139 courses in the 1967–68 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Faculty of Mathematics
stochastic processes. with applications to Brownian movement, diffusion, and noise. 3 lectures, one term.
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.
2 lectures, | hour problems, one term.
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.
2 lectures, | hour problems, one term.
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.
Prerequisite: Math 32.
3 lectures, one term.
Fundamental properties of vector spaces. Matrices as operators in vector spaces. Quadratic forms. Functions of matrices. Applications.
Prerequisite: Math 21.
3 lectures, one term.
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 séries. The binomial series. Properties of the binomial coefficients. Permutations and combinations.
3 lectures.
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.
3 lectures.
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 matric notation. Elementary solid geometry, planes and lines, the standard quadric surfaces. Co-ordinate systems. 2 lectures, one hour problems.
Introduction to finite differences. Interpolation. Numerical integration. Introduction to the use of electronic computers or electric calculators.
1 lecture, 2 hours problems.
The topics of Mathematics 130, presented with a view ot the special needs of Social Science students. Emphasis will be on basic concepts rather than on the more difficult manipulative techniques.
3 lectures.
Introduction to the theory of sets and groups. Introduction to rings and fields. Vector spaces and matrices. 3 lectures.
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.
2 lectures.
Methods of formal integration. Differential equations. Fourier series. Riemann integration and applications. Calculus of variations. Line integrals. Stokes’ and Green’s theorems.
3 lectures.
Frequency distribution. Probability. Binomial. Normal, and Poisson laws. Sampling theory. Curve fitting. Chi squared, F and t distributions. Hypothesis testing. Quality control. Regression theory. Analysis of variance, introduction to experimental design.
2 lectures, 1 hour problems.
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.
2 lectures.
Faculty of Mathematics
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.
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.
2 lectures.
Real numbers, sequences, limits, continuity, derivatives. Functions ot several variables, implicit functions, Jacobians, Taylor’s series. Methods of formal integration; differential equations. Fourier series. Riemann integration; line integrals.
Characteristics and design of digital computing machines. Programming languages. Algorithms and flow diagrams. Design of assembly systems, interpreters and compilers. Advanced programming techniques and operating systems.
2 lectures.
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.
Prerequisite: Mathematics 140 or equivalent.
3 lectures.
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.
3 lectures.
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.
3 lectures.
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.
2 lectures.
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.
2 lectures.
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.
2 lectures, 2 hours laboratory.
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 course on problems of single lives and on the death and survival of multiple lives. 3 lectures.
Lagrangian and canonical equations of motion. Canonical transformations. Hamilton-Jacobi equations. Relativistic mechanics. 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.
2 lectures.
Electrostatics and magnetostatics. The theorem of Gauss. Development of the Maxwell equations. 2 lectures.
A discussion of the hardware and software required in a computer system. Overlapped channels, interrupt facilities, memory protection, buffers, input-output control systems, macro-programming, monitor systems. Relocation schemes, multi-programming, multi-processing, dynamic memory allocation, time-sharing. Special purpose computer systems and simulation of computer systems. Peripheral equipment. Introduction to the theory of sequential machines and the logical design of computers.
2 lectures.
2 lectures.
Topological spaces. Cartesian products, continuous mappings, separation axioms, connectedness, compact and locally compact space metrizability.
2 lectures.
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Faculty of Mathematics
Introduction to basic concepts and theorems, connectivity, -_planarity, arboricity, directed graphs, partial orderings, girth and regularity, the four-colour problem.
2 lectures.
Ordered sets, lattices, Galois connections. Special attention is given to geometric lattices (matroid theory).
Prerequisite: Mathematics 230.
2 lectures, one term.
Homology theory of complexes. Theorems of invariance, covering, and duality.
Prerequisite: Mathematics 230.
2 lectures, one term.
Representations by fields, groups and algebras. Finite Euclidean geometries. Sub-geometries. Collineation groups. Tactical configurations.
2 lectures.
2 lectures.
Entire functions, Meromorphic functions, Riemann surfaces, Analytic continuation, Conformal mapping, Function spaces. Linear Operators.
2 lectures.
Theory of metric spaces, completeness and compactness, measure in Euclidean n-space, the Lebesgue integral, convergence theorems, the Fubini theorem, differentiability, absolute continuity. A study of Banach spaces.
2 lectures.
