38 courses in the 1977–78 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Undergraduate Course Descriptions
Note Course descriptions are given under the new course numbers introduced in 1976.
AM 230, 240, 330, 340, 430, 440 is a sequence of courses designed to illustrate the representation of a real situation by a mathematical model. The mathematical techniques necessary to formulate the model and to discuss its behaviour are developed as required. Examples will be taken from diverse fields since one of the aims of each course is io formutate models to describe unfamiliar situations.
Ordinary differential equations will be applied to models drawn from biology, economics, physiology and physics. Prereq: Math 120, 130 or consent of instructor
Note AM 230 is not open to Honours Mathematics students. Credit will be given for only one of AM 230, 260.
Other examples from biology, ecology, economics, physiology and physics will be discussed using sets of differential equations.
Prereq: AM 230 or Math 220
Note AM 240 is not open to Honours Mathematics students. Credit will be given for only one of AM 240, 270.
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 130
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
Partial differential equations are applied to diffusion processes, blood flow and wave phenomena.
Prereq: Math 220 or equivalent, or consent of instructor
Course Descriptions . 353 Applied Mathematics
Laplace transforms are applied to problems in ecology, physiology and other fields.
Prereq: Math 220 or equivalent, or consent of instructor
formulae; surfaces in E*® and their intrinsic geometry, Gaussian curvature and the Gauss-Bonnet theorem. Co-ordinate transformations and tensors in
- n-dimensions; n-dimensional Riemannian spaces.
covariant differentiation; geodesics; the curvature, Ricci and Einstein tensors. Prereq: Math 230, or consent of instructor
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 230, or consent of instructor '
Introduction to partial differential equations with motivating examples; linear first-order equations, derivation of equations for wave motion, vibrating membrane and heat flow, separation of variables, cylindrical and spherical co-ordinates, Besse! and Legendre functions, Fourier analysis, introduction to vector analysis.
Prereq: AM 260, 270, Math 230, or consent of instructor
Flat space-time and Lorentz transformations, relativistic mechanics and collision phenomena, Maxwell's . equations; curved space-time and the Einstein field equations, the Schwarzschild solution and some experimental tests of general refativity, the weak field limit; introduction to black holes: introduction to cosmology.
Prereq: AM 362 or consent of instructor
Existence and uniqueness theorems, second and higher order equations, series solutions and Special Functions, Laplace transforms. Application to Mathematical Physics.
Prereq: Math 230
Euler-Lagrange equaitons 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 sufficient conditions.
Prereq: Math 230, or consent of instructor
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. Canonical transformations. Lagrange and Poisson bracket relations. Integral invariants.
Prereq: Math230, AM 382, or consent of instructor
Integral equations and integral transforms will be applied to systems with memory.
Prereq: Consent of instructor
Asa project, students will develop a mathematical model and interpret its behaviour.
Prereq: Consent of instructor
Course Descriptions Applied Mathematics
Non-linear mechanics, stability, quasi-linear and strongly non-linear systems, linear periodic systems, non-linear integral equations.
Prereq: AM 381/391, or consent of instructor
The theory of measure and the Lebesque integral.
Differentiable manifolds, vector fields, linear connections, tensor fields, differential forms, and the structure equations.
Prereq: AM 362, 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 231, AM 371, or consent of instructor
Fundamental equations of inviscid fluids, compressibility, vorticity: two and three-dimensional irrotational, incompressible flow, Blasius’ theorem, Joukowski hypothesis.
Prereq: AM 365
A selection of topics given by members of the Applied Mathematics Department. Typical topics are: elasticity, fluid mechanics, electromagnetic theory, statistical mechanics, perturbation theory, calculus of variations, partial differential equations, distribution theory. Prereq: Consent of instructor
Linear operators in Hilbert spaces. Compact operators. Introduction to functional analysis.
Parallel propagation and Fermi-Walker transport, geometrical interpretation of the curvature tensor, Lie derivatives and Killing vector fields, conformally related and projectively related Riemannian spaces, submanifolds. Frobenius’ theorem, frame fields and spinors.
Prereq: AM 362, or consent of instructor
Shock wave theory, supersonic flow around a corner, Prandtl-Meyer flow. Dynamics of real fluids, Navier-Stokes equations, exact solutions, Stokes and Oseen flow; introduction to boundary layer theory. Prereq: Am 466
Same as in 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: Consent of instructor
Applications of the Maxwell equations. Reflection and refraction. Introduction to wave guides and antennae. Prereq: Consent of instructor.
Applications of probability theary to theoretical Physics.
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 365
Course Descriptions 355
Models using difference equations will be formulated for examples drawn from biology, economics and psychology.
