37 courses in the 1983–84 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Courses not offered in the current academic year are listed at the end of this section.
Review of basic algebra, geometry, and trigonometry. Sets, relations, operations, and functions. Complex numbers. Exponential and logarithmic functions. Difference equations. Interpolation, estimation, and approximation. introduction to linear algebra and matrix theory.
Not open to students in the Faculty of Mathematics -
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.
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
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.
transforms applied to discrete and continuous mathematical models taken from ecology, biology, economics and other fields.
Prereq: MATH 220b or consent of instructor.
AM 362, FS 2C,1T 05
Elementary Differential Geometry and Tensor Analysis
Curves in Euclidean 3-space (E3) and the Serret-Frenet formulae; surfaces in E3 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 365.
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 efasticity. Various applications. Prereq: MATH 2306 or consent of instructor.
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 2306, or consent of instructor.
Flat space-time and Lorentz 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 AM 372 or 364.
Course Descriptions
Mathematics.
Applied Mathematics
Existence and uniqueness theorems, second and higher order equations, series solutions and Special Functions, Laplace transforms. Application ta Mathematical Physics.
Prereq: MATH 230b
Sturm-Liouville problems and eigenfunction expansions. Non-linear mechanics, phase plane method and stability analysis.
Prereq: AM 381.
Three-dimensional rigid body motion. - Lagrange’s equations of mation. 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.
Integral equations and integral transforms will be applied to systems with memory.
Prereq: Consent of instructor.
As a project, students will develop a mathematical model and interpret its behaviour.
Prereq: Consent of.instructor.
A Survey of undergraduate mathematics with emphasis on the unifying effect of algebraic concepts. This is a crossdisciplinary problem-solving course; theorems of modern algebra are applied to specific exargples chosen from analysis, geometry, probability, graphs and matroids, numerical and multilinear approximation, tensors, and special functions.
Prereq: MATH 2246
Measure and integration
The theory of measure and the Lebesgue integral.
Prereq: MATH 332a or PMATH 351a.
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.
Schrédinger equation. Solution of one dimensional problems, commutation relations, uncertainty principie, W.K.B. approximation. Hydrogen atom, angular momentum. Scattering theory. Matrix mechanics, symmetry groups.
Prereq: MATH 234a, AM 371 or consent of instructor.
Fundamental equations of mviscid fluids, compressibility, vorticity; two and three-dimensiona! irrotational, incompressible flow, Blasius' theorem, Joukowski hypothesis. Watery Wave Motion.
Prereq: AM 365.
A selection of special topics given by members of the Applied Mathematics Department.
Prereq: Consent of instructor.
Linear operators in Hilbert spaces. Compact operators. introduction to functional analysis.
Prereq: AM 462 or consent of instructor.
Grassman algebras, differential forms, Lie.derivatives, isometries, Killing vector fields, applications to continuum mechanics, differentiable manifolds and appiications of differential forms to physics. Prereq: AM 362/PMATH 365 or consent of instructor. Cross-listed as PMATH 465.
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.
Same as in AM 468.
Prereq: Consent of instructor.
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, integra! transforms, inverse transforms by contour integration. Applications to physical problems.
Prereq: AM 371, 381, 391 or consent of instructor.
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
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 Weierstrass sufficent conditions.
Prereq: MATH 230b or consent of instructor.
Course Descriptions
Mathematics.
363
Combinatorics & Optimization
Applications of Maxwell's equations. Introduction to wave guides and antennae.
Prereq: PHYS 253 or consent of instructor.
Applications of probability theary to theoretical Physics.
Prereq: Consent of instructor.
Dynamical systems, controllability and observability. Minimization of functions and functionals. Optimal control. Pontryagin’s Maximum Principle. Prereq: Consent of instructor.
Basic equations of elasticity for homogeneous isotropic bodies; bending of beams; plane elastic waves; Rayleigh surface waves, Love waves. Solution of problems by potentials, variational methods and Saint Venants’ principle. Prereq: AM 3685.
Not Offered 1983-84.
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