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 ²ÝÝ®ÎÛÊÓƵµ¼º½ Calendar 2010-2011 COURSES OF INSTRUCTION Course Descriptions A Applied Mathematics AMAT
Applied Mathematics AMAT

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Department Head - T. Bisztriczky

Note: For listings of related courses, see Actuarial Science, Mathematics, Pure Mathematics and Statistics.
 
Junior Courses
 
Applied Mathematics 217       Calculus for Engineers and Scientists
Functions, limits, continuity, derivatives, Mean Value Theorem, integrals, Fundamental Theorem of Calculus, applications to the physical sciences.
Course Hours: H(3-1T-1.5)
Prerequisite(s): A grade of 70% or higher in Pure Mathematics 30 and credit in Mathematics 31; or admission to the Faculty of Engineering including credit in Pure Mathematics 30 and Mathematics 31.
Antirequisite(s): Credit for more than one of Mathematics 249, 251, 281 or Applied Mathematics 217 will not be allowed.
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Applied Mathematics 219       Multivariable Calculus for Engineers
Techniques of integration, double and triple integrals, partial derivatives, applications.
Course Hours: H(3-1T-1.5)
Prerequisite(s): Applied Mathematics 217; or Mathematics 249 or 251 or 281 plus Mathematics 117; or consent of Applied Mathematics Division.
Antirequisite(s): Credit for more than one of Mathematics 253, 263, 283 or Applied Mathematics 219 will not be allowed.
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Senior Courses
 
Applied Mathematics 307       Differential Equations for Engineers
Definition, existence and uniqueness of solutions, first and second order equations with applications, series solutions about regular points and singular points, special functions. Laplace transform, systems of equations.
Course Hours: H(3-1.5T)
Prerequisite(s): One of Mathematics 211 or 213 or 221; and Applied Mathematics 219 or Mathematics 253.
Antirequisite(s): Credit for both Applied Mathematics 307 and 311 will not be allowed.
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Applied Mathematics 309       Vector Calculus for Engineers
Functions of several variables, chain rule and differentials. Vector calculus, line, surface and volume integrals, Green's, Gauss' and Stokes' theorems. Students will complete a project using a computer algebra system.
Course Hours: H(3-1.5T)
Prerequisite(s): Applied Mathematics 219 or Mathematics 114 and one of Mathematics 253 or 263 or 283.
Antirequisite(s): Credit for more than one of Mathematics 353, 381, and Applied Mathematics 309 will not be allowed.
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Applied Mathematics 311       Differential Equations I
Classification of ordinary differential equations, first and second order equations with applications, series solutions about regular points and singular points, special functions, Laplace transform.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 253 or 263 or 283 or Applied Mathematics 219.
Antirequisite(s): Credit for both Applied Mathematics 307 and 311 will not be allowed.
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Applied Mathematics 411       Differential Equations II
Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, Sturm-Liouville problems, systems of equations, phase portraits, stability.
Course Hours: H(3-1T)
Prerequisite(s): One of Applied Mathematics 311 or 307, and one of Mathematics 331, 353, 381, Applied Mathematics 309, or consent of the Division.
Notes: It is recommended that students complete Pure Mathematics 435 or 455 before taking this course.
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Applied Mathematics 413       Introduction to Partial Differential Equations
Orthogonal sets of functions, Fourier series, solution of potential equation, heat equation and wave equation. Numerical solution of partial differential equations.
Course Hours: H(3-1T)
Prerequisite(s): One of Mathematics 353, 381, Applied Mathematics 309, Mathematics 331; or consent of the Division.
Antirequisite(s): Credit for both Applied Mathematics 413 and 407 will not be allowed. Credit will be not be allowed for more than one of Applied Mathematics 413, or 415, or 433.   
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Applied Mathematics 415       Mathematical Methods
Mathematical analysis of linear systems. Fourier and Laplace transforms, applications and numerical methods. Functions of a complex variable and applications.
Course Hours: H(3-1T)
Prerequisite(s): One of Applied Mathematics 311, 307, Mathematics 331, 353, 381, or Applied Mathematics 309.
Antirequisite(s): Credit will be not be allowed for more than one of Applied Mathematics 415, or 413, or 433.
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Applied Mathematics 425       Introduction to Optimization
Examples of optimization problems. Quadratic forms, minimum energy and distance. Least squares, generalized inverse. Location and classification of critical points. Variational treatment of eigenvalues. Lagrange multipliers. Linear programming.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 311; and Mathematics 353 or 381 or Applied Mathematics 309 or Mathematics 331.
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Applied Mathematics 433       Mathematical Methods in Physics
Topics include Fourier analysis; Partial differential equations; Complex analysis; Residue integrals; Extensive physical applications.
Course Hours: H(3-1T)
Prerequisite(s): Applied Mathematics 307 or 311; one of Applied Mathematics 309 or Mathematics 353 or 381 or 331; one of Mathematics 211, 213 or 221.
Antirequisite(s): Credit will be not be allowed for more than one of Applied Mathematics 433, or 415, or 413.
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Applied Mathematics 481       Introduction to Mathematical Finance
Introduction to financial markets and derivatives, asset price random walks, Black-Scholes option pricing model, American options and other generalizations.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 323 and one of 353 or 381.
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Applied Mathematics 483       Computational Methods in Mathematical Finance
Review of financial models, Monte-Carlo simulation, binomial and trinomial trees, finite-difference method, aspects of time series and parameter estimation, volatility modelling and estimation.
Course Hours: H(3-1T)
Prerequisite(s): Applied Mathematics 481 and 491.
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Applied Mathematics 491       Numerical Analysis I
Interpolation and approximation, numerical integration, numerical methods for the solution of nonlinear equations, systems of linear equations and the eigenvalue problem.
Course Hours: H(3-1T)
Prerequisite(s): Mathematics 311 and 381 or 349 and 353 or Applied Mathematics 309 and Computer Science 231 or 217; or consent of the Division.
Antirequisite(s): Not open to students with credit in Computer Science 491.
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Applied Mathematics 493       Numerical Analysis II
Numerical differentiation, numerical solution of ordinary and partial differential equations.
Course Hours: H(3-1T)
Prerequisite(s): Applied Mathematics 311, 413, and 491 or Computer Science 491.
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Applied Mathematics 501       Seminar in Applied Mathematics
Topics will be chosen according to the interests of instructors and students and could include analysis of optimization algorithms, approximation theory, control theory, differential equations, mathematical physics.
Course Hours: H(3-0)
Prerequisite(s): Consent of the Division.
MAY BE REPEATED FOR CREDIT
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Applied Mathematics 503       The Mathematics of Wavelets, Signal and Image Processing
Continuous and discrete Fourier transforms, the Fast Fourier Transform, wavelet transforms, multiresolution analysis and orthogonal wavelet bases, and applications.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 491 or Computer Science 491.
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Applied Mathematics 505       Calculus on Manifolds
Integral and differential calculus on manifolds including tensor fields, covariant differentiation, Lie differentiation, differential forms, Frobenius' theorem, Stokes' theorem, flows of vector fields.
Course Hours: H(3-0)
Prerequisite(s): Pure Mathematics 445 or 545; and one of Applied Mathematics 311 or 307; or consent of the Division.
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Applied Mathematics 507       Introduction to Relativity Theory
Mathematical theories of space and time. Special Relativity. Electro-dynamics. General Relativity.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 505 or consent of the Division.
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Applied Mathematics 509       Analytical Dynamics
Symplectic geometry, Hamilton's equation, Hamilton-Jacobi theory, constraints and reduction.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 505 or consent of the Division.
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Applied Mathematics 581       Advanced Futures and Options
Stochastic calculus and the dynamics of asset prices, martingale theory and risk-neutral valuation, interest rate models, energy and commodity markets, value-at-risk and risk management.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 483 and Statistics 407.
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Graduate Courses