Boundary-value problems. Orthogonal functions. Bessel functions. The Legendre polynomials. The Fourier integral. The Laplace transform. The wave equation.
2 lectures, 1 hour problems.
Numerical problems arising in actuarial science and statistics. 2 hours laboratory.
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.
2 lectures.
Methods of constructing and graduating mortality. tables. 2 lectures.
The mathematics and logic of estimation and hypothesis testing. Information. Consistency. Efficiency. Sufficiency. Fiducial and confidence intervals. The problems of large and small samples. 2 lectures.
The logic of experimental design. Randomization. Experimental and sampling errors. Mathematical methods of constructing various designs. Applications to problems in the sciences.
2 lectures.
Recurrent events. Markov processes and applications to Physics and Biology. including diffusion processes and epidemics. 2 lectures.
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.
2 lectures.
Covariant and contravariant tensors. Riemannian space. Gaussian curvature. The Lorentz transformation and Einstein’s special theory. Introduction to the general theory of relativity.
2 lectures.
Applications of the Maxwell equations. Reflection and refraction. Introduction to wave guides and antennae. 2 lectures.
444, Elasticity. Problems in stress and strain. Isotropic bodies. Equilibrium equations. Torsion and flexure. 2 lectures.
Continuous and discontinuous flow. Aerofoil theory. Viscous flow. 2 lectures.
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.
Applications of probability theory to theoretical Physics. 2 lectures.
Curves in space. Gaussian curvature. Tensorial notation. Introduction to differentiable manifolds. 2 lectures.
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Faculty of Mathematics
Logic of experimental designs. Randomization. Experimental and sampling errors. Designs applied in biology. Methods of analysis for factorial designs. Latin squares, etc.
2 lectures.
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 faculty 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.
The University of Waterloo’s computing facilities presently include four computer systems, namely, IBM 1620, IBM 1710, IBM 7040 and IBM SYSTEMS/
analogue computer in conjunction with the 1710 to give a hybrid system.
The IBM 1620 computer is available to undergraduate students at all times. The IBM 1710 is used by undergraduates, graduates, faculty and staff according to schedules made up one week in advance. Both the 7040 and the Systems/360 are run on a closed shop basis, but all members of the University can get programmes processed within a reasonably short time.
Systems planned for the future include an IBM System/360, Model 44, and, at a later date, an even more powerful Systems/360 Computer.
Extensive opportunities for fellowship assistance are available through National Research Council Fellowships and Province of Ontario Graduate Fellowships. In addition, the Faculty 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. Math., M. Phil. and Ph.D. are accepted under the general regulations set forth in the section of the calendar pertaining to the Graduate Studies.
PURE MATHEMATICS: Current research in pure mathematics includes studies in functional equations for analytic functions, categories of incidence geometries, theory of integration and measure, the enumeration of planar maps, matrixlike representations of infinite groups, homotopy theory, contact manifolds, theory of generalized decompositions of groups, logic and foundations of set-theory. and general functional equations.
Functional equations — that is, roughly speaking, the theory of determining
functions from elementary equations containing them — is a field of mathematics looking back into a history of more than two centuries. the somewhat general theory of which has been developed however only in the last two decades and it has applications in and is connected with such modern disciplines as the theory of information, mathematical psychology and universal algebra.
At the University of Waterloo we work on these problems, on general methods and uniqueness theorems, and also on applications to and relations with differential geometry, homological algebra, functional analysis, theories of continuous groups of nets and of complex functions. etc.
COMPUTER SCIENCE: Research in compiler construction has produced the WATFOR fast FORTRAN IV compiler, completed in 1965 and currently used by over seventy 7040-7044 computing centres throughout the world. Research and development work on similar compilers for the 360 series machines is progressing well.
A graphic display unit will permit research in new techniques in computer-aided design, computer graphics, graphic programming and simulation. Also, a process control computer is currently used to perform and analyze complex experiments, some of which wouid be difficult to handle by conventional methods. In numerical analysis, algorithms for two-point boundary problems, stiff systems of differential equations, unilateral matrix equations and optimization problems are under investigation.
In addition, many computer-oriented research projects by faculty and graduate students in science, engineering and the humanities are pursued with the assistance of the Computer Science department. It is this wide variety of problems which makes the department environment so stimulating to faculty and students alike.