Course Descriptions Mathematics Electives
Sets of difference equations, probability and matrix theory will be used to describe models from biology, ecology, economics, psychology and physiology.
Ordinary and partial differential equations. Laplace and Fourier transforms. Special functions. Fourier series.
Vector and matrix methods. Calculus of variations. Other topics in advanced calculus.
Mathematics Electives
Departmental of Mechanical Engineering
Professor, Chairman of the Department D. J. Burns, BSc, PhD (Bristol), CEng, PEng
Professor, Associate Chairman Graduate Studies C.E.Hermance, BE (Yale), MA, MSE, PhD (Princeton)
Professor, Associate Chairman Undergraduate Studies P. Niessen, 8Sc (McMaster), MASc, PhD (Toronto), PEng
Professor, Vice President Academic
T. A. Brzustowski, BASc (Toronto), AM, PhD (Princeton), PEng
Professors
S.A. Alpay, Dip! ingr, Dring (Berlin)
E. Brundett, BSA (OAC), BASc, MASc, PhD (Toronto), PEng.
M. B. Danard, BASc (UBC), MA (Toronto), PhD (Chicago)
D. French, BSc, CEng, PEng
E.L. Holmes, BSc (Bristol), MASc, PhD (Toronto), PEng
J.H.G. Howard, BSc (Queen’s), MSc, PhD (Birmingham), PEng
H.R. Martin, BSc, MSC (Queen’s Belfast), PhD (Nottingham), PEng
W. B. Nicoll, SB (MIT), Engineer (Stanford), PhD (London), PEng
G. F. Pearce, BASc (UBC), MASc (Toronto), PEng
J.A. Schey, Dipl ing, CSc (Budapest), PEng
D.M.R. Taplin, BSc (Aston), DPhil (Oxford), PEng
M. M. Yovanovich, BSc (Queen's), MS (Buf.), MEScD (MIT)
Associate Professors
K.G. Adams, BSc (Queen’s), MASc, PhD (Waterloo), PEng.
G.C. Andrews, BASc, MASc (UBC), PhD (Waterloo), PEng.
G. M. Bragg, BASc (Toronto), PhD (Cambridge), PEng
R.N. Dubey, BSc (Hons) (Patna), BSc (Eng) Bihar), PhD (Waterloo), PEng
A.M. Hale, BSc, MA (New Brunswick), BASc (Toronto), MASc, PhD (Waterloo), PEng
K.G.T. Hollands, BASc (Tororto), PhD (McGill), PEng
H.W. Kerr, BASc, PhD (Toronto), PEng
W.M. Mansour, BSc (Cairo). MASc. PhD (Toronto)
R. J. Pick, BAS¢ (UBC), MSe (Imperial College), PhD (Waterloo), PEng
K. R. Piekarski, Dip! ing (London), PhD (Cambridge), PEng.
A. Plumtree, BSc, PhD (Nottingham), PEng
G.D. Raithby, BESc, MESc (Western), PhD (Minnesota), PEng
P.R.Slawson, BASc, MASc, PhD (Waterloo), PEng
A.B. Strong, BASc (Waterloo), MSc (Imperial College, London), PhD (Waterloo), PEng.
Course Descriptions 373 Mechanical Engineering
Assistant Professors
G.A. Davidson, BASc (Hons) (Toronto), PhD (Toronto)
U.H. Mohaupt, BASc, MASc, PhD (Waterloo), PEng
H.F. Sullivan, BASc (Waterloo), AM, PhD (Princeton), PEng
Adjunct Professor R.G.R. Lawrence, QC
Undergraduate Programmes
Details of the undergraduate programme in Mechanical Engineering are to be found in chapter 8. All. courses extend over one term only, and consist of 3 hours of lectures per week unless otherwise specified. In general, the only prerequisites are the core courses, unless otherwise specified.
Undergraduate Course Descriptions
MEO1 FW 5
Advanced Calculus.
Infinite series: Tests for absolute, conditional, uniform convergence; power series; series expansions; diffentiation and integration. Partial differentiation: total derivatives; estimation of errors; chain rule; geometry; maxima and minima; Taylor series; Jacobians. Multiple integration: areas, centroids, moments of inertia, centres of gravity. Vector analysis: gradient divergence, curl, Laplacian; integral theorems.
ME02 5 Statistics for Engineers (Equivalent to MSci21)
Frequency distributions; measures of central tendency.
standard deviation and other measures of dispersion; moments, skewness, kurtosis. Probability. Binomial, Poisson, normal, multinomial distributions. Theory of sampling and statistical estimation. Tests of hypotheses; significance. The t-test and chi-squared test. Curvefitting by least squares. Correlation and regression. Analysis of variance. Experimental design.