36 courses in the 1978–79 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
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 to formulate 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 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
Course Descriptions Applied Mathematics
Note 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 applied to diffusion problems, blood flow, wave phenomena; mathematical ° models in ecology, physiology, economics 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
First order partial differential equations and method 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 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 Schwarzchild solution and some experimental tests of general relativity, 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
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: Math 230, or consent of instructor
2C,1T 0.5
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
Course Descriptions 339. 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 Lebesgue 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 principle, 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
AM472, W- 2C 0.5
Linear Operators
Linear operators in Hilbert spaces. Compact operators. Introduction to functional analysis.
Prereq: AM 462, or consent of instructor
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
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 .
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 sufficient conditions.
Prereq: Math 230, or consent of instructor
Applications of Maxwell’s equations. Introduction to wave guides and antennae.
Prereq: Consent of instructor
Applications of probability theory to theoretical Physics.
Course Descriptions
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
Department of Combinatorics and Optimization Course Descriptions
Note Course descriptions are given under the new course numbers introduced in 1976.
Models using difference equations wil be formulated for examples drawn from biology, economics and
psychology.
Course Descriptions 355° Mathematics Service Courses
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.
Prereq: Consent of instructor.
Course Descriptions ‘357 Mechanical Engineering.
Department 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)
Associate Professor, Associate Chairman Undergraduate Studies
A.B. Strong, BASc (Waterloo), MSc (London), PhD (Waterloo), PEng
Professor, Vice President Academic T. A. Brzustowski, BASc (Toronto), AM, PhD (Princeton), PEng
Professors
S.A. Alpay, Dipi Ingr, Dr Ing (Berlin)
E. Brundrett, 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, 8Sc (Queen's), MSc, PhD (Birmingham), PEng
H.W. Kerr, BASc, PhD (Toronto), PEng
H.R. Martin, BSc, MSC (Queen's Belfast), PhD (Nottingham), PEng
W. B. Nicoll, SB, SM (MIT), Engineer (Stanford), PhD (London), DIC (Imperial)
P. Niessen, BSc, (McMaster), MASc, PhD (Toronto), PEng
G.F.Pearce, BASc (UBC), MASc (Toronto), PEng
K. R. Piekarski, Dip! Ing (London), PhD (Cambridge), PEng
A. Plumtree, BSc, PhD (Nottingham), PEng, FIM
J.A. Schey, Dip! ing, CSc (Budapest), PEng
D. M.R. Taplin, BSe (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 (Toronto), PhD (McGill), PEng
W. M. Mansour, BSc (Cairo), MASc, PhD (Toronto)
U.H. Mohaupt, BASc, MASc, PhD (Waterloo), PEng R. J. Pick, BASc (UBC), MSc (Imperial College).
PhD (Waterloo), PEng
G.D. Raithby, BESc, MESc (Western), PhD (Minnesota), PEng P.R. Slawson, BASc, MASc, PhD (Waterloo), PEng H.F. Sullivan, BASc (Waterloo), AM, PhD (Princeton), PEng
Assistant Professors G. A. Davidson, BASc (Hons) (Toronto), PhD (Toronto) G.E. Schneider, BASc, MASc, PhD (Waterloo) J. L. Tevaarwerk, BASc, MASc (Waterloo), PhD (Cambridge)
Adjunct Professors A.G.R. Lawrence, QC R. M. Pilliar, BASc (Toronto), PhD (Leeds)
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.
Course Descriptions
MEO1 FW 0.5
Advanced Calculus
Infinite series: Tests for absolute; conditional, uniform convergence; power series; series expansions; differentiation 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.
ME 02 0.5
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.
ME03 SF 3C,1T 0.5
Ordinary Differential Equations
First and simple higher order equations. Solution of linear equations. Solution of linear equations by various methods; equations transformable to linear form. Simultaneous equations. Laplace transforms. Series solutions. Fourier series.