STATISTICS: Research in the Department of Statistics centres on the controversial problem of formulating exact statistical inferences in many diverse situations using generalizations of the approach introduced by the late Sir Ronald Fisher in his foundation of the theory of fiducial inference, the theory of the likelihood function and the theory of estimation in general. The extensive computing facilities available at the University of Waterloo have given rise to investigations into the uses of computers to obtain exact results on the basis of these theories in situations previously treated by asymptotic methods, and also research into exact tests in multivariate analysis.
Closely related to this research, there is active interest in problems of experimental design, with particular reference to incomplete designs, multivariate analysis, estimation theory, mathematical genetics and stochastic processes.
Members of the department are also interested in problems in combinatorial mathematics, such as the construction of balanced incomplete block designs, which arise in the design of experiments. Other combinatorial questions under consideration include edge-chromatic graphs and the Ramsey numbers.
Faculty of Mathematics
Increasing contact with the departments of Chemistry, Physics and Psychology provides a variety of new problems and also gives advanced students a valuable opportunity to apply lecture material to useful practical situations. An arrangement with the Statistics Unit of the Department of Agriculture in Ottawa provides potential summer employment for advanced undergraduates and at the same time, a further opportunity for practical experience.
APPLIED MATHEMATICS: Research in this department is being carried out in a number of areas directly or indirectly applicable to problems in the Physical Sciences. The range of interests of the members of the department reflects the diversity of problems of a mathmatical nature which arise in the real world.
The major areas of specialization include Nonlinear Ordinary Differential Equations, Spectral Theory of Differential Operators, Partial Differential Equations, Potential Theory, Functional Equations, Calculus of Variations, Boundarylayer Problems in Fluid Dynamics, Harmonic Analysis and Differential Geometry.
Graduate Course Descriptions
§50. Axiomatic Set Theory. First order theories and their properties. Formal number theory. Set theory as a first order theory. Elimination of the logical paradoxes. Comparison of several axiom systems for set theory. Basic concepts of mathematics. Bourbaki’s structure theory and the theory of categories. The theory of ordinals. Transfinite arithmetic. The axiom of choice. The axiom of restriction. The generalized continuum hypothesis. Summary of recent independence proofs.
(a) Introduction to Numerical Analysis
1 term.
(b) Solution of Ordinary Differential Equations 1 term.
(c) Constructive Theory of Functions (Approximation Theory) 1 term.
(d) Numerical Methods in Linear Algebra 1 term.
(e) Solution of Partial Differential Equations 1 term.
(f) Problems in Numerical Integration 1 term.
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 revolution, and slender body theory. The similarity rules of high-speed flow. Transonic flow. The method of characteristics. Effects of viscosity and conductivity. Laminar and turbulent boundary layers. Concepts from gas kinetics.
Elliptic functions. The hypergeometric function. The gamma and beta functions. The functions of Laplace, Legendre, Lamé, Mathieu.
and Bessel. Orthogonal functions; the functions of Laguerre, Hermite, Chebyshev.
(a) Introduction to Random Variables. Probability, random variables, distribution functions, expectation, discrete transform methods. 1 term.
(b) Theory of Probability. Measures on a sample space, types of convergence, limit theorems, laws of large numbers.
1 term.
(c) Stochastic Processes I. Discrete space — discrete time processes. Discrete space —- continuous time processes. Applications in Physics, Biology, Queuing Theory, etc.
1 term.
(d) Stochastic Processes IT. Mathematical foundations of stochastic processes, continuous space processes. Time-series. analysis.
(e) Special Topics in Probability. 1 term.
(a) Integral Transforms
1 term.
(b) Complex Variable Techniques 1 term.
(c) Fourier Series and Orthogonal Functions 1 term.
(d) Group Theory in Physical Problems 1 term.
(a) The Theory and Construction of Compilers. Some theoretical aspects of mechanical language translation with references to compilers and compiling techniques both past and present, including general compiler organization, statement decomposition, syntax analysis, code optimization and compiler compilers.
One term.
(b) Computer Systems. A discussion of the hardware and software required in a computer system. Including overlapped channels, interrupt facilities, memory protection, buffers, input-output control systems, macro-programming, multi-processing, dynamic memory allocation, time-sharing.
One term.
