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Program Requirements
Required Courses (46 credits)

ATOC 214 Introduction: Physics of the Atmosphere (3 credits)
Overview
Atmospheric & Oceanic Sciences : An introduction to physical meteorology designed for students in the physical sciences. Topics include: composition of the atmosphere; heat transfer; the upper atmosphere; atmospheric optics; formation of clouds and precipitation; instability; adiabatic charts.
Terms: Fall 2010
Instructors: Eyad Hashem Atallah, John Richard Gyakum (Fall)
 Fall
 3 hours lecture
 Prerequisite: CEGEP Physics

ATOC 215 Oceans, Weather and Climate (3 credits)
Overview
Atmospheric & Oceanic Sciences : Laws of motion, geostrophic wind, gradient wind. General circulation of the atmosphere and oceans, local circulation features. Airsea interaction, including hurricanes and seaice formation, extratropical weather systems and fronts, role of the atmosphere and oceans in climate.
Terms: Winter 2011
Instructors: Man K Yau (Winter)
 Winter
 3 hours lecture
 Prerequisite: ATOC 214

ATOC 309 Weather Radars and Satellites (3 credits)
Overview
Atmospheric & Oceanic Sciences : Basic notions of radiative transfer and applications of satellite and radar data to mesoscale and synopticscale systems are discussed. Emphasis will be put on the contribution of remote sensing to atmospheric and oceanic sciences.
Terms: Winter 2011
Instructors: Frederic Fabry, Gerard Szejwach (Winter)
 Winter
 3 hours lecture
 Prerequisite: ATOC 215

ATOC 315 Water in the Atmosphere (3 credits)
Overview
Atmospheric & Oceanic Sciences : Global distribution of water in the atmosphere. Moist processes. Global and mesoscale precipitation systems. Quantitative forecasting of precipitation. Extreme precipitation events. Largescale influences. Precipitation modification.
Terms: Fall 2010
Instructors: SeokWoo Son (Fall)
 Fall
 3 hours lecture
 Prerequisite: ATOC 214

ATOC 412 Atmospheric Dynamics (3 credits)
Overview
Atmospheric & Oceanic Sciences : Equations of motion in rotating coordinates, elementary applications, circulation and vorticity, the planetary boundary layer, synoptic scale motions, Rossby waves and inertial oscillations.
Terms: Fall 2010
Instructors: David N Straub (Fall)
 Fall
 Prerequisites: MATH 314, MATH 315.

ATOC 540 Synoptic Meteorology 1 (3 credits)
Overview
Atmospheric & Oceanic Sciences : Analysis of current meteorological data. Description of a geostrophic, hydrostatic atmosphere. Ageostrophic circulations and hydrostatic instabilities. Kinematic and thermodynamic methods of computing vertical motions. Tropical and extratropical condensation rates. Barotropic and equivalent barotropic atmospheres.
Terms: Fall 2010
Instructors: Eyad Hashem Atallah (Fall)
 Fall
 2 hours lecture; 2 hours laboratory
 Prerequisite (Undergraduate): Permission of instructor

ATOC 541 Synoptic Meteorology 2 (3 credits)
Overview
Atmospheric & Oceanic Sciences : Analysis of current meteorological data. Quasigeostrophic theory, including the omega equation, as it relates to extratropical cyclone and anticyclone development. Frontogenesis and frontal circulations in the lower and upper troposphere. Cumulus convection and its relationship to tropical and extratropical circulations. Diagnostic case study work.
Terms: Winter 2011
Instructors: Eyad Hashem Atallah (Winter)
 Winter
 2 hours lecture; 2 hours laboratory
 Prerequisite (Undergraduate): ATOC 412 and ATOC 540 or permission of instructor.

ATOC 546 Current Weather Discussion (1 credit)
Overview
Atmospheric & Oceanic Sciences : Halfhour briefing on atmospheric general circulation and current weather around the world using satellite data, radar observations, conventional weather maps, and analyses and forecasts produced by computer techniques.
Terms: Winter 2011
Instructors: Eyad Hashem Atallah (Winter)
 Winter
 2 hours
 Prerequisite (Undergraduate): ATOC 540 or permission of instructor
 Restriction: Graduate students and finalyear Honours Atmospheric Science students. Others by special permission.

COMP 208 Computers in Engineering (3 credits)
Overview
Computer Science (Sci) : Introduction to computer systems. Concepts and structures for high level programming. Elements of structured programming using FORTRAN 90 and C. Numerical algorithms such as root finding, numerical integration and differential equations. Nonnumerical algorithms for sorting and searching.
Terms: Fall 2010, Winter 2011
Instructors: Nathan Friedman, Amin Ranjbar, Amir Hossein Rabbani (Fall) Nathan Friedman, Amir Hossein Rabbani, Seyed Sina Meraji (Winter)
 3 hours
 Prerequisite: differential and integral calculus.
 Corequisite: linear algebra: determinants, vectors, matrix operations.
 Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computations. Credits for either of these courses will not count towards the 60credit Major in Computer Science. COMP 208 cannot be taken for credit with or after COMP 250.

