Office of the Registrar
Faculty of Science (2017/2018)
11.10 Physics and Physical Oceanography

Physics courses are designated by PHYS.

1020

Introductory Physics I

is an algebra-based introduction to Newtonian mechanics. Topics covered include motion in one and two dimensions, Newton’s laws, momentum, energy and work, and rotational motion. Previous exposure to physics would be an asset but is not essential.

CO: Mathematics 1090 or 109B

CR: PHYS 1050

LH: 3; six laboratory sessions per semester

OR: tutorial sessions may be held on weeks when no laboratory is scheduled

PR: Level III Advanced Mathematics or Mathematics 1090 or 109B and Science 1807. It is recommended that students have completed at least one of level II and level III high school physics courses

1021

Introductory Physics II

is an algebra-based introduction to oscillations, fluids, wave motion, electricity and magnetism, and circuits.

LH: 3; normally there will be six laboratory sessions per semester

OR: tutorial sessions may be held on weeks when no laboratory is scheduled

PR: PHYS 1020 or 1050, Mathematics 1090 or 109B or 1000, Science 1807

1050

General Physics I: Mechanics

is a calculus-based introduction to mechanics. The course emphasizes problem solving, beginning with a review of vectors and one-dimensional kinematics. The main part of the course covers motion in two dimensions, forces and Newton’s Laws, energy, momentum, rotational motion and torque, and finally oscillations. For details regarding recommendations for students taking PHYS 1050, see Note 4 under Physics and Physical Oceanography.

CO: Mathematics 1000

CR: PHYS 1020

LH: 3

PR: Mathematics 1000 and Science 1807

1051

General Physics II: Oscillations, Waves, Electromagnetism

is a calculus-based introduction to oscillations, wave motion, and electromagnetism. Topics include: simple harmonic motion; travelling waves, sound waves, and standing waves; electric fields and potentials; magnetic forces and fields; electric current and resistance; and electromagnetic waves.

CO: Mathematics 1001

LH: 3

PR: PHYS 1050, or 1021, or 1020 (with a minimum grade of 70%), Mathematics 1001, Science 1807

2053

Fluids and Thermodynamics

introduces the student to basic concepts in fluid statics and dynamics as well as the fundamental concepts in thermal physics: kinetic theory, the laws of thermodynamics, thermodynamic processes, entropy, and heat engines and refrigerators.

CO: Mathematics 1001 and PHYS 1051 (or PHYS 1021 with a minimum grade of 70%)

LH: 3

PR: Mathematics 1001 and PHYS 1051 (or PHYS 1021 with a minimum grade of 70%), Science 1807

2055

Electricity and Magnetism

builds upon the concepts of electric and magnetic forces and fields, Gauss's Law, electric potential and electromagnetic induction introduced in PHYS 1051, expanding them to introduce capacitance, their application in DC and AC circuits, electromagnetic waves, wave optics, and geometric optics.

CO: Mathematics 2000

LH: 3

PR: Mathematics 2000, PHYS 1051, Science 1807

2151

Stellar Astronomy and Astrophysics

introduces concepts in modern astronomy including: the celestial sphere, eclipses, parallax, and Kepler's laws; radiation; the Sun; spectroscopy; telescopes, resolution, and detectors; magnitudes, spectral classifications, and the Hertzsprung-Russell diagram; the interstellar medium, star formation, stellar evolution, nucleosynthesis, white dwarfs, neutron stars, pulsars, nebulae, supernovae, black holes, and gamma-ray bursts; galaxies, dark matter, and active galactic nuclei; cosmology, the cosmic microwave background, inflation and dark energy; and the search for extraterrestrial intelligence.

PR: 6 credit hours in Mathematics courses at the first year level

2300

Introductory Physical Oceanography

(same as Ocean Sciences 2300) provides an introduction to general oceanography with a primary focus on physical oceanography. Topics include how oceans form and evolve on a planetary scale. Ocean characteristics studied include: the properties of seawater; elementary dynamics of fluids on the rotating Earth; ocean circulation; wind-forcing in the ocean; tides and waves. Contemporary methods used in oceanographic study are covered including satellite oceanography. Interactions that occur between physical and chemical processes and biological activity are reviewed.

