AM 101A Applications of Mathematics 1
Models using difference equations will be formulated for examples drawn from biology, economics and psychology. 3 hours lectures, 1 hour tutorial. Fall term.
Applied Mathematics (AM)
34 courses in the 1976–77 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Undergraduate Course Descriptions
Note Course descriptions are given under the new course numbers introduced in 1976.
AM 230, 240, 330, 340, 430, 440 is a sequence of courses designed to illustrate the representation of a real situation by a mathematical model. The mathematical techniques necessary to formulate the model and to discuss its behaviour are developed as required. Examples will be taken from diverse fields since one of the aims of the course is to formulate models to describe unfamiliar situations.
AM 101B Applications of Mathematics 2
Sets of difference equations, probability and matrix theory will be used to describe models from biology, ecology, economics, psychology and physiology.
3 hours lectures, 1 hour tutorial, Winter term.
AM 230 Applications of Mathematics
Ordinary differential equations will be applied to models drawn from biology, economics, physiology and physics. Prerequisite: M101, 120, 130, or consent of instructor.
2 hours lectures, 1 hour tutorial.
AM 204 Applications of Mathematics
Other examples from biology, ecology, economics, physiology and physics will be discussed using sets of differential equations.
Prerequisite: AM 230 or M 220
2 hours lectures, | hour tutorial.
AM 260 Mathematical Modelling
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.
Prerequisite: M 130
AM 270 Mathematical Modelling
Further mathematical models from various disciplines. An introduction to Newtonian mechanics will also be included in the course.
Prerequisite: AM 260 or consent of instructor.
AM 330 Applications of Mathematics
Partial differential equations are applied to diffusion processes, blood flow and wave phenomena. Prerequisite: M 220 or equivalent, or consent of instructor 2 hours lectures, | hour tutorial.
Course Descriptions ; 317 Applied Mathematics
AM 340 Applications of Mathematics
Laplace transforms are applied to problems in ecology, physiology and other fields.
Prerequisite: M 220 or equivalent, or consent of instructor 2 hours lectures, | hour tutorial
AM 361 Differential Equations
Existence of solutions. Second-order linear equations. Sturm-Liouville boundary-value problems. Fourier series. Partial differential equations.
Prerequisites: M 230 or equivalent; M 332 (Real Variables) may be taken concurrently.
2 hours lectures, I hour tutorial, two terms.
AM 362 Tensor Analysis
Elementary introduction to classical differential geometry and tensor analysis. Curves and surfaces in Euclidean spaces, coordinate transformation, invariance of length, introduction to tensors and Riemannian spaces, convariant differentiation, geodesics, curvature and Einstein tensors. Prerequisite: M 230 or consent of instructor.
2 hours lectures, 1 hour tutorial. Fall term
AM 365 Introduction to Continuum Mechanics
Vector Integral Calculus, motion of a system of particles, methods of continuum mechanics. Stress and strain tensors; analysis of stress and strain. Lagrangian and Eulerian methods for describing flow. Equations of continuity, motion and energy. Navier-Stokes equation. Basic equations of elasticity.
Prerequisite: M 230 or consent of instructor.
2 hours lectures, 1 hour tutorial, Fall term
AM 371 Partial Differential Equations of
Applied Mathematics
Derivation of the equations of heat flow, the vibrating membrane and the electro-magnetic field equations by various elementary techniques and illustrations of the use of calculus of variations in the derivation of equations; solutions of the above equations by separation of variables; Fourier analysis and Fourier integral.
Prerequisite: AM 260, 270, M 230 or consent of instructor. 2 hours lectures, 1 hour tutorial, Winter term
AM 372 Differential Geometry
Intermediate level course on Riemannian spaces (continuation of AM, 362). Conformal spaces, spaces with corresponding geodesics, theory of subspaces. Prerequisites: M 230, AM 362 or consent of instructor. 2 hours lectures, | hour tutorial. Winter term
AM 382 Calculus of Variations
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.
Prerequisite: M 230 or consent of instructor.
2 hours lectures, | hour tutorial. Fall term
AM 395 Mechanics .