MATH 222 Calculus 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Wilbur Jonsson, Neville G F Sancho (Fall) Wilbur Jonsson (Winter)
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227

MATH 223 Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Terms: Fall 2010, Winter 2011
Instructors: James G Loveys, Hongnian Huang (Fall) James G Loveys (Winter)
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs

MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Wilbur Jonsson (Fall) Wilbur Jonsson (Winter) Charles Roth (Summer)
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248

MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Neville G F Sancho (Fall) JianJun Xu (Winter)
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.

PHYS 230 Dynamics of Simple Systems (3 credits)
Overview
Physics : Translational motion under Newton's laws; forces, momentum, work/energy theorem. Special relativity; Lorentz transforms, relativistic mechanics, mass/energy equivalence. Topics in rotational dynamics. Noninertial frames.
Terms: Fall 2010
Instructors: Hong Guo (Fall)
 Fall
 3 hours lectures
 Prerequisite: CEGEP Physics or PHYS 131.
 Corequisite: MATH 222
 Restriction: Not open to students taking or having passed PHYS 251

PHYS 232 Heat and Waves (3 credits)
Overview
Physics : The laws of thermodynamics and their consequences. Thermodynamics of PVT systems and simple heat engines. Free, driven, and damped harmonic oscillators. Coupled systems and normal modes. Fourier methods. Wave motion and dispersion. The wave equation.
Terms: Winter 2011
Instructors: Dominic Ryan (Winter)
 Winter
 3 hours lectures
 Prerequisites: CEGEP Physics or PHYS 142, and CEGEP chemistry or CHEM 120, and PHYS 230.
 Restriction: Not open to students taking or having passed PHYS 253

PHYS 257 Experimental Methods 1 (3 credits)
Overview
Physics : Introductory laboratory work and data analysis as related to mechanics, optics and thermodynamics. Introduction to computers as they are employed for laboratory work, for data analysis and for numerical computation. Previous experience with computers is an asset, but is not required.
Terms: Fall 2010
Instructors: Bradley Siwick (Fall)
 Fall
 6 hours of laboratory and classroom work
 Corequisite: PHYS 230 or PHYS 251
Complementary Courses (15 credits)
36 credits to satisfy a statistics requirement.
Students usually take MATH 203 or both MATH 323 and MATH 324.

MATH 203 Principles of Statistics 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions).
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: Abbas Khalili Mahmoudabadi, Jose Andres Correa (Fall)
 No calculus prerequisites
 Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar. Students should consult http://www.mcgill.ca/studentrecords/transfercredits/ for information regarding transfer credits for this course.

MATH 323 Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Terms: Fall 2010, Winter 2011, Summer 2011
Instructors: William J Anderson (Fall) Vahid Partovi Nia (Winter)
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2010, Winter 2011
Instructors: Masoud AsgharianDastenaei (Fall) William J Anderson (Winter)
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
3 credits selected from:

PHYS 333 Thermal and Statistical Physics (3 credits)
Overview
Physics : Introductory equilibrium statistical mechanics. Quantum states, probabilities, ensemble averages. Entropy, temperature, Boltzmann factor, chemical potential. Photons and phonons. FermiDirac and BoseEinstein distributions; applications.
Terms: Winter 2011
Instructors: Richard Harris (Winter)
 Winter
 3 hours lectures
 Prerequisite: PHYS 232
 Restriction: Not open to students taking or having passed PHYS 362

PHYS 340 Majors Electricity and Magnetism (3 credits)
Overview
Physics : The electrostatic field and scalar potential. Dielectric properties of matter. Energy in the electrostatic field. Methods for solving problems in electrostatics. The magnetic field. Induction and inductance. Energy in the magnetic field. Magnetic properties of matter. Maxwell's equations. The dipole approximation.
Terms: Fall 2010
Instructors: Robert Rutledge (Fall)
 Fall
 3 hours lectures
 Prerequisites: CEGEP physics or PHYS 142, MATH 222
 Corequisite: MATH 314
 Restriction: Not open to students who have passed PHYS 242 or PHYS 350
69 credits ordinarily selected from the courses below:
* Students may take either ATOC 419 or CHEM 419
** Students may take either PHYS 332 or MATH 555

ATOC 419 Advances in Chemistry of Atmosphere (3 credits) *
Overview
Atmospheric & Oceanic Sciences : Selected areas of atmospheric chemistry from field and laboratory to theoretical modelling are examined. The principles of atmospheric reactions (gas, liquid and heterogeneous phases in aerosols and clouds) and issues related to chemical global change will be explored.
Terms: Winter 2011
Instructors: Parisa A Ariya (Winter)
 Winter
 3 hours lecture
 Prerequisites: CHEM 243, and CHEM 263 or CHEM 213 and CHEM 273, MATH 222 and MATH 315 (or equivalents) or permission of instructor.
 Restriction: Not open to students who have taken CHEM 419, CHEM 619, and ATOC 619
 Offered in odd years. Students should register in CHEM 419 in even years

