AM 340 Applications of Mathematics Difference equations, LaplaceW 2C 0.5
transforms applied to discrete and continuous mathematical models taken from ecology, biology, economics and other fields.
Prereq: MATH 220b or consent of instructor
Applied Mathematics (AM)
38 courses in the 1984–85 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
AM 362 El tary Differential GeometryF,S 3C 0.5
Applied Mathematics
Course Descriptions
Courses not offered in the current academic year are listed at the end of this section.
AM 101 Applications of Mathematics 1 (For Biology Students)F 3C,1T 0.5
Review of basic algebra, geometry, and trigonometry. Sets, relations, operations and functions. Complex numbers. Exponential and togarithmic functions. Difference equations. Interpolation, estimation, and approximation. Introduction to linear algebra and matrix theory.
Not open to students in the Faculty of Mathematics.
AM 111, W 3C,1T 05 Applications of Mathematics 2 (For Biology Students) An introduction to probability and statistics, Deterministic and nondeterministic modelling. Numerical methods using a pocket calculator. Prereq: AM 101 or consent of instructor Not open to students in the Faculty of Mathematics.
AM 260 Mathematical ModellingF,W 3C 0.5
Mathematical models for problems in the physical and biological sciences. Typical problems chosen from ecology, special relativity, spread of epidemics, rumours and tumors. Solutions to problems will be obtained primarily by differential equations.
Prereq: MATH 130B
AM 270 Mathematica! ModellingF,W 3C 0.5
Further mathematical models from various disciplines. An introduction to Newtonian mechanics will also be included in the course.
Prereq: AM 260 or consent of instructor *
and Tensor Analysis Curves in Euclidean 3-Space (E5) and the Serret-Frenet formulae; surfaces in E® and their intrinsic geometry. Gaussian curvature and the Gauss- Bonnet theorem. Co-ordinate transformations and tensors in ndimensions; n-dimensional Riemannian spaces; covariant differentiation; geodesics; the curvature, Ricci and Einstein tensors. Applications of tensors in Relativity and Continuum Mechanics.
Prereq: MATH 230b or consent of instructor
Cross-listed as PMATH 368.
AM 365 Introduction to Continuum MechanicsW 2C,1T 0.5
Stress and strain tensors; analysis of stress and strain. Lagrangian and Eulerian methods for describing flow. Equations of continuity, motion and energy, constitutive equations. Navier- Stokes equation. Basic equations of elasticity. Various applications.
Prereq: MATH 230b and AM 371 or consent of instructor
Coreq: MATH 332b
AM 371 Partial Differential Equations of Applied Mathematica 1F,S 2C1T 0.5
First order partial differential equations and methods of characteristics, second order partial differential equations, boundary value problems and related numerical methods, vibrating string, 2-D membranes, heat equation and related
problems; introduction to vector analysis.
Prereq: AM 260, MATH 230b, or consent of instructor
16.89
AM 372 Introduction to General Relativity Flat space-time and LorentzW 2C,1T 0.5
transformations, relativistic mechanics, - Maxwell's equations; curved space-time and the Einstein field equations, the Schwarzschild solution and some experimental tests of general relativity, the weak field limit; introduction to black holes and cosmology.
Prereq: AM 362/PMATH 365 or consent of instructor
A student may receive credit for only 1 of AM 372 or 364.
AM 380A Introduction to Information Theory with ApplicationsF,S 3C 0.5
Variable length coding. The Shannon entropy as measure of uncertainty and expected information. Minimal average length coding; the Shannon entropy as lower bound. Source entropy. Channels. Transinformation. Capacity. Applications to problem solving, information transmission, logics, science, linguistics and communications (TV, music, etc.). Determination of pratical measures of information. Prereq: Consent of instructor Cross-listed as PMATH 380a.
AM 380B Information Theory with ApplicationsW 3C 0.5
Measures of conditional uncertainty (entropy). Maximizing conditional entropies. Applications to statistical physics, statistics, pattern recognition. Special entropies in questionnaire theory. Design of optimal questionnaires. Special entropies in dynamical systems. Basics in dynamical systems. Prereq: Consent of instructor Cross-listed as PMATH 380b.
AM 381 Ordinary Differential Equations 1F,S 2C,1T 0.5
Existence and uniqueness theorems, second and higher order equations, series solutions and Special Functions, Laplace transforms. Application to Mathematical Physics.
Prereq: MATH 230b
AM 391 Ordinary Differential Equations 2W 2C\1T 0.5
Sturm-Liouville problems and eigenfunction expansions. Non-linear mechanics, phase plane method and Stability analysis.
Prereq: AM 381.
AM 395 MechanicsF 2C,1T 0.5
Three-dimensional rigid body motion, Lagrange’s equations of motion. ignorable co-ordinates. Hamilton's principle. Noether’s theorem and
conservation laws. Canonical equations.
Canonical transformations. Lagrange and Poisson bracket relations. Integral invariants.
Prereq: MATH 230b or consent of instructor
AM 389 Reading CourseF 0.5
AM 399 Reading CourseW 0.5
AM 430 Applications of MathematicsF 2C 0.5
- Integral equations and integral transforms will be applied to systems with memory. ©
Prereq: Consent of instructor
AM 440 Applications of MathematicsW 2C 0.5
As a project, students will develop a mathematical model. and interpret its behaviour.