Three-dimensional rigid body motion. Lagrange’s equations of motion. Ignorable coordinates. Hamilton’s principle. Noether’s theorem and conservation laws. Canonical equations. Canonical transformations. Lagrange and Poisson bracket relations. Integral invariants.
Prerequisites: M 230, AM 382 or consent of instructor. 2 hours lectures, | hour tutorial. Winter term
AM 389 Reading Course _ AM 399 Reading Course
AM 405 Applied Analysis 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 hours lectures.
AM 430 Applications of Mathematics
Integral equations and integral transforms will be applied to systems with memory. Prerequisite: Consent of instructor. 2 hours lectures. Fall term
AM 440 Applications of Mathematics
Students will construct a model and interpret it as a project. Prerequisite: Consent of instructor.
2 hours lectures. Winter term
AM 461 Non-Linear Differential Equations
Non-linear mechanics, stability, quasi-linear and strongly non-linear systems, linear periodic systems, non-linear integral equations.
Prerequisite: AM 361 or consent of instructor.
2 hours lectures. Two terms
AM 462 Measure and Integration
The theory of measure and the Lebesgue integral. 2 hours lectures. Fall term
Course Descriptions Applied Mathematics
AM 465 Quantum Mechanics
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. Introduction to relativistic
wave equations.
Prerequisites: M 231, AM 371 or consent of instructor. 2 hours lectures, two terms.
AM 466 Fluid Mechanics ;
Fundamental equations of inviscid fluids, compressibility, vorticity; two and three dimensional irrotational, incompressible flow, Blasius’ theorem, Joukowski hypothesis.
Prerequisite: AM 365.
2 hours lectures, 1 hour tutorial. Fall term
AM 468 Topics in Applied Mathematics
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. Prerequisite: Consent of instructor.
2 hours lectures. Fall term
AM 472 Linear Operators
Linear operators in Hilbert spaces. Compact operators. Introduction to functional analysis.
2 hours lectures. Winter term
AM 473 Theory of Relativity
Flat space-time and special relativity, curved space-time and the Einstein gravitational field equations. The Schwarzschild solutions and the experimental tests of relativity. Maxwell’s equations, the Reissner-Nordstrom solution. Topics from cosmology, Petrov classification, spinors, gravitational waves, special solutions. Prerequisite: AM 362. Consent of instructor.
2 hours lectures. Winter term
AM 476 Fluid Dynamics
Shock wave theory, supersonic flow around a corner, Prandtl-Meyer flow. Dynamics of real fluids, Navier-Stokes equations, exact solutions, Stokes and QOseen flow; introduction to boundary layer theory. Prerequisite: AM 466.
2 hours lectures, | hour tutorial. Winter term
AM 478 Topics in Applied Mathematics
Same as in 468.
Prerequisite: Consent of instructor.
2 hours lectures, Winter term
AM 481 Differential Equations
Green's functions. Cauchy problems. Classification of partial differential equations. Orthogonal functions. Bessel functions. Legendre polynomials. Fourier Integral and Laplace transform. Variational properties of eigenvalues and eigenfunctions.
Prerequisite: Consent of instructor. Two terms.
AM 482 Differential Geometry
Differentiable manifolds, tensors and forms, Connexions, Riemannian manifolds.
Prerequisites: M 231 and 230
2 hours lectures. Two terms.
AM 485 Electromagnetism
Applications of the Maxwell equations. Reflection and refraction. Introduction to wave guides and antennae. Prerequisite: Consent of instructor.
2 hours lectures. Fail term
AM 486 Statistical Mechanics
Applications of probability theory to theoretical Physics. 2 hours lectures. Fall term
AM 488 Control Theory
Dynamical systems, controllability and observability. Minimization of functions and functionals. Optimal control. Pontryagin’s Maximum Principle. Prerequisite: Consent of instructor.
2 hours lectures, Fall term
AM 489 Reading Course
2 hours a week. One term.
AM 495 Elasticity
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.
2 hours lectures, | hour tutorial. Winter term. Prerequisite: AM 365.
AM 499 Reading Course
2 hours a week, One term.
Course Descriptions 319