| Course Winter Timetable |

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: APM261H1, ECO331H1
Prerequisite: MAT223H1/240H1 (Note: no waivers of prerequisites will be granted)

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: MAT235Y1/237Y1/257Y1, 244H1

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: MAT267H1
Co-requisite: MAT334H1/354H1

APM362H1
Nonlinear Optimization 39L

An introduction to first and second order conditions for finite and infinite dimensional optimization problems with mention of
available software. Topics include Lagrange multipliers, Kuhn-Tucker conditions, convexity and calculus variations. Basic numerical
search methods and software packages which implement them will be discussed.
Prerequisite: MAT224H1, 235Y1
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: MAT337H1/357H1

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: MAT363H1

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: APM351Y1

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: APM346H1/351Y1, MAT334H1

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: APM346H1/351Y1

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: MAT357H1 or MAT244H1/267H1, 337H1

APM461H1
Combinatorial Methods 39L

A selection of topics from such areas as graph theory, combinatorial algorithms, enumeration, construction of combinatorial identities.
Prerequisite: MAT224H1
Recommended preparation: MAT344H1/CSC238H1

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: APM346H1, STA347H1
Co-requisite: CSC446H1, STA457H1

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