39 courses in the 1985–86 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Courses not offered in the current academic year are listed at the end of this section.
Mathematical models for problems in the physical and biological sciences. Typical problems chosen from ecology, special relativity, spread of epidemics, tumours and tumors. Solutions to problams will be obtained primarily by differential equations.
Prereq: MATH 1308
Further rnathematical models from various disciplines. An introduction to Newtonian mechanics will also be included in the course.
Prereq: AM 260, or MATH 2308, or consent of instructor
Credit will be granted for only 1 of AM 270, 280
Case studies of typical problems in Applied Mathematics. Dimensional Analysis and the Pi theorem. Elementary group-theoretic methods. Scaling and perturbation theory.
Prereq: MATH 240A, or MATH 230A and consent of instructor.
Credit will be granted for only 1 of AM 270, 280 .
Difference equations, Laplace transforms applied to discrete and continuous mathematical models taken from ecology, biology, economics and other fields.
Prereq: MATH 220b or consent of instructor
Curves in Euclidean 3-Space (E°) and the Serret-Frenet 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. Applications of tensors in Relativity and Continuum Mechanics.
Prereq: MATH 230b or consent of instructor
Cross-listed as PMATH 365.
Stress and strain tensors; analysis of stress and strain. Lagrangian and Eulerian methods for describing flow. Equations of continuity, motion and energy, constitutive equations. Navier-Stokes equation. Basic equations of elasticity. Various applications.
Prereq: MATH 230b, AM 371, or consent of instructor
Coreq: MATH 332b (or PMATH 352)
First order partial differential equations
and methods 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 230b, or consent of instructor
Course Descriptions Mathematics: Applied Mathematics
Flat space-time and Lorentz transformations, relativistic mechanics, Maxwell's equations; curved space-time and the Einstein field equations, the Schwarzschild solution and some experimental tests of general relativity, the weak field limit; introduction to black holes and cosmology.
Prereq: AM 362/PMATH 365 or consent of instructor
Credit will be granted for only 1 of AM 364, 372.
Variable length coding. The Shannon entropy as measure of uncertainty and expected information. Minimal average length coding; the Shannon entropy as lower bound, Source entropy. Channels. Transinformation. Capacity. Applications to problem solving, information transmission, logics, science, linguistics and communications (TV, music, etc.
Determination of practical measures of
information. ‘ Prereq: Consent of instructor Cross-listed as PMATH 380a.
Measures of conditional uncertainty (entropy). Maximizing conditional entropies. Applications to statistical physics, statistics, pattern recognition. Special entropies in questionnaire theory. Design of optimal questionnaires. Specia! entropies in dynamical systems. Basics in dynamical systems. Prereq: Consent of instructor Cross-listed as PMATH 380b.
Existence and uniqueness theorems, second and higher order equations, | series solutions and Special Functions, Laplace transforms. Application to Mathematical. Physics.
Prereq: MATH 230b
Sturm-Liouville problems and eigenfunction expansions. Non-linear mechanics, phase plane method and stability analysis.
Prereq: AM 381.
Mathematics: Applied Mathematics
Three-dimensional rigid body motion, Lagrange’s equations of motion. ignorable co-ordinates. Hamilton’s principle. Noether’s theorem and, conservation. Jaws. Canonical equations. Canonical transformations. Lagrange and Poisson bracket relations. Integral invariants. Prereq: MATH 230b or consent of instructor
Integral equations and integral trans- . forms 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
A survey of undergraduate mathematics with emphasis on the unifying effect of algebraic concepts. This is a crossdisciplinary problem-solving course; theorems of modern algebra are applied to specific examples chosen from analysis, geometry, probability, graphs and matroids, numerical and multilinear approximation, tensors, and special functions.
Prereq: MATH 224b
The theory of measure and the Lebesgue integral.
Prereq: PMATH 331 or 351a
Basic ideas of relativistic cosmology (Friedmann-Robertson-Walker universes, observationa! status of cosmological theories, black hole theory (the Schwarzschild and Kerr solutions, their event horizons and singularities, gravitational collapse, observable properties of black holes), and an introduction to gravitational waves. Other topics of current interest may be discussed. Prereq: AM 362, 372, or consent of instructor
Historical origins of quantum theory. Uncertainty principle, wave packets and the Schrédinger equation. The Hamiltonian operator. Solutions of one- . dimensionat problems: harmonic oscillator, hydrogen atom, hydrogen molecular ion.
Prereq: Consent of instructor
AM 4655 W 2C 05
Quantum Mechanics 2
Electronic properties of solids. Matrix
mechanics. Symmetry and conservation
laws. WKB method. Variation principle.
Perturbation theory and applications.
Scattering theory. Symmetry groups. Prereq: AM 465a
Fundamental equations of inviscid fluids.
compressibility, vorticity; two and three-
dimensional irrotational, incompressible
flow. Blasius’ theorem, Joukowski
hypothesis. Water Wave Motion. — Prereg: AM 365
A selection of special topics given by members of the Applied Mathematics Depariment.
Prereq: Consent of instructor
Linear operators in Hilbert spaces.
Compact operators. Introduction to
functional analysis. i Prereq: AM 462 or consent of
instructor
Grassman algebras, differential forms, Lie derivatives, isometries, Killing vector fields, applications to continuum mechanics, differentiable manifolds and applications of differential forms to physics.
Prereq: AM 362/PMATH 385 or consent of instructor
Cross-listed as PMATH 468.
Shock wave theory, supersonic flow around a corner, Prandtl-Meyer flow. Dynamics of real fluids, Navier-Stokes equations, exact solutions, Stokes and Oseen flow; Turbulence, Boundary layer theory. introduction to Geophysical Fluid Dynamics.
Prereq: AM 466
16.93
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, inverse transforms by contour integration. Applications to Physical problems.
Prereq: AM 371, 381, 391, or consent of instructor
Applied Mathematics 3
Variational properties of eigenvalues and
eigenfunctions, Rayleigh-Ritz method.
special functions, Hankel transforms.
Fourier-Besse! series, asymptotic series.
Applications to Physical problems. Prereq: AM 481a
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 compiete figure. Fields and the Legendre and Weierstrass sufficient conditions.
Prereq: MATH 230b or consent of instructor
Applications of Maxwell’s equations. Introduction to wave guides and antennae.
Prereq: PHYS 253 or consent of instructor
Applications of probability theory to
theoretical Physics. , Prereq: Consent of instructor
Dynamical systems, controllability and
observability. Minimization of functions
and functionals. Optimal control.
Pontryagin’s Maximum Principle. Prereq: Consent of instructor
Basic equations of elasticity tor 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 -
Not offered in 1985–86.
Not offered in 1985–86.
Not offered in 1985–86.