136 courses in the 1966–67 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Faculty listed in 1966–67
R. G. Stanton, B.A. (Western), M.A., Ph.D. (Toronto) Professor and Chairman of the Department, Dean of the Faculty of Graduate Studies
K. D. Fryer, B.A. (Western), M.A., Ph.D. (Toronto) Professor and Associate Chairman of the Department J. Aczel, Ph.D. (Budapest). Habil, D.Sc. (Hung. Ac. of Science) - Professor
G. Berman, M.A., Ph.D. (Toronto) - - - - - Professor J. Edmonds, M.A. (Maryland) ~~ - - - - - Visiting Professor W. T. Tutte, M.Sc., M.A., Ph.D. (Cambridge) - - - Professor H. H. Crapo, A.B. (Michigan), Ph.D. (Massachusetts Institute
of Technology) - - - - - - Associate Professor
Faculty listed in 1966–67
G. E. Cross. M.A. (Dalhousie). Ph.D. (British Columbia) Associate Professor
H. F. Davis. S.M., Ph.D. (Massachusetts Institute of Technology) Associate Professor
Faculty listed in 1966–67
M. A. McKiernan. M.A. (Loyola), Ph.D. (Illinois Institute of Technology) Associate Professor
R. A. Staal, M.A., Ph.D. (Toronto) - - - Associate Professor F.C. Y. Tang, B.Sc. (Hong Kong), M.S. (South Carolina), Ph.D. (Illinois) - - - - - - Associate Professor
D. G. Wertheim, B.A. (McMaster), M.A., Ph.D. (Toronto) Associate Professor
C. F. A. Beaumont, B.A. (McMaster), M.A. (Toronto) - Assistant Professor
T. M. K. Davison, B.Sc. (Sir George Williams), M.A., Ph.D. (Toronto) Assistant Professor
A. Kerr-Lawson, B.A. (Toronto), S.M. (Chicago), Ph.D. (McMaster) Assistant Professor
Department of Mathematics
Faculty listed in 1966–67
.C. Mullin, B.A. (Western), M.A., Ph.D. (Waterloo) - Assistant Professor P. J. Ponzo, B.A.Sc., M.A. (Toronto), Ph.D. (Illinois)
rv]
Faculty listed in 1966–67
Assistant Professor
K. A. Rowe, B.A. (Toronto), M.S. (Wisconsin), Ph.D. (Illinois) Assistant Professor
R. A. Wentzell, B.Sc. (Acadia), M.Sc., Ph.D. (Western) - Assistant Professor
J. Wilkinson, B.S., Ph.D. (California Institute of Technology)
Faculty listed in 1966–67
Assistant Professor E. R. Bishop, B.S. (Acadia), M.Sc. (Waterloo) - - - Lecturer E. G. Butz, B.Sc. (Toronto), M.A. (Waterloo) - - - Lecturer R. A. Honsberger, B.A. (Toronto) - - - - - Lecturer E. Koch, B.Sc., M.A. (Waterloo) - - - - - - Lecturer W. P. Kotorynski, B.Sc. (Western), M.A. (Waterloo) - - Lecturer D. J. Miller, B.Sc. (McMaster) - - - - - - Lecturer J. P. McClure, B.Sc. (Waterloo) - - - - - - Lecturer G. N. Robertson, M.A. (Manitoba) - - - - - Lecturer P. L. J. Ryall, B.Sc. (London), M.A. (Cambridge), A.S.A. - Lecturer K. Salkauskas, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - Lecturer R. S. D. Thomas, B.Sc. (Toronto), M.A. (Waterloo) - - Lecturer B. S. Thomson, B.Sc. (Toronto), M.Sc. (Waterloo) - Lecturer H. I. McIntosh, B.A. (Toronto), F.S.A. (American Society of Actuaries)
Adjunct Professor D. B. Sumner, B.A., M.A. (Witwatersrand), M.Sc. (Cambridge).