CR: Environmental Science 2371, Ocean Sciences 2300

PR: 6 credit hours in any first-year courses in Physics

2750

Modern Physics

explores the fundamental ideas that are still driving technological developments. Einstein's theory of special relativity, and the microscopic world described by quantum physics are introduced through crucial historical observations. The course covers the dual nature of light and particles, quantum well and quantum tunneling phenomena, which play a key role in modem electronics. Atomic and nuclei structure, and elementary particles are also described.

CO: Mathematics 1001; PHYS 1051

CR: PHYS 2056

PR: Mathematics 1001; PHYS 1051 (or PHYS 1021 with a minimum grade of 70%)

2820

Computational Mechanics

introduces computational methods in the context of Newtonian mechanics. Numerical differentiation and integration, numerical solutions to differential equations and data analysis are applied to projectile motion, N-body systems, oscillations and problems from astrophysics and geophysics. Implementation of numerical methods using computer programming is emphasized.

CO: Mathematics 2000

LH: 2

PR: Mathematics 2000 and PHYS 1051

3000

Physics of Device Materials

is an introduction to the physics of materials, particularly group IV and III-V semiconductors, used in common technological devices. It covers fundamental concepts including structures of crystalline solids, quantum mechanics and statistical mechanics of charge carriers, equilibrium charge carrier concentrations, carrier transport and excess carrier phenomena. These concepts are applied to multi-material devices including pn and metal semiconductor junctions, metal-oxide-semiconductor field-effect transistors, photovoltaic devices, light-emitting diodes, and solid-state lasers.

PR: PHYS 1051

3150

Astrophysics I

covers macroscopic and microscopic physics related to stellar structure, energy production, and evolution. This includes stellar observables, gravity and other forces, the Virial Theorem, light and matter in stars, stellar spectra and classification, Hertzsprung-Russell diagrams and properties of main sequence dwarf stars, radiation in the stellar atmosphere, structural relationships and stellar models, energy sources and energy transport in stars, star formation and stellar evolution, nucleosynthesis, variable stars, Chandrasekhar’s limit, and degenerate remnants.

CR: PHYS 3160

PR: PHYS 2053, 2750 (or 2056), and 2820

3151

Astrophysics II

deals with galactic and cosmological scale astrophysics. Topics include: galaxies including Hubble classification, dark matter, and structure of the Milky Way Galaxy; globular and open star clusters; compact objects including compact binary systems, novas and supernovas, pulsars and magnetars, X-ray binaries; black holes, active galactic nuclei, quasars, the Lyman forest, and the Gunn-Peterson trough; and cosmology including the cosmic microwave background, the FLRW metric, the Friedmann equations, cosmological expansion, and dark energy.

CR: PHYS 3160

PR: PHYS 3150 and 3220

3220

Classical Mechanics I

covers vector operations, coordinate transformations, derivative of vectors, Newton’s laws, differential equations, kinematics and dynamics of a particle, linear and quadratic air resistance, terminal velocity, momentum of a time varying mass, center of mass systems, angular momentum, moment of inertia, energy, work-energy theorem, forces as the gradient of potential energy, time dependent potential energy, curvilinear one-dimensional systems, energy of a multiparticle system, calculus of variations, and Lagrangian Dynamics.

CO: PHYS 2820, Mathematics 2260 and 3202

PR: PHYS 2820, Mathematics 2260 and 3202

3230

Classical Mechanics II

covers noninertial frames of reference, Newton's second law in a rotating frame, centrifugal force, Coriolis force, motion of rigid bodies, center of mass, rotation about a fixed axis, rotation about any axis, inertia tensor, Euler's equations with zero torque, coupled oscillators, chaos theory, bifurcation diagrams, state-space orbits, Poincare sections, Hamiltonian dynamics, ignorable coordinate, phase-space orbits, Liouville's theorem, scattering angle, impact parameter, differential scattering cross section, and Rutherford scattering.

