barrier; Exercises.

A. Physical Constants.

B. Useful Mathematrics. Calculus; Series Expansions; Trigonometric Identities.

C. Electromagnetic Theory.

Bibliography.