37 courses in the 1982–83 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Biology Students) : Review of basic algebra, geometry, and trigonometry. Sets, relations, operations, and functions. Complex numbers. Exponential and logarithmic functions. Difference equations. Interpolation, estimation, and approximation. tntroduction to linear algebra and matrix theory.
Prereq: none
Not open to students in the Faculty of Mathematics
Mathematics.
Course Descriptions 347
Applied 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 wi!l be obtained primarily by differential equations.
Prereq: MATH 120b
Further mathematical models from various disciplines. An introduction to Newtonian mechanics will also be inciuded 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.
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. Prereg: MATH 230b or consent of instructor.
Cross-listed with PMath 365.
A tensorial formulation of special relativity, Lorentz transformations and flat space-time; relativistic mechanics and collision phenomena; Maxwell's equations in tensorial form and some of their solutions: energy-momentum tensor of the electromagnetic field and of a fluid; spinors and representations of the Lorentz group. Reference will be made throughout to the experimental verification of special relativity.
Prereq: AM 362/PMATH 365, PHYS 364, or consent of instructor. Not offered 1982-83.
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, or consent of instructor.
First order partial differential equations and methods of characteristics, second order partial differential equations, boundary vaiue 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.
Flat space-time and Lorentz transformations, relativistic mechanics, Maxweil’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, one of AM 372, AM 364 and for only one of AM 372, AM 464.
”
Existence and uniqueness theorems, second and higher order equations, series solutions and Special Functions, Laplace transforms. Application to 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 motion. Ignorable co-ordinates. Hamilton's principle. Noether's theorem and
conservation laws. Canonical equations.
Canonica! transformations. Lagrange and Poisson bracket relations. tntegra! 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 mode! 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 examples chosen from analysis, geometry, probability, graphs and matroids, numerical and muitilinear approximation, tensors, and special functions.
Prereq: MATH 224b
Course Descriptions
Mathematics.
Applied Mathematics
Non-linear mechanics, stability, quasilinear and strongly non-linear systems, linear periodic systems, non-linear integrai equations.
Prereq: AM 381/391, or consent of instructor.
Measure and integration
The theory of measure and the Lebesgue integral.
Prereq: MATH 332a and PMATH 351a.
Differentiable manifolds, vector fields, linear connections, tensor fields, differential forms, and the Cartan structure equations.
Prereq: AM 362 or consent of instructor. Cross-listed with PMATH 463.
solution; experimental tests of general relativity; the weak field limit; introduction to black holes; construction of stellar models; introduction to cosmology; 3 + 1 decomposition of space-time and the Cauchy initial value problem; methods of solving the field equations.
Schrédinger equation. Solution of one dimensional problems, communtation relations, uncertainty principle, W.K.B. approximation. Hydrogen atom, angular momentum. Scattering theory. Matrix _ mechanics, symmetry groups.
Fundamental equations of inviscid fluids, compressibility, vorticity; two and three-dimensional irrotational, incompressible flow, Blasius’ theorem, Joukowski hypothesis. Water Wave Motion.
Prereq: AM 368.
A selection of special fopics 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.
Depending on instructor, topics from pseudo-Riemannian and Riemannian geometry such as: isometries and Killing vector fields; sectional curvatures; submanifolds; normal coordinates; variation of geodesics and Jacobi fields; conformally related spaces. ‘
Prereq: PMATH 463/AM 463 or consent of instructor. Cross-listed with PMATH 465.
Shock wave theory, supersonic flow around a corner, Prandati-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, integral transforms, integral equations, variational properties of eigenvalues and eigenfunctions, special functions, asymptotic series. All these methods are applied to physical problems.
Prereq: AM 371, 381, 391, or consent of instructor.
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.
Applications of Maxwell's equations. Introduction to wave guides and antennae.
Prereq: PHYS 253 or consent of instructor.
Applications of probability theory to theoretical Physics.
Prereq: Consent of instructor.
Dynamical systems, controtiability and observability. Minimization of functions and functionals. Optima! 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 365.
Course Descriptions : 349
Mathematics.