CO: Mathematics 3202

PR: PHYS 3220, Mathematics 2260 and 3202

3300

Intermediate Physical Oceanography

provides a physics-based introduction to both dynamical and descriptive physical oceanography. Topics include properties of seawater, geostrophy, conservation equations, wind-forced dynamics, large-scale ocean circulation and waves and tides. A survey of analytical, observational, numerical, and laboratory approaches is presented.

PR: PHYS 2053 and Mathematics 2000 or registration in Academic Term 5 of the Ocean and Naval Architectural Engineering program

3340

Principles of Environmental Physics

applies basic physical principles to the environment of the Earth with a focus on problem solving and developing physical understanding. Key topics to be covered include the climate system and climate change, energy production and use, and the role of science in guiding public decision-making.

PR: Mathematics 2000 and PHYS 2053

3400

Thermal Physics

covers central concepts in thermodynamics and statistical mechanics, including temperature, entropy, the laws of thermodynamics, the Einstein model of solids, paramagnetism, Helmholtz and Gibbs free energies, chemical potential, thermodynamic identities, Boltzmann statistics, the partition function, and quantum statistics.

PR: Mathematics 2000, PHYS 2053 and PHYS 2750 or (2056)

3500

Electromagnetic Fields I

examines the laws of electrostatic and magnetostatic fields based on vector calculus and a local formulation. Topics covered include Gauss's law,potentials, energy and work, the multipole expansion, Laplace's equation and boundary conditions, linear dielectrics, electric polarization, electric displacement, capacitance. magnetic fields B and H. vector potentials, Lorentz force, magnetization and Maxwell's equations.

CR: Engineering 5812

PR: PHYS 2055 and Mathematics 3202

3550

Electric Circuits

covers circuit elements. Simple resistive circuits. Techniques of circuit analysis. Topology in circuit analysis. Operational amplifiers. Reactive circuit elements. Natural response and step response of RL, RC and RLC circuits. Circuits driven by sinusoidal sources. Mutual inductance. Series and parallel resonance. Laplace transforms in the analysis of frequency response.

CO: Mathematics 2260

CR: Engineering 3821

LC: 6

LH: 6

PR: Mathematics 2050, Mathematics 2260 or (the former Mathematics 3260), PHYS 2055

3551

Analogue Electronics

- inactive course.

3600

Optics and Photonics I

covers topics in geometrical and physical optics and applications of associated phenomena, principles, and concepts to photonics. Topics include geometrical optics (thin lenses, mirrors, and optical instruments), physical optics (two-beam and multiple-beam interference, Fraunhofer diffraction, reflection, transmission, and polarization), and applications (fibre-optic light guides, modulation of light waves, and optical communication systems).

PR: Mathematics 2000 and PHYS 2055

3750

Quantum Physics I

introduces the foundational techniques that are required to understand the physics of atoms and molecules. Beginning with the wave-particle duality of nature, the wave function and the time-independent Schrodinger equation, techniques to calculate wave functions and macroscopic observables in simple one-dimensional models are covered. The three-dimensional hydrogen atom, the simplest real-life system that allows for a quantitative quantum description, is then examined in detail.

CO: Mathematics 2000. PHYS 3220 is recommended.

PR: PHYS 2750 (or 2056 or CHEM 2302). PHYS 3220 is recommended.

3751

Quantum Physics II

is an introduction to the physics of elementary particles. After a brief overview of special relativity and non-relativistic quantum mechanics. this course covers relativistic quantum mechanics (KleinGordon and Dirac equations, antiparticles, spin, transition probability, and Feynman diagrams) and particle physics (leptons and quarks, strong and weak interaction, conservation laws, and the standard model of elementarv particles).