Ph.D. (Witwatersrand) - - - - - Adjunct Professor
Computer Science Division J. W. Graham, M.A. (Toronto) Associate Professor and Director of Computing Department
Faculty listed in 1966–67
D. D. Cowan, B.A.Sc., (Toronto), M.Sc., Ph.D. (Waterloo) Assistant Professor
J. D. Lawson, B.A.Sc. (Toronto), M.Sc., Ph.D. (Waterloo) Assistant Professor
J. C. Wilson, B.A.Sc. (Toronto), M.Sc. (Waterloo) - Assistant Professor Mrs. S. Aczel, M.A. (Szeged) - - Assistant Professor (part-time) J. W. Dodd, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - Lecturer P. W. Shantz, B.Sc., M.A. (Waterloo) - - - - - Lecturer
Statistics Division
Faculty listed in 1966–67
D. A. Sprott, M.A., Ph.D. (Toronto) . - - - - - Professor G. W. Bennett, B.Sc., Ph.D. (Adelaide) - - - Assistant Professor
J. G. Kalbfleisch, B.Sc. (Toronto), M.Sc. (Waterloo) - - Lecturer A. C. Madgett, B.Sc. (Toronto), M.A. (Waterloo) - - Lecturer C. Springer, B.Sc., M.Sc. (McGill) - - - - - Lecturer M. Behara, M.Sc. (Utkal), Dr.rer.oec. (Saarland), F.S.S. - Adjunct Professor
Undergraduate Course Descriptions
Note: The number of hours or lectures shown after the course description is an attempt to indicate the “normal”; each instructor determines how often his particular class will meet
Functions and limits, the derivative. Differentiation formulae. Applications to tangents, rates, extremes. The indefinite and definite integrals, fundamental theorem of integral calculus. Applications to area, volume, centroids, moments of inertia, fluid pressure, work, potential. Introduction to the trigonometric, inverse trigonometric, exponential, logarithmic functions. Transcendental functions. Parametric and polar equations. Formal integration and applications to physical problems. Students will work selected problems under supervision. A certain proportion of the problems will include mathematical formulation of physical problems.
The rational, real, and complex number systems. Polynomial functions. Theory of equations. Determinants. Vector and matric notation. Co-ordinates in three dimensions. Systems of planes and lines. Standard equations of quadric surfaces. Spherical and cylindrical co-ordinates. 2 lectures, 1 hour problems.
A continuation of course 12. Infinite series and power series. Partial derivatives. Multiple integration and applications to areas, volumes, centroids, moments. Introduction to differential equations.
Introduction to the use of desk calculators. Simple problems on interpolation, solution of algebraic equations, numerical evaluation of integrals, systems of equations.
Standard methods of solution. Applications to physical and engineering problems. Linear equations with constant co-efficients. Systems of differential equations. Solution by series. Numerical methods of solution. Partial differential equations; applications of partial differential equations.
Ordinary, divided, and central difference interpolation formulae. Graphic and numerical solutions of algebraic and transcendental equations. Computation with series and integrals. Systems of linear equation. Determinants and matrices. Eigenvalue problems. Iterative procedures. Relaxation methods. Difference equations. Mathematical principles associated with electronic computers.
Real numbers, sequences, limits, continuity. The derivative. General Theorem of Mean Value. Functions of several variables. implicit functions, Jacobians. Power series with complex terms, the Taylor series for functions of several variables, constrained extrema. The elementary functions for a complex variable.
Systematic treatment of formal integration. Differential equations. Calculus of variations. Fourier series. Riemann integration, improper integrals, multiple integrals with applications. Line integrals, theorems of Green and Stokes.
Scalar and vector products; curl, divergence, and gradient. Use of vectors and matrices in discussion of physical problems in mechanics, fluid flow, and electromagnetism. Introduction to tensors. Prerequisites: Math 22, 31, and consent of instructor.
2 lectures, 1 hour problems, one term.
44, Complex Variable. Cauchy-Riemann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration. 2 lectures, 1 hour problems, one term.
Frequency distributions; probability; Binomial, Normal, and Poisson laws. Sampling theory. Distribution of Chi-squared, F, and t. Hypothesis testing, quality control, regression theory. Curve fitting. Analysis of variance, introduction to experimental design.
