Fluids, Waves and Optics

This material was developed for the first-year calculus-based, introductory physics courses at the University of Alberta. It contains a richer, more in-depth mathematical treatment of the material than many standard texts for first-year courses and starts with the assumption that the reader is already familiar with basic Newtonian mechanics, the calculus of polynomials and trigonometric and exponential functions.

The book has the following chapters each of which has its own end of chapter problems:

Mathematics - Small angle approximations, complex numbers, complex exponentials, partial derivatives, experimental uncertainties.

Elasticity - Stress, strain, moduli of elasticity, bulk stress, strain and modulus

Fluid Statics - pressure, Pascal's law, measuring pressures, Archimedes' principle

Fluid Dynamics - continuity equation, Bernoulli's equation, Torricelli's law, viscosity, Poiseuille's law, Stokes' law

Simple Oscillations - simple harmonic motion, mass-spring systems, simple and compound pendulums

Damped and Driven Oscillations - damped harmonic motion, damping ratio, driven oscillators, resonance

Waves - types of waves, mathematical description of a wave, waves on a string, acoustic waves, wave power and intensity

Wave Phenomena - principle of superposition, reflection at a boundary, interference, beats, standing waves, the relativistic and non-relativistic doppler effect, shock waves

Optics - laws of reflection and refraction, spherical mirrors, thin lenses

Optical Instruments - lensmaker’s equation, compound microscope, simple telescope, spherical and chromatic aberrations

Light Waves - Huyghens' principle, dispersion, polarization, thin film interference, diffraction, diffraction gratings

Introduction to Quantum Mechanics - atomic spectra, blackbody spectrum, photoelectric effect, Bohr atom, de Broglie wavelength, Schrodinger equation

In addition, there are two appendices which cover some of the more mathematically challenging topics in detail:

Wave Equations - derivation and general solution of the partial differential wave equation, derivation of the pressure and displacement wave equation for acoustic waves

Blackbody Spectrum - 2D and 3D standing waves, density of states for a cavity, calculation of Planck's spectrum, derivation of Wien's displacement law

This material was developed for the first-year calculus-based, introductory physics courses at the University of Alberta. It contains a richer, more in-depth mathematical treatment of the material than many standard texts for first-year courses and starts with the assumption that the reader is already familiar with basic Newtonian mechanics, the calculus of polynomials and trigonometric and exponential functions.

The book has the following chapters each of which has its own end of chapter problems:

Mathematics - Small angle approximations, complex numbers, complex exponentials, partial derivatives, experimental uncertainties.

Elasticity - Stress, strain, moduli of elasticity, bulk stress, strain and modulus

Fluid Statics - pressure, Pascal's law, measuring pressures, Archimedes' principle

Fluid Dynamics - continuity equation, Bernoulli's equation, Torricelli's law, viscosity, Poiseuille's law, Stokes' law

Simple Oscillations - simple harmonic motion, mass-spring systems, simple and compound pendulums

Damped and Driven Oscillations - damped harmonic motion, damping ratio, driven oscillators, resonance

Waves - types of waves, mathematical description of a wave, waves on a string, acoustic waves, wave power and intensity

Wave Phenomena - principle of superposition, reflection at a boundary, interference, beats, standing waves, the relativistic and non-relativistic doppler effect, shock waves

Optics - laws of reflection and refraction, spherical mirrors, thin lenses

Optical Instruments - lensmaker’s equation, compound microscope, simple telescope, spherical and chromatic aberrations

Light Waves - Huyghens' principle, dispersion, polarization, thin film interference, diffraction, diffraction gratings

Introduction to Quantum Mechanics - atomic spectra, blackbody spectrum, photoelectric effect, Bohr atom, de Broglie wavelength, Schrodinger equation

In addition, there are two appendices which cover some of the more mathematically challenging topics in detail:

Wave Equations - derivation and general solution of the partial differential wave equation, derivation of the pressure and displacement wave equation for acoustic waves

Blackbody Spectrum - 2D and 3D standing waves, density of states for a cavity, calculation of Planck's spectrum, derivation of Wien's displacement law