PR: PHYS 3750

3800

Computational Physics

is a project-based course that trains students to become functional in computational methods by writing and compiling computer code (C/Fortran) in a Unix environment to solve problems from different areas of physics. Students complete one or more projects that introduce students to a particular class of numerical methods. Lectures and tutorials cover the theory that underlies the computational methods and background for code development and the application of the required numerical methods.

LH: 2

PR: Computer Science 1510, or 1001, or Engineering 1020 (or other computer programming course as approved by the instructor). PHYS 2820, Mathematics 2260 (or the former Mathematics 3260), and Mathematics 3202

3810

Mathematical Analysis

- inactive course.

3820

Mathematical Physics I

focuses on applications of mathematical techniques to solve problems in physics. Vectors, vector calculus, matrices and tensors, coordinate systems and transformations, and summation notation are reviewed. Topics in complex numbers, functions and calculus are introduced, including branch cuts, differentiation, integration, Cauchy formula, series, residue theorem, and the gamma function. Other topics include differential equations using series solutions and separation of variables, and Fourier series of real and complex functions.

PR: Mathematics 2260 (or the former Mathematics 3260), and Mathematics 3202

3900

Experimental Physics I

develops experimental, analytical, and communications skills through extended experiments in fields of physics including optics, magnetism, fluids, spectroscopy, materials characterization, and modern physics. Students select from a range of experiments that illustrate concepts encountered in previous courses to apply existing knowledge and problem solving skills, while other experiments introduce more advanced techniques and phenomena.

CR: PHYS 4880

LC: 0

LH: 6

PR: at least two of PHYS 2053, 2820, 2055, PHYS 2750 (or 2056), Science 1807

4000

Solid State Physics

focuses on the relation between structure and physical properties in crystalline materials. An introduction to crystal structure addresses symmetry and reciprocal space. Phonons and lattice vibrations are linked with thermal properties of solids. Electrons in solids, including energy bands and semiconductors, lead to discussions of transport in solids.

PR: PHYS 3400 and 3750

4200

Classical Mechanics III

- inactive course.

4205

Introduction to Fluid Dynamics

(same as Mathematics 4180) covers basic observations, mass conservation, vorticity, stress, hydrostatics, rate of strain, momentum conservation (Navier-Stokes equation), simple viscous and inviscid flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's theorems, potential flows, water waves, thermodynamics.

CR: Mathematics 4180

PR: PHYS 3220 and either Mathematics 4160 or the former PHYS 3821 or waiver approved by the instructor

4210

Continuum Mechanics

- inactive course.

4220

Introduction to general Relativity

(Mathematics 4130) studies both the mathematical structure and physical content of Einstein’s theory of gravity. Topics include the geometric formulation of special relativity, curved spacetimes, metrics, geodesics, causal structure, gravity as spacetime curvature, the weak-field limit, geometry outside a spherical star, Schwarzschild and Kerr black holes, Robertson-Walker cosmologies, gravitational waves, an instruction to tensor calculus, Einstein’s equations, and the stress-energy tensor.

CO: Mathematics 4230

CR: Mathematics 4130

PR: Mathematics 3202 and one of PHYS 3220, Mathematics 4230 or waiver approved by the instructor

4300

Advanced Physical Oceanography

covers dynamical physical oceanography. The equations of motion in oceanography are derived and analysed. Topics include.geostrophy, conservation equations, linear and non-linear wave theory, and open ocean and shelf circulation dynamics.

PR: PHYS 3300 and 3820

4330

Topics in Physical Oceanography

- inactive course.

4340

Modelling in Environmental Physics

covers the basic principles underlying environmental modelling. Techniques for numerical modelling are introduced with applications to simulation of terrestrial, atmospheric and oceanic environments. Concepts and principles of free and forced dynamical systems are introduced and applied to the analysis and interpretation of simplified climate and environment model simulations. Includes some discussion of dynamics and transition to chaos in environmental systems, uncertainty in their simulations and predictability of future environmental and climate changes.