The Heaviside Calculus and the Laplace Transform. Admittance, impedance, and other operators. Applications of operator techniques to problems in electricity, mechanics, and heat.
Prerequisites: Math 22, 31, and consent of instructor.
MATH 54Differential Equations of Mathematical Physics
The wave equation. Potentials. Boundary-value problems. Eigenvalue problems. Expansions in series of orthogonal functions. Spherical, cylindrical, and ellipsoidal harmonics. Prerequisites: Math 22, 31, and consent of instructor.
Fundamentals of digital computers, including memory types, arithmetic components, input-output and control units. Binary numbers, floating-point arithmetic, flow charting, machine-language coding. Automatic coding, including assemblers, compilers, and translators. Interpretive routines.
Cartesian Co-ordinates. The distance formula. Functions and their graphical representation. The linear function. Forms of the line equation. The quadratic function and roots of quadratic equations. Algebraic and geometric approach to loci. Standard forms for the circle, parabola, ellipse, hyperbola. The number system. Polynomial functions. Remainder theorem. Functions of more than one variable. Equations in one or more variables. The general trigonometric functions, their values and graphs. Radian measure. Compound angle formulae. Trigonometric formulae. Trigonometric equations. The sine and cosine laws for triangles. The logarithmic function. The law of logarithms. Arithmetic and geometric series. The binomial series. Properties of the binomial coefficients. Permutations and combinations.
A terminal course designed for Arts students who wish to learn something of the fundamental ideas of mathematics but who will not be encountering technical problems of application. The course will include discussion of the fundamental concepts involved in a selection of topics chosen from mathematical areas such as Calculus, Statistics, Probability, Projective Geometry, Non-Euclidean Geometry, Set Theory, Group Theory, Field Theory, Boolean Algebra, Mathematical Logic, Vector Spaces, Matrices, Numerical Analysis.
Functions and limits. The derivative. Differentiation of algebraic functions. Applications to tangents, rates, minima and maxima. Integration as the limit of a sum. Fundamental theorem of integral calculus with applications to areas, volumes, and moments. Power series. Partial differentiation. 3 lectures.
The real and complex number systems. Polynomial functions. Theory of equations. Determinants. Vector and matrix notation. Elementary solid geometry, planes and lines, the standard quadric surfaces. Co-ordinate systems. 2 lectures, one hour problems.
The topics of Mathematics 130, presented with a view to the special needs of Social Science students. Emphasis will be on basic concepts rather than on the more difficult manipulative techniques.
Real numbers, sequences. Limits. Continuity. Derivatives. Functions of several variables. Implicit functions. Jacobians. Taylor’s series with geometric applications. Power series with complex terms. The elementary functions for a complex variable.
Methods of formal integration. Differential equations. Fourier series. Riemann integration and applications. Calculus of variations. Line integrals. Stokes’ and Green’s theorems.
Frequency distributions. Probability. Binomial. Normal, and Poisson laws. Sampling theory. Curve fitting. Distributions of Chisquared, F, and t. Hypothesis testing. Quality control. Regression theory. Analysis of variance. Introduction to experimental design.
The statics of particles and rigid bodies, work and the stability of equilibrium. Motion of a particle in a uniform field. Oscillatory motion in one dimension. Motion of a system of particles and of a rigid body. Central forces. Accelerated reference systems. Motion of a rigid body in three dimensions.
The theory of compound interest and of life contingencies. An elementary course on the mathematics of investment and
on applications of probability to problems of life and death. Annuities, single and annual premiums. Reserves. Standard actuarial notation. 2 lectures.
An introduction to first order differential equations. Applications to growth, decay, reactions. Linear equations with constant coefficients. Systems of equations; vector and matric methods. Solutions in series. Introduction to partial differential equations.
Characteristics of design of digital computing machines. Programming languages. Algorithms and flow diagrams. Design of assembly systems, interpreters and compilers. Advanced programming techniques and operating systems.
The topics of Mathematics 233 presented with a view to the special needs of Social Science students. Emphasis will be on basic concepts rather than on the more difficult manipulative techniques.