In addition to the prerequisites listed below, consent of the Applied Mathematics Division is a prerequisite for all graduate courses in Applied Mathematics.
 
Applied Mathematics 601       Topics in Applied Mathematics
Topics will be chosen according to the interests of instructors and students.
Course Hours: H(3-0)
Prerequisite(s): Consent of the Division.
MAY BE REPEATED FOR CREDIT
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Applied Mathematics 605       Differential Equations III
Linear systems, classification. Nonlinear systems: Existence and uniqueness. Flow and one parameter groups of transformations. Stability theory. Hyperbolicity, Unstable/Stable/Center manifold theorems. Poincare-Bendixson.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 411 and Pure Mathematics 445 or 545 or equivalents.
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Applied Mathematics 613       Partial Differential Equations II
Fundamental solutions, integral equations, eigenvalue problems, non-linear problems.
Course Hours: H(3-0)
Prerequisite(s): Consent of the Division.
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Applied Mathematics 617       Analysis IV
Analysis in abstract spaces. Function spaces.
Course Hours: H(3-0)
Prerequisite(s): Pure Mathematics 545.
Also known as: (formerly Pure Mathematics 617)
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Applied Mathematics 621       Research Seminar
Reports on studies of the literature or of current research.
Course Hours: Q(2S-0)
Notes: All graduate students in Mathematics and Statistics are required to participate in one of Applied Mathematics 621, Pure Mathematics 621, Statistics 621 each semester.
MAY BE REPEATED FOR CREDIT NOT INCLUDED IN GPA
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Applied Mathematics 643       Perturbation Theory
Perturbation problems for ordinary differential equations, matrices and more general operators. Applications. Methods will be motivated by discussion of physical problems.
Course Hours: H(3-0)
Prerequisite(s): Familiarity with complex variables, linear algebra and differential equations.
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Applied Mathematics 671       Numerical Linear Algebra
Iterative and elimination methods for linear systems of equations, determination of eigenvalues, linear and convex programming.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 441 or Mathematics 411; and Applied Mathematics 491.
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Applied Mathematics 673       Approximation Theory
Existence, uniqueness of minimal solutions, Haar systems, characterization by alternation, Remez algorithm, monotone operators, spline approximation.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 491; and Pure Mathematics 435 or 455.
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Applied Mathematics 677       Numerical Solution of Partial Differential Equations
Explicit and implicit methods for PDE, difference equations.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 311 and 491.
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In addition to the numbered and titled courses shown above, the department offers a selection of advanced level graduate courses specifically designed to meet the needs of individuals or small groups of students at the advanced doctoral level. These courses are numbered in the series 800.01 to 899.99. Such offerings are, of course, conditional upon the availability of staff resources.