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Faculty of Mathematics
General concepts of computer types, the stored programme, computers with different addressing schemes. Machine language and assembly language coding. Input and output devices and their uses. Number representations. Number systems. Automatic programming and universal computer languages, the recursive definition of a programming language, the design of compilers for algebraic languages, the use of algebraic languages (FORTRAN and ALGOL) in matrix and other calculations in numerical analysis, other special purpose languages for mathematical calculations, list processing, inductive inference. Mathematical theory of automata.
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, hydro-dynamics, electricity, and general relativity.
This course is intended for behavioral scientists who wish to use computers in their research. Introduction to computer systems and their components. Algorithms and flow charts. Programming in a procedure oriented language (Fortran IV) and machine and assembly languages. An application of computers to areas in behavioral science including statistical analysis, linear programming, simulation and file processing.
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.
A selection of topics
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.
(b) Linear Programming. Simplex method; flows in networks; application to transportation problem, assignment problem and project cost curves.
(c) Competitive Models. Game theory; gaming; decision theory.
(d) Model Analysis. Partially ordered models; stochastic models; general models; general model logic; examples from business, industry and the military, including PERT* CPM, and the Leontiev model; construction of models.
simulation, optimization, computational methods.
(a) Analytic Methods. Review of classical methods; optimization of discrete functions; convex functions.
(b) Sequential Optimization. Methods including Fibonacci search, steepest descent, conjugate gradients and successive approximations; application to the solution of equations, curve fitting, likelihood estimates.
(c) Programming. Non-linear programming; stochastic programming; linear integer programming; dynamic programming; applications, including optimal digital control.
Prerequisite: 641, 642 or equivalent.
Categories and functors. Categories of Modules. Types of rings and modules. The standard functors. Derived functors. Homology and cohomology theory of algebraic systems. Kiinneth formulae. Spectral sequences. Dimension.
Introductory lectures concerning the standard axiomatizations and classical examples of matroids (i.e.: incidence geometry, or the theory of combinatorial dependence). Outlines of current research in the combinatorial, algebraic, geometric, latticial, and integer-programming schools of matroid theory will be drawn.
Manifolds, tangent bundles, differential forms, deRham cohomology, deRham’s theorems. Whitney’s embedding theorem, existence of differentiable structures, obstructions to differentiable structures, characteristic classes, almost-complete manifolds.
(a) Partial Differential Equations. 1 term.
(b) Hyperbolic Partial Differential Equations. 1 term.
(c) Elliptic Partial Differential Equations. 1 term.
(d) Parabolic Partial Differential Equations. 1 term. 262
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Faculty of Mathematics
The Euler equations and the Legendre 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.
Definitions and basic theorems. Planar graphs and Kuratowski’s theorem. Selected topics from advanced graph theory.
Effective computability. Primitive recursive and recursive functions. Recursively enumerable sets. Formal systems. Church’s thesis. Port’s normal form theorem and recent developments. Turing and Markov algorithms. Arithmetization of first order theories. Universal systems. Undecidable problems. Incompleteness theorems. Recursive function theory (stricto sensu).
Department of Mechanical Engineering
G. T. Csanady, Dipl. Ing. (Munich), Ph.D. (New South Wales) Professor and Chairman of the Department
S. A. Alpay, Dipl. Ing., Dr. Ing. (Berlin) - - - Professor T. A. Brzustowski, B.A.Sc. (Toronto), A.M., Ph.D.
(Princeton) - - - - Professor H. L. Evans, M.Sc. (Wales), D. 1 C., Ph. D.
(London) - - - Professor M. J. Hillier, B.Sc. (Eng.), B. Se. (Gen. ) (London).
D.LC., M.S. (Eng.) (London) - - - Professor
E. L. Holmes, B.Sc. (Bristol), M.A.Sc., Ph.D. (Toronto) Professor and Associate Dean of the Faculty of Engineering G. F. Pearce, B.A.Sc. (British Columbia), M.A.Sc. (Toronto) Professor and Associate Chairman of the Department E. Brundrett, B.S.A. (Ontario Agricultural College, Guelph).
B.A.Sc., M.A.Sc., Ph.D. (Toronto) - - Associate Professor A. A. Bruneau, B.A.Sc. (Toronto), D.LC., Ph.D.