The topics of Mathematics 243 treated without the use of Calculus. In addition to the basic statistical methods, emphasis will be placed on the nature of evidence and inference.
The nine-point circle. The Simson line. Cross ratio. Projection. Harmonic ranges and involutions. Properties of circles. Axioms of incidence for projective geometry. Duality. Theorems of Pappus and Desargues. Introduction of co-ordinates. Conic sections. Introduction to non-Euclidean geometry.
Vectors and vector spaces; transformations and matrices; quadratic and Hermitian forms. Algebraic structures, rings and ideals. Matrices with entries from a ring. Canonical forms and eigenvalues; the orthogonal group.
The real number system. Uniform convergence. Theory of Fourier series. The complex number system. Analytic functions. The Cauchy theorems. Contour integration. Singularities. Conformal mapping. 3 lectures.
First-order differential equations. Linear equations with constant coefficients. Solutions in series. Systems of differential equations. Introduction to partial differential equations. Introduction to integral equations.
Finite differences. Solution of equations. Computation with series and integrals. Linear systems and matric methods. Difference equations and relaxation methods. Numerical solution of partial differential equations. Methods employing electronic computers.
A theoretical course in the calculus of finite differences to include summation, the differences of zero, numerical integration, the relation between integration and summation. An introduction to difference equations. 2 lectures.
An advanced mathematical course including the multivariate normal law and related distributions. Normal regression theory. Applications to hypothesis testing and analysis of variance.
Introduction to basic concepts and theorems, connectivity, planarity, arboricity, directed graphs, partial orderings, girth and regularity, the four-colour problem.
Topological concepts. Analytic continuation. The Riemann surface. Entire meromorphic functions. Periodic functions. Special functions. General metric spaces. Function spaces. The integral as an operator.
Theory of metric spaces, completeness and compactness, measure in Euclidean n-space, the Lebesque integral, convergence theorems, the Fubini theorem, differentiability, absolute continuity. A study of Branch spaces.
MATH 434Differential Equation of Mathematical Physics
Boundary-value problems. Orthogonal functions. Bessel functions. The Legendre polynomials. The Fourier integral. The Laplace transform. The wave equation.
An informal introduction to the logic of sentences and predicates, with emphasis on analogies with familiar mathematical structures. Syllogisms and the algebra of sets related to predicate logic. Simplification, logical deduction, duality, consistency and completeness. The concepts of constant, variable, function, and set. Axiomatics.
The Schroedinger wave equation, interpretation of wave functions, harmonic oscillator in wave mechanics. The hydrogen atom. Perturbation theory. The variation methods. The W.K.B. approximation.
Covariant and contravariant tensors. Riemannian space. Gaussian curvature. The Lorentz transformation and Einstein’s special theory. Introduction to the general theory of relativity.
The development of Mathematics from ancient to modern times, including study of prominent mathematicians and _ their works. Problems will be worked using both modern and historical approaches. 2 lectures.
Logic of experimental designs. Randomization. Experimental and sampling errors. Designs applied in biology. Methods of analysis for factorial designs. Latin squares, etc.
Applied Mathematics for Science majors. Ordinary and partial differential equations. Laplace and Fourier transforms. Special functions. Fourier series. Vector and matric methods. Calculus of variations. Other topics in advanced calculus.
2 lectures.
Graduate and Research Programmes
While the department offers graduate work over a broad spectrum of the various branches of Mathematics, fields of special interest include: Abstract Algebra, Combinatorial Analysis, Computer Science, Decision Theory, Differential Equations, Differential Geometry, Foundations, Functional Analysis, Functional Equations, Graph Theory, Harmonic Analysis, Mathematical Logic, Number Theory, Numerical Analysis, Operations Research, Probability, Statistical Inference.
Extensive computer facilities are available in the Computer Center and include an IBM 1401, an IBM 1620, an IBM 1710 system, and an IBM 7040. Each year, one or more Visiting Professors spend a term with the Department. Recent visitors include G. Temple (Oxford), W.B. Pennington (Aberystwyth), H. Rund (South Africa), G. Menges (Saarbrucken), C. St. J. Nash- Williams (Aberdeen).