ATOC 515 Turbulence in Atmosphere and Oceans (3 credits)
Overview
Atmospheric & Oceanic Sciences : Application of statistical and semiempirical methods to the study of geophysical turbulence. Reynolds' equations, dimensional analysis, and similarity. The surface and planetary boundary layers. Oceanic mixed layer. Theories of isotropic two and three dimensional turbulence: energy and enstrophy inertial ranges. Beta turbulence.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Winter
 3 hours lecture
 Prerequisite (Undergraduate): ATOC 512 or permission of instructor

CHEM 419 Advances in Chemistry of Atmosphere (3 credits) *
Overview
Chemistry : Selected areas of atmospheric chemistry from field and laboratory to theoretical modelling are examined. The principles of atmospheric reactions (gas, liquid and heterogeneous phases in aerosols and clouds) and issues related to chemical global change will be explored.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Winter
 3 lectures
 Prerequisites: CHEM 243, and CHEM 263 or CHEM 213 and CHEM 273, MATH 222 and MATH 315 (or equivalents) or permission of instructor.
 Restriction: Not open to students who have taken ATOC 419, CHEM 619, or ATOC 619
 Offered in even years. Students should register in ATOC 419 in odd years.

GEOG 322 Environmental Hydrology (3 credits)
Overview
Geography : Quantitative, experimental study of the principles governing the movement of water at or near the Earth's surface and how the research relates to the chemistry and biology of ecosystems.
Terms: Winter 2011
Instructors: Bernhard Lehner (Winter)
 Winter
 3 hours
 Prerequisite: GEOG 203 or equivalent

GEOG 372 Running Water Environments (3 credits)
Overview
Geography : The course focuses on the physical habitat conditions found in streams, rivers, estuaries and deltas. Based on the laws governing flow of water and sediment transport, it emphasizes differences among these environments, in terms of channel form, flow patterns, substrate composition and mode of evolution. Flooding, damming, channelisation, forestry impacts.
Terms: Fall 2010
Instructors: Michel F Lapointe (Fall)
 Fall
 3 hours
 Prerequisites: GEOG 203 and GEOG 272, or ENVR 200 and ENVR 202

MATH 317 Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Fall 2010
Instructors: Peter Bartello (Fall)
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2011
Instructors: Gantumur Tsogtgerel (Winter)
 Winter
 Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315

MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2010
Instructors: Abbas Khalili Mahmoudabadi (Fall)
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.

MATH 555 Fluid Dynamics (4 credits) **
Overview
Mathematics & Statistics (Sci) : Kinematics. Dynamics of general fluids. Inviscid fluids, NavierStokes equations. Exact solutions of NavierStokes equations. Low and high Reynolds number flow.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Fall
 Prerequisite (Undergraduate): MATH 315 and MATH 319 or equivalent

PHYS 241 Signal Processing (3 credits)
Overview
Physics : Linear circuit elements, resonance, network theorems, diodes, transistors, amplifiers, feedback, integrated circuits.
Terms: Winter 2011
Instructors: Jean Barrette (Winter)
 Winter
 2 hours lectures; 3 hours laboratory alternate weeks
 Prerequisite: CEGEP physics or PHYS 142.

PHYS 331 Topics in Classical Mechanics (3 credits)
Overview
Physics : Forced and damped oscillators, Newtonian mechanics in three dimensions, rotational motion, Lagrangian mechanics, small vibrations, normal modes. Introduction to Hamiltonian mechanics.
Terms: Winter 2011
Instructors: Guillaume Gervais (Winter)
 Winter
 3 hours lectures
 Prerequisite: PHYS 230
 Corequisite: MATH 315
 Restriction: Not open to students having passed PHYS 451 or PHYS 351

PHYS 340 Majors Electricity and Magnetism (3 credits)
Overview
Physics : The electrostatic field and scalar potential. Dielectric properties of matter. Energy in the electrostatic field. Methods for solving problems in electrostatics. The magnetic field. Induction and inductance. Energy in the magnetic field. Magnetic properties of matter. Maxwell's equations. The dipole approximation.
Terms: Fall 2010
Instructors: Robert Rutledge (Fall)
 Fall
 3 hours lectures
 Prerequisites: CEGEP physics or PHYS 142, MATH 222
 Corequisite: MATH 314
 Restriction: Not open to students who have passed PHYS 242 or PHYS 350

PHYS 342 Majors Electromagnetic Waves (3 credits)
Overview
Physics : Maxwell's equations. The wave equation. The electromagnetic wave, reflection, refraction, polarization. Guided waves. Transmission lines and wave guides. Vector potential. Radiation. The elemental dipole; the halfwave dipole; vertical dipole; folded dipoles; Yagi antennas. Accelerating charged particles.
Terms: Winter 2011
Instructors: Michael Hilke (Winter)
 Winter
 3 hours lectures
 Prerequisites: PHYS 340 or PHYS 242, Mathematics MATH 314, MATH 315