(London) - - - - Associate Professor D. J. Burns, B.Sc., Ph.D. (Bristol) - - Associate Professor D. E. Coates, B.A.Sc. (Toronto), M.S. (Illinois) - Associate Professor C. E. Hermance, B.E. (Yale), M.A., M.S.E., Ph.D.
(Princeton) - - - Associate Professor J. H. G. Howard, B.Sc. (Queen’s), M. Sc., Ph. D.
(Birmingham) - - Associate Professor W. B. Nicoll, S.M. (Massachusetts Inst. of Tech. ), Engineer
(Stanford) - - - - Associate Professor K. R. Piekarski, Dipl. Ing. (London) - Associate Professor (on leave of
: absence 1966-67)
R. F. Scrutton, B.Sc., M.Sc. (Melbourne) - Associate Professor G. M. Bragg, B.A.Sc. (Toronto), Ph.D. (Cambridge) - Assistant Professor A. M. Hale, B.Sc., M.A. (New Brunswick), B.A.Sc. (Toronto).
M.A.Sc. (Waterloo) - - - - Assistant Professor P. Niessen, B.Sc. (McMaster), M.A.Sc., Ph.D.
(Toronto) - - - Assistant Professor P. T. FitzRoy, B.E. (Melbourne), M. S. LE., Ph. D.
(Purdue ) - - - Assistant Professor A. Plumtree, B.Sc., Ph.D. (Nottingham) - - Assistant Professor C. J. Beingessner, B.Sc., M.A.Sc., Ph.D.
(Toronto) - - Assistant Professor (half-time) K. G. Adams, B.Sc. (Queen’ s), M. A. Sc. (Waterloo) = - - Lecturer T. Kowalski, B.Sc. (Glasgow), M.S. (Stevens Institute) - Lecturer T. A. Ledwell, B.Eng., M.Eng. (Nova Scotia) Lecturer W. K. Luk, D.I.C. (Imperial College, London), Dipl. of f Hong Kong
Tech. College) Lecturer V. K. Rao, B.E. (Mysore), ALISc., M. Ss. (Cornell) - Lecturer A. B. Strong, B.A.Sc. (Waterloo), M.Sc.
(Imperial College, London) - - - - Lecturer
Department of Mechanical Engineering
Undergraduate Programmes
Details of the undergraduate programme in Mechanical Engineering are to be found on page 72. All courses extend over one semester only.
Undergraduate Course Descriptions
A basic course in kinematics emphasizing the creative approach. Uniform rotary motion including rolling cylinders, gears and the synthesis of gear trains including planetaries. Non-uniform motion including cams, gears and linkages. Programming non-uniform motion and the synthesis of cam mechanisms, non-circular gear trains and linkages.
3 lectures, 3 hours laboratory.
The effects of dynamic forces in machines; introduction to mechanical vibrations. Transient forces. Static force analysis, dynamic force analysis, balancing, cam dynamics, dynamics of feedback systems. Prerequisite: ME 13.
2 lectures, 3 hours laboratory.
Factors affecting working stresses, fatigue, creep and impact considerations. Design of shafting, springs, screws, clutches, brakes and gears.
Prerequisite ME 21.
2 lectures, 2 hours laboratory.
Principles of optimum design of machine elements; minimum cost, minimum weight, maximum power, etc. Statistical consideratfons in factors of safety and tolerances. Effect of manufacturing errors on product performance.
Prerequisite: ME 22.
3 lectures.
A second course in engineering dynamics. Topics: rocket and space dynamics, inertia tensor and Euler’s Equations, energy methods, gyroscopic motion, generalized co-ordinates and Lagrange Equations, vibrations.
3 lectures, one term.
Prerequisite: GE 42.
Fundamentals of mechanical vibration. Forced, transient and non-linear vibrations. Numerical methods for multi-degree-of-freedom systems. Continuous systems. Vibration isolation. Measurements of vibration. Use of models and the analogue computer.
-26. Mechanical Design ITT — Human Factors Engineering. 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.
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.
2 lectures.
Elasticity and plasticity of metals. Recovery, recrystallization and grain growth. Hardening mechanisms. Heat treatment of metals and alloys. Shear transformations. Failure in métals.
2 lectures.
34, Impurities and Imperfections in Solids. 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.
3 lectures.
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.
2 lectures.
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, rolling, sheet-drawing and deep drawing. Modern developments: high velocity forming; chemical, electro-magnetic and spark discharge methods.
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.
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