Extensive opportunities for fellowship assistance are available through National Research Council Fellowships and Province of Ontario Graduate Fellowships. In addition, the Department of Mathematics offers a number of Teaching Fellowships which may be held singly, or in conjunction with other Fellowships. For details, correspondence should be addressed to the Department Chairman.
Candidates for the degrees of M.A., M.Sc., M.Phil. and Ph.D. are accepted under the general regulations set forth in the section of the calendar pertaining to the Faculty of Graduate Studies. Candidates for the M.A. or M.Sc. degrees in Mathematics are normally advised to take the degree by course work rather than by thesis.
Concepts from Thermodynamics. One-dimensional gas dynamics. One-dimensional wave motion. Waves in supersonic flow. Flow in ducts and wind tunnels. Methods of measurement. Equations of frictionless flow. Small-perturbation theory. Bodies of evolution, and slender body theory. The similarity rules of high-speed flow. Transonic flow. The methed of characteristics. Effects of viscosity and conductivity. Laminar and turbulent boundary layers. Concepts from gas kinetics.
Department of Mathematics
604, Special Functions. Elliptic functions. The hypergeometric function. The gamma and beta funtions. The functions of Laplace, Legendre, Lamé, Mathieu, and Bessel. Orthogonal functions; the functions of Laguerre, Hermite, Chebyshev.
General concepts of computer types and applications. Flow charting, Coding, instruction formats. Editing. Storage elements and buffers. Control and accuracy in digital computers. Input and output devices and their use. Number systems. Automatic programming and universal computer languages. Logic and Boolean Algebra. Heuristic programming. Elements of logical design.
Vector spaces, linear transformations, matrices. Euclidean spaces, groups of transformations, algebra of tensors; covariant
differentiation, divergence, Laplacian, curl. Generalizations to Riemannian spaces. Applications to other fields including differential geometry, mechanics, elasticity, hydrodynamics, electricity, and general relativity.
Non-numeric computing. List processors and their application to the calculation of recursive functions, language translation, analytic differentiation and integration, mathematical logic, sorting, heuristic programming. Polish strings. Simulation of a List Processor.
MATH 641Mathematical Methods for Operations Research
A series of courses with emphasis on mathematical techniques having direct application to business, industrial, military, and scientific problems.
(a) Special Methods. Algebra of probability distributions; Monte Carlo methods; application to queuing theory, replacement theory, and inventory control.
1 term.
(b) Model Analysis. Partially ordered models, stochastic models, general model logic; exampies from business, industry, and the military including the Leontiev model from Economics; construction of models, optimization, computational methods.
1 term.
(c) Competitive Models. A selection of topics from game theory, gaming, and decision theory. 1 term.
(a) Analytic Methods. Review of classical methods; optimization of discrete functions, inequalities, introduction to linear programming, steepest descent and optimal control.
(c) Linear Programming. Simplex methods; flows in networks; application to transportation problems; assignment problems, and project cost curves. 1 term.
Department of Mathematics
(d) Programming. A selection of topics from non-linear programming including the simplex method for quadratic programming, Lagrangian differential, gradiant and gradient projection; introduction to integer programming and dynamic programming.
The Euler equations and the Lengendre and Jacobi conditions. The Weierstrass E function and sufficient conditions. The theory of transversals and isoperimetric problems. Hilbert’s existence theorem. Selected topics from the theories of Kneser and Caratheodory, the problem of Bolza.
G. T. Csanady, Dipl. Ing.. (Munich), Ph.D. (New South Wales) Professor and Chairman of Department
S. Alpay, Dipl. Ing., Dr. Ing. (Berlin) - - - - Professor T. A. Brzustowski, B.A.Sc. (Toronto), A.M., Ph.D.
(Princeton) - - - - - - - Professor M. J. Hillier, B.Sc. (Eng.), B.Sc. (Gen.) (London).
