| Course Winter Timetable |

APM233Y1
Mathematical Methods in Economics 52L

The application of mathematical techniques to economic analysis. Mathematical topics include linear and matrix algebra, partial differentiation, optimization, Lagrange multipliers, differential equations. Economic applications include consumer and producer theory, theory of markets, macroeconomic models, models of economic growth.
Exclusion: MAT223H, 224H, 235Y, 237Y
Prerequisite: ECO100Y(63%/CGPA 2.5), MAT133Y(60%)/MAT137Y(55%)

APM236H1
Applications of Linear Programming 39L

Introduction to linear programming including a rapid review of linear algebra (row reduction, linear independence), the simplex method, the duality theorem, complementary slackness, and the dual simplex method. A selection of the following topics are covered: the revised simplex method, sensitivity analysis, integer programming, the transportation algorithm.
Exclusion: APM261H, ECO331H
Prerequisite: MAT223H/240H (Note: no waivers of prerequisites will be granted)

APM261H1
Theory and Applications of Linear Programming 39L

Formulation of problems in LP form, convexity and structure of LP constraint sets, simplex algorithm, degeneracy, cycling and stalling, revised method, two-phase method, duality, fundamental theorem, dual algorithm, integer programming, sensitivity analysis, Karmarkar algorithm, network flows, transportation algorithm, two-person zero-sum games.
Exclusion: APM236H, ECO331H
Prerequisite: MAT223H/240H

APM346H1
Differential Equations 39L

Sturm-Liouville problems, Green’s functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.
Prerequisite: MAT235Y/237Y/257Y, 244H

APM351Y1
Partial Differential Equations 78L

Diffusion and wave equations. Separation of variables. Fourier series. Laplace’s equation; Green’s function. Schrödinger equations. Boundary problems in plane and space. General eigenvalue problems; minimum principle for eigenvalues. Distributions and Fourier transforms. Laplace transforms. Differential equations of physics (electromagnetism, fluids, acoustic waves, scattering). Introduction to nonlinear equations (shock waves, solitary waves).
Prerequisite: MAT267H
Co-requisite: MAT334H/354H

APM361H1
Mathematics of Operations Research 39L

Topics selected from applied stochastic processes, queuing theory, inventory models, scheduling theory and dynamic programming, decision methods, simulation. A project based on a problem of current interest taken from course files or the student’s own experience is required.
Prerequisite: APM236H/261H, MAT235Y/237Y, STA250H

APM366H1
Mathematical Methods in Economic and Decision Theory 39L

Convexity, fixed points, stable mappings optimization. Relations orderings and utility functions; choice and decision making by individuals and groups. Non-cooperative and cooperative games, core, Shapley value; market games. Decision making by economic agents: consumers, producers, banks, investors, and financial intermediaries.
Prerequisite: MAT223H/240H, 237Y/257Y
Recommended preparation: A background in ordinary differential equations and statistics
400-SERIES COURSES
NOTE:
Some courses at the 400-level are cross-listed as graduate courses and may not be offered every year. Please see the Department’s undergraduate brochure for more details.

APM421H1
Mathematical Foundations of Quantum 39L

The general formulation of non-relativistic quantum mechanics based on the theory of linear operators in a Hilbert space, self-adjoint operators, spectral measures and the statistical interpretation of quantum mechanics; functions of compatible observables. Schrödinger and Heisenberg pictures, complete sets of observables, representations of the canonical commutative relations; essential self-adjointedness of Schrödinger operators, density operators, elements of scattring theory.
Prerequisite: MAT337H/357H

APM426H1
General Relativity 39L

Einstein’s theory of gravity. Special relativity and the geometry of Lorentz manifolds. Gravity as a manisfestation of spacetime curvature. Einstein’s equations. Cosmological implications: big bang and inflationary universe. Schwarzschild stars: bending of light and perihelion precession of Mercury. Topics from black hole dynamics and gravity waves.
Prerequisite: MAT363H

APM436H1
Fluid Mechanics 39L

Boltzmann, Euler and Navier-Stokes equations. Viscous and non-viscous flow. Vorticity. Exact solutions. Boundary layers. Wave propragation. Analysis of one dimensional gas flow.
Prerequisite: APM351Y

APM441H1
Asymptotic and Perturbation Methods 39L

Asymptotic series. Asymptotic methods for integrals: stationary phase and steepest descent. Regular perturbations for algebraic and differential equations. Singular perturbation methods for ordinary differential equations: W.K.B., strained co-ordinates, matched asymptotics, multiple scales. (Emphasizes techniques; problems drawn from physics and engineering)
Prerequisite: APM346H/351Y, MAT334H

APM446H1
Applied Nonlinear Equations 39L

Nonlinear partial differential equations and their physical origin. Fourier transform; Green’s function; variational methods; symmetries and conservation laws. Special solutions (steady states, solitary waves, travelling waves, self-similar solutions). Calculus of maps; bifurcations; stability, dynamics near equilibrium. Propogation of nonlinear waves; dispersion, modulation, optical bistability. Global behaviour solutions; asymptotics and blow-up.
Prerequisite: APM346H/351Y

APM456H1
Control Theory and Optimization 39L

Differential systems with controls and reachable sets. Non-commutativity, Lie bracket and controllability. Optimality and maximum principle. Hamiltonian formalism and symplectic geometry. Integrability. Applications to engineering, mechanics and geometry.
Prerequisite: MAT357H or MAT244H/267H, 337H

APM461H1
Combinatorial Methods 39L

A selection of topics from such areas as graph theory, combinatorial algorithms, enumeration, construction of combinatorial identities.
Prerequisite: MAT224H
Recommended preparation: MAT344H/CSC238H

APM466H1
Mathematical Theory of Finance 39L

Introduction to the basic mathematical techniques in pricing theory and risk management: Stochastic calculus, single-period finance, financial derivatives (tree-approximation and Black-Scholes model for equity derivatives, American derivatives, numerical methods, lattice models for interest-rate derivatives), value at risk, credit risk, portfolio theory.
Prerequisite: APM346H, STA348H
Co-requisite: CSC446H, STA457H

APM496H1/497H1/498Y1/499Y1
Readings in Applied Mathematics TBA

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings.
Prerequisite: minimum GPA 3.5 for math courses. Permission of the Associate Chair for Undergraduate Studies and prospective supervisor