PR: PHYS 3340 and PHYS 3820 or waiver approved by the instructor

4400

Statistical Mechanics

covers ensembles. Classical and quantum statistical mechanics. Statistical mechanics of phase transitions. Advanced topics in statistical mechanics.

CO: PHYS 3750

PR: PHYS 3400 and 3750

4500

Electromagnetic Fields II

covers electrodynamics and the applications of Maxwell's equations. Topics covered include electrodynamics (Maxwell's equations and boundary conditions), conservation laws (continuity equation, Poynting's theorem, and momentum conservation), electromagnetic waves {wave properties, reflection and transmission, absorption and dispersion, guided waves), radiation {potential and fields, dipole radiation, and radiation from point charges), and relativistic electrodynamics. Selected topics in electrodynamics and applied electromagnetism may be introduced.

CR: Engineering 6813

PR: PHYS 3500 and 3820

4600

Optics and Photonics II

covers principles of lasers, interactions of laser light and matter, and new developments in the fields of optics and photonics. Topics include wave optics, optical resonators, interaction of radiation and atomic systems, principles and techniques of lasers, nonlinear optics and devices, guided-wave optics, and fibre-optic communication. Recent development in the fields, such as photonic crvstal optics, ultrafast optics, and nano-optics will be introduced.

PR: PHYS 3500 and 3600

4700

Atomic and Molecular Physics

- inactive course.

4710

Nuclear Physics

- inactive course.

4820

Mathematical Physics II

covers topics on the common partial differential equations of Mathematical Physics and boundary value problems; Sturm-Liouville theory, introduction to the theory of distributions, Dirac delta function, Laplace and Fourier transforms, Green’s functions, Bessel functions, Legendre functions, spherical harmonics, and other topics such as group theory.

PR: PHYS 3820 or all of Mathematics 2051, 2260, 3202, 3210

4850

Quantum Mechanics

is a mathematically-based course that covers: the postulates of quantum mechanics; Hermitian operators; x, p and matrix representations of quantum mechanics; the harmonic oscillator; spin and orbital angular momentum and addition of angular momentum; stationary perturbation theory; time dependent perturbation theory.

PR: PHYS 3750 and 3820

4851

Advanced Quantum Mechanics

is a continuation of PHYS 4850 that covers: density operators; unitary operators, including symmetry operations and the time-evolution operator; gauge transformations and Berry's phase; quantum mechanical entanglement; systems of identical particles.

PR: PHYS 4820 and 4850

4852

Quantum Information and Computing

(same as Mathematics 4252) covers postulates of quantum mechanics, matrix theory, density matrices, qubits, qubit registers, entanglement, quantum gates, superdense coding, quantum teleportation, quantum algorithms, open systems, decoherence, physical realization of quantum computers.

CR: Mathematics 4252

PR: Mathematics 2051 or PHYS 3820

4900

Experimental Physics II

builds on the skills developed in Experimental Physics I through advanced and open-ended experiments in fields of physics including optics, magnetism, fluids, spectroscopy, materials characterization, and modern physics.

LC: 0

LH: 6

PR: PHYS 3900, Science 1807

490A/B

Honours Physics Thesis

is required of the Honours program.

6317

Underwater Acoustics

covers basic theory of sound, sound in the ocean environment, wave equation, ray tracing, sonar system operation, transducers, applications.

PR: PHYS 3810 (or the former Mathematics 3220) and 3220, or waiver approved by the instructor

6318

Ocean Climate Modelling

covers numerical techniques, finite difference, finite element and spectral methods. Introduction to the climate system. Ocean climate models. Box models. Variability on interdecadal, centennial and geological scales. Zonally averaged models. 3-D ocean modelling. Thermohaline circulation. General circulation models. Climate modelling and global warming.

PR: PHYS 3810 (or Mathematics 3202), PHYS 3300 and the completion of any 15 credit hours in core courses at the 3000 or 4000 level in the Faculty of Science or waiver approved by the instructor

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).