D.LC., M.Sc. (Eng.) (London) - - - - Professor A. A. Bruneau, B.A.Sc. (Toronto). D.I.C., Ph.D.
(London) - - - - - - Associate Professor E. W. Brundrett, B.S.A. (Ontario Agricultural College, Guelph).
B.A.Sc., M.A.Sc., Ph.D. (Toronto) - - Associate Professor H. L. Evans, M.Sc. (Wales), D.I.C., Ph.D. (London) - Associate Professor J. H. G. Howard, B.Sc. (Queen’s), M.Sc., Ph.D.
(Birmingham) - - - - - Associate Professor W. B. Nicoll, S.M. (Massachusetts Institute of Technology).
Engineer (Stanford) - - - - Associate Professor G. F. Pearce, B.A.Sc. (British Columbia), M.A.Sc.
(Toronto) - - - - - - Associate Professor G. M. Bragg, B.A.Sc. (Toronto), Ph.D. (Cambridge) - Assistant Professor D. E. Coates, B.A.Sc. (Toronto), M.S. (Illinois) - Assistant Professor C. E. Hermance, B.E. (Yale), M.A., M.S.E., Ph.D.
(Princeton) - - - - - - Assistant Professor K. R. Piekarski, Dipl. Ing. (London) - - Assistant Professor A. Plumtree, B.Sc., Ph.D. (Nottingham) - - Assistant Professor A. M. Hale, B.Sc., M.A. (New Brunswick), B.A.Sc. (Toronto).
M.A.Sc. (Waterloo) - - - - - - Lecturer T. Kowalski, B.Sc. (Glasgow), M.S. (Stevens Institute) - Lecturer V. Kuppu Rao, B.E. (Bangalore), M.S. (Cornell) - - Lecturer A. B. Strong, B.A.Sc. (Waterloo) - - - - - Lecturer
Department of Mechanical Engineering
a aa
Undergraduate Programmes
Details of the undergraduate programme in Mechanical Engineering are to be found on page 72. All courses extend over one semester only.
The effects of dynamic forces in machines; introduction to mechanical vibrations. Transient forces. Static force 3 a mic force analysis, balancing, cam dynamics, dynamics of feed'
An analytical treatment of various machine elements in a form suitable for making design calculations. Working stresses, creep, impact considerations. Design of shafting, springs, screws, clutches and brakes, ball bearings, gears, pipe bends and simple plates.
Principles of optimum design, optimizing for minimum cost, maximum power capability, minimum weight, effects of manufacturing errors on product performance, statistical considera-
tion for the factor of safety, optimum design of machine elements; torsion shafts, beams, gears, etc. Fluctuating loads, impact forces. Analog methods. Prerequisite: ME 22.
A broad development of mechanical vibration and impact. Transient phenomena, self-excited vibration, torsional oscillations, multi-mass systems, analogies and analog computer. Forced vibrations, elimination and absorption of vibration. Measurement of vibration.
Nucleation and growth in metals. Diffusion and sintering. Fundamental aspects of condensed phase equilibria in binary metal systems. Dinary and ternary entectic phases. Non-equilibria in metal systems. Surface phenomena. Corrosion and oxidation in metals.
Elasticity and plasticity of metals. Recovery, recrystallization and grain growth. Hardening mechanisms. Heat treatment of metals and alloys. Shear transformations. Failure in meétals.
Bravais lattices and Miller indices. Electronic, atomic, electron-atomic and quantum imperfections. Slip dislocations and twinning dislocations. Grain boundaries and domain walls. Shear transformations. Techniques for observing imperfections. Diffusion.
An introductory course in nuclear reactions and their engineering applications, including neutron/fission chain reactors, and nuclear radiation uses. Topics covered will include kinds and characteristics of nuclear reactions and radiations, principles of fission and decay chain reactions, elementary nuclear reactor design, radiation detection, effects of radiation, hazards and shielding.
Prerequisite: Physics 15 or equivalent, at least 3B standing.
3 hours lecture per week, 2 hours laboratory every second week.
The crystallography of ionic and co-valent compounds. A study of the mechanical properties of single crystals and polycrystals. Properties of special ceramic materials.
