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, Pascals law, measuring pressures, Archimedes principle
Fluid Dynamics - continuity equation, Bernoullis equation, Torricellis law, viscosity, Poiseuilles 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 - lensmakers 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 Plancks spectrum, derivation of Wiens displacement law