Course Descriptions Mechanical Engineering
ME04 SF 3C,1T 05
Numerical Analysis
A survey of numerical procedures with emphasis upon computer implementation using the WATFIV programming language. In particular, the following topics are covered: Interpolation, curve fitting, solution of non-linear equations, numerica! integration, numerical solution of Ordinary Differential Equations, matrix algebra and solution of systems of linear equations, and
‘problems in the solution of partial differential equations.
MEOS SW 30,1T 0.5
Partial Differential Equations
Modelling physical systems with distributed parameters. Boundary and initial conditions. Division into hyperbolic, parabolic and elliptic equations by means of discriminant.
Characteristics. Separation of variables; eigenvalues and eigenfunctions. Orthogonality. Fourier series. Gamma functions. Bessel and Legendre equations. Numerical solution of Laplace and diffusion equations. Analogue simulation techniques.
ME 12 FW Dynamics
An introduction to the kinematics of particle and rigid body motion. impulse-momentum equations. Work-energy methods and Euler’s equations. Simple gyroscopes. Vibrations.
3C,1T 05.
ME15 FW 2C,3L 0.5 .
The Mechanical Behaviour of Materials
The relevance of materials engineering to the ascent of man, the internal structure of materials, electrical, magnetic and optical properties of materials, structure of imperfect solids, microscopy of materials, elasticity and anelasticity, stress-strain behaviour in metals, plasticity in metals, non-metallic behaviour, fracture of materials, improving materials.
ME19 F,W 2C,1D,1T 0.5
Mechanics of Deformable Solids 1
An analytical treatment of statics and resistance of materials. Equilibrium of particles, rigid bodies and deformable bodies. Vector fields. Introduction to stress and strain. Stress-strain relationships. Elastic and inelastic behaviour of prismatic members subjected to axial, shearing, torsional and flexural deformations.
ME20 S\F 2C,1D,1T 0.5
Mechanics of Deformable Solids 2
A general treatment of the behaviour of structural components from the study of stress and strain in solids. Topics include super-position, energy theorems, theories of failure, elastic and inelastic analysis of unsymmetrical bending, torsion of circular members, columns and stability, and virtual work.
ME21 3C,iL 0.5
Kinematics and Dynamics of Machines
Principles of the geometry of motion. Uniform and non-uniform motion, linkage, gears, cams. Synthesis and analysis of mechanisms. Consideration of the dynamic forces in machines. Gyroscopic torque. Vibration analysis, response to shock, motion and force transmissibility, vibration isolation.
ME22 FLW 3C,1T 0.5
Mechanical Design 1
Analysis and synthesis of machine elements. Factors affecting working stresses, fatigue, creep and iripact considerations. Design of shafting, springs, screws, clutches, brakes and gear.
ME30 SF 2C3L 05 ‘
Control of the Behaviour of Materiais
The stability and control of micro-structure, phase diagrams, vacancies and diffusion, reaction rate theory, solid state transformations in materials, materials at high temperatures, alloying and strengthening, composite materials and bio-materials, environmental degradation of materials, review of materials engineering.
ME32 SF 3C 05
Physical Metallurgy 2
Elasticity and plasticity of metals. Hardening mechanisms. Failure in metals.
ME33 FW 6L 05
Experimental Materials Science
This course is designed to acquaint students with materials phenomena using an experimental approach. Microstructural changes and their effects on the mechanical properties in various materials will be studied using such techniques as optical and scanning electron microscopy together with electron probe microanalysis and X-ray analysis. The’student may work on a project of his own choice provided it meets the objectives of this course.
ME35 F,W 3c 0.5
Industrial Metallurgy
This course is intended for those students interested in acquiring a working knowledge of metallurgy. ft will cover: Metals and alloy systems, iron-carbon alloys, heat treatment and the function of alloying elements in steel, corrosion and scale resistant alloys, copper and nickel base alloys, light metals and their alloys; casting, hot and cold working of metals; soldering, brazing and welding; corrosion and oxidation; metal failure analysis.
Course Descriptions 359