Mechanical and physical requirements of materials used as fuels, moderators, shields and structural components in reactors. Special problems related to corrosion, radiation damage and high temperatures. Materials selection. Radioactive waste disposal.
Models of a plastically deforming ‘metal; yield and flow. Analysis and mechanics of mechanical working operations. Patterns of flow, limiting factors; force, instability and temperature. Influence of processes on work piece properties. Applications to forging, drawing, extrusion.
Mechanics of metal cutting operations. Geometrical, force and energy analysis of single and multipoint tools, rotary cutters and grinding. Modern developments: electrochemical, spark discharge and ultrasonic methods. Economics, variability, tolerances and quality control.
Moulding from the liquid state. Review of applicable heat transfer and fluid flow theory. Influence of time in casting. Solidification time, freezing waves and riser design. Pouring time, fluidity, gating and running. Hot tears, distortion, shrinkage and residual stresses. Die casting: thermal balance, thermal stability, pressure pulse effects. Other casting methods.
Prerequisite: ME 53, GE 32.
44, Manufacturing Science V. Welding. Phase relations, equilibrium diagrams, solubility, fluidity, wetting, solidification in single and ultiphase materials, segregation and heterogeneity, weldability, adhesion, oxidation, corrosion. Thermal and residual stresses. Applications in welding, brazing, diffusion bonding. Modern developments.
Manufacturing. for design engineers. Ciassification of processes. Influence of choice of materials on processes and of choice of processes on design. Process limitations; tolerances; influence of scale of manufacture. Economic considerations.
Interactions of design and manufacturing functions. Information flow, data specification.
Theory and practice of high precision mechanical measurements under strict control conditions —- super micrometry; measurements by comparators; profiiometry; surface profilography; environmentai effects on measurements accuracy; theodolite techniques in the measurements of large structures; collimator applications in machine installation; photography as a mensuration tool for moving (dynamics) conditions, stroboscopic measurements for frequency drift in rotating machinery.
Introduction to heat transfer mechanisms. The formulation of heat transfer problems. Temperature distributions in solids under steady and transient heat conduction. Laminar forced convection, the use of boundary layer theory and the integral method for evaiuating the heat transfer coefficient. Laminar and turbulent free convection, empirical correlations and introductory analysis. Reynolds and Colburn analogies.
3 lectures, 3 hours laboratory, alternative weeks.
§4, Therm
: 54, Thermodynamics IT. Review of the basic concepts and postulates of thermodynamics and the conditions for equilibrium. Reactive systems. An introduc- Han tn ieravarcihle th ndunamicng A linatinna + galarta, anginsar.
tion to irreversible thermodynamics. Applications to selected engineering syetam "7 adie : tt Ramer met nan a) Pee ath a L + soln
Kinetic theory of an ideal gas, velocity distribution function, simple theory of transport properties. Maxwell-Boltzmann statistics, energy levels from classical and quantum mechanics. The partition function, evaluation of thermodynamic properties from partition functions with examples for gases, liquids and solids. Chemical equilibrium, equilibrium constants, the third law of thermodynamics. Fluctuations.
Forced convection in high-speed flow. Boiling and condensation. Ablation. Mass transfer in laminar and turbulent flows, empirical correlations and an introduction to analysis by the boundary-layer theory and by the integral approach. Radiation heat transfer, radiative properties, geometrical factors, analogue methods. Simple kinetic theory of transport properties.
Fluid properties. Basic relationships. Inertance, capacitance, resistance. Input and output devices. Transfer functions. Spool forces for steady-state and transient conditions. Design of spools. Reduction of undesirable forces. Fluid-power transmission. Simulation of hydraulic sytsems.
Ideal Fluids: Equations of motion of non-viscous fluid; sample solutions of two and three-dimensional problems; Fourier analysis; conformal mapping in two-dimensional flow; shortcomings of ideal fluid models. Real Fluids: viscosity, the Navier-Stokes equations, flows at low Reynolds number; laminar boundary layers; short introduction to turbulent flow.