Prereq: Consent of instructor
AM 444 Applications of AlgebraW 3C 0.5
A survey of undergraduate mathematics with emphasis on the unifying effect of algebraic concepts. This is a crossdisciplinary probiem-solving course; theorems of modern algebra are applied to specific examples chosen from analysis, geometry, probability, graphs and matroids, numerical and multilinear” approximation, tensors, and special functions.
Prereq: MATH 224b
AM 462 Measure and IntegrationF 3C 0.5
The theory of measure and the Lebesque integral. Prereq: MATH 332a or PMATH 351a
AM 464 Topics in General RelativityF 2C 0.5
Basic ideas of relativistic cosmology (Friedmann-Robertson-Walker universes, observational status of cosmological theories, black hole theory (the Schwarzschild and Kerr solutions, their event horizons and singularities, gravitational collapse, observable properties of black holes), and an introduction to gravitational waves. Other topics of current interest may be discussed.
Prereq: AM 362 and 372 or consent of instructor ‘
AM 465A Quantum Mechanics 1F 2C 0.5
Historical origins of quantum theory. Uncertainty principle, wave packets and the Schrédinger equation. The Hamiltonian operator. Solutions of onedimensional problems: harmonic oscillator, hydrogen atom, hydrogen molecular ion.
Prereq: Consent of instructor
AM 465B Quantum Mechanics 2W 2C 0.5
Electronic properties of solids. Matrix
mechanics. Symmetry and conservation
laws. WKB method. Variation principle.
Perturbation theory and applications.
Scattering theory. Symmetry groups. Prereq: AM 465a
AM 466 Fluid Mechanics AF 3C 0.5
Fundamental equations of inviscid fluids.
compressibility, vorticity; two and three-
dimensional irrotational, incompressible
flow. Blasius’ theorem, Joukowski
hypothesis. Water Wave Motion. Prereq: AM 365
AM 468 Topics in Applied MathematicsF 2C 0.5
A selection of special topics given by members of the Applied Mathematics Department.
Prereq: Consent of instructor
AM 472 Linear OperatorsW 3C 0.5
Linear operators in Hilbert spaces. Compact operators. introduction to functional analysis.
Prereq: AM 462 or consent of instructor
AM 474 Topics in Differential GeometryW 2C,1T 0.5
Grassman algebras, differential forms, Lie derivatives, isometries, Killing vector fields, applications to continuum mechanics, -differentiabie manifolds and applications of differential forms to physics.
Prereq: AM 362/PMATH 365 or consent of instructor
Cross-listed as PMATH 465.
AM 476 Fluid Mechanics BW 3C 0.5
Shock wave theory, supersonic flow around a corner, Prandtl-Meyer flow. Dynamics of real fluids, Navier-Stokes equations, exact solutions, Stokes and Oseen flow; Turbulence, Boundary layer theory. Introduction to Geophysical Fluid Dynamics.
Prereq: AM 466
Course Descriptions Applied Mathematics
AM 478 Topics in Applied Mathematics Same as in AM 468W 2C 0.5
Prereq: Consent of instructor
AM 4861a F 2C 05 Partial Differential Equations of Applied Mathematics 2 Second-order partial differential equations and characteristics; d‘Alemberts’ solution of the wave equation, concepts of distributions, construction of Green’s functions, Fourier integral theorem, integral transforms, inverse transforms by contour integration. Applications to physical problems.
Prereq: AM 371, 381, 391 or consent of instructor
AM 481B Partial Differential Equations ofW 2C 0.5
Applied Mathematics 3
Variational properties of eigenvalues and
eigenfunctions, Rayleigh-Ritz method.
special functions, Hankel transforms.
Fourier-Bessel series, asymptotic series.
Applications to Physical problems. Prereq: AM 481a
AM 482 Calculus of VariationsF 2C,1T 0.5
Euler-Lagrange equations for constrained and unconstrained single and double integral variational problems. Parameter-invariant single integrals. General variational formula. The canonical formalism. Hilbert’s independent integral. Hamilton-Jacobi equation and the Caratheodory complete figure. Fields and the Legendre and Weier-strass sufficient conditions.
Prereq: MATH 230b or consent of instructor
AM 485 ElectromagnetismF 2C 05 .
Applications of Maxwell’s equations.
Introduction to wave guides and
antennae. . Prereq: PHYS 253 or consent of
instructor
AM 486 Statistical MechanicsF 2C 0.5
Applications of probability theory to theoretical Physics.
Prereq: Consent of instructor
AM 488 Control TheoryW 3C 0.5
Dynamical systems, controllability and
observability. Minimization of functions
and functionals. Optimal control.
Pontryagin’s Maximum Principle. Prereq: Consent of instructor
Applied Mathematics
AM 489 Reading CourseF 0.5
AM 495 ElasticityW 2C,1T 0.5
Basic equations of elasticity for
homogeneous isotropic bodies; bending
of beams; plane elastic waves; Rayleigh
surface waves, Love waves. Solution of
problems by potentials, variantionat
methods and Saint Venants’ principle. Prereq: AM 365
AM 499 Reading CourseW 0.5
AM 364 Special Relativity
Not offered in 1984–85.
AM 461 Non-Linear Differential Equations
Not offered in 1984–85.