Performance characteristics, laws of modelling, classification and selection of turbomachines. Cavitation, suction specific speed. Reynolds number and Mach number effects, small stage efficiency. Dynamic analysis of the energy transfer in the turbomachine, application to the principal types of pumps, compressors and turbines. Cascade mechanics.
The problems of incorporating human beings into engineering systems. The topics discussed are: the human visual, auditory and musculo-skeletal system, multiple sensory inputs, man-machine dynamics, environmental factors, human stress, group dynamics, and work-place design; the evaluation and testing of man-machine systems.
Designed to give the student personal experience in oral presentation of technical information. Also provides an opportunity for students to attend seminars on topics of interest presented by recognized workers in the field.
Engineering assignments requiring the student to demonstrate initiative and assume responsibility. Student activity is guided and co-ordinated by faculty supervisor. In selecting and assigning projects, particular account is taken of the student’s field of specialization. Projects, in general, involve technical disciplines beyond the strictly mechanical engineering field.
Engineering problems arising from utilization of nuclear reactions. Topics covered include multi-group diffusion theory, kinetics and stability, heat removal and materials problems in nuclear power reactors, direct conversion of nuclear energy to electricity, accelerator design and shielding, and process applications of nuclear radiations.
Prerequisite: Math 55 or equivalent, ME 35 or equivalent and 4B standing. Two hours lecture per week, 2 hours laboratory every second week.
Graduate and Research Programmes
A. The Master’s Degree. Two types of Master’s degree are awarded in mechanical engineering: one based on a research thesis, type R, supplemented by some course work, the other based entirely on course work or “scholarship,” type S.
Master’s degree by course work: Type S is intended mainly for the student entering after some years in industry to bolster his technical background. Part-time or full-time co-operative graduate students may be particularly interested in this degree. The requirements for the degree consist of not Jess than 8 one-semester courses which must be passed with an average of 66% or better. The courses are selected with a view to ensuring that the student becomes a competent specialist in a certain branch of engineering science. Areas of specialization in which a Master’s degree, type S, is offered are, at present.
1) Materials Science
3) Fluid Dynamics 4) Manufacturing Science
A student desirous of entering this programme is advised to consult the coordinator of the area of specialization in which he is interested. Course work programmes for the degree are drawn up by the co-ordinator in consultation
with the student. No financial assistance, in the form of teaching or research fellowships is offered to candidates working toward a Master’s degree, type S.
The Master’s degree, type S, is regarded as a terminal qualification and it is not normally contemplated to admit a graduate having this degree to our Ph.D. programme.
Master’s degree by research work: The Master’s degree, type R, may, on the other hand, also be regarded as the first year of a coherent three-year course of study toward the Ph.D. degree. However, this is not intended to mean that such is the exclusive purpose of a type R Master’s degree: many students may wish to proceed no further than this degree. Also from the University’s point of view the M.A.Sc. is a complete qualification and students attaining it are not necessarily admitted to further study toward a Ph.D. degree, but only if they have demonstrated the required ability to carry out independent fundamental research.
In a field of applied science such as mechanical engineering the core of graduate work is normally (excepting the Master’s degree, type S, described before) a thesis project with substantial experimental content. The choice of the thesis project is an important decision, because a later change in the student’s field of research usually entails loss of time. The most satisfactory way to choose a topic is for the prospective graduate student to interview several faculty members active in research in a field of possible interest to the student, and select a project with the concurrence of a faculty member who will then act as thesis supervisor. Normally, such a faculty member also arranges financial support for the graduate student with the aid of externally obtained research grants. Financial commitments for the support of students are usually made by the faculty early in April so that it is advisable to complete negotiations before the end of March. Arrangements with overseas students and others unable to visit Waterloo several months prior to registration are made on the basis of their interests described on the application form. A faculty member may under such circumstances offer to a prospective student financial support for research in a specific area of the faculty member’s interest. Active fields of research in which students may at present be accepted are listed and described in the faculty research brochure. It must be kept in mind, however, that the list is only intended as a guide since new topics are added frequently as the sphere of interest of the faculty expands while some projects are completed or abandoned.