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.
Applied Mathematics 001 E(12 hours)
Module M1
Introduction to Maple, Mathematica and Matlab.
Prerequisites: Mathematics 221]MATH221] and 253 or 263 or Applied Mathematics 219.
NOT INCLUDED IN GPA
Applied Mathematics 002 E(12 hours)
Module M2
Advanced use of Maple, Mathematica and Matlab with applications.
Prerequisites: Applied Mathematics 001.
NOT INCLUDED IN GPA
Junior Courses
Applied Mathematics 217 H(3-1T-1.5)
Calculus for Engineers and Scientists
Functions, limits, continuity, derivatives, Mean Value Theorem, integrals, Fundamental Theorem of Calculus, applications to the physical sciences.
Prerequisites: 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.
Note: Credit for both Applied Mathematics 217 and either Mathematics 249 or 251 will not be allowed.
Applied Mathematics 219 H(3-1T-1.5)
Multivariable Calculus for Engineers
Techniques of integration, double and triple integrals, partial derivatives, applications.
Prerequisites: Applied Mathematics 217; or Mathematics 249 or 251 and consent of Applied Mathematics Division.
Note: Credit for both Applied Mathematics 219 and either Mathematics 253 or 263 will not be allowed.
Senior Courses
Applied Mathematics 307 H(3-1.5T)
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.
Prerequisites: Applied Mathematics 219 and Mathematics 221.
Note: Credit for both Applied Mathematics 307 and 311 will not be allowed.
Applied Mathematics 309 H(3-1.5T)
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.
Prerequisites: Applied Mathematics 219.
Note: Credit for both Applied Mathematics 309 and either Mathematics 331 or 353 will not be allowed.
Applied Mathematics 311 H(3-1T)
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.
Prerequisites: Mathematics 253 or 263 or Applied Mathematics 219.
Note: Credit for both Applied Mathematics 307 and 311 will not be allowed.
Applied Mathematics 371 H(3-0)
Computing for Mathematicians
Modules M1 (Applied Mathematics 001)[AMAT001], M2 (Applied Mathematics 002)[AMAT002] and the completion of a project in Computational Mathematics.
Prerequisites: Mathematics 221 and 253 or 263 or Applied Mathematics 219.
Applied Mathematics 411 H(3-1T)
Differential Equations II
Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, Sturm-Liouville problems, systems of equations, phase portraits, stability.
Prerequisites: One of Applied Mathematics 311 or 307, and one of Mathematics 331, 353, Applied Mathematics 309, or consent of the Division.
Note: It is recommended that students complete Pure Mathematics 435 before taking this course.
Applied Mathematics 413 H(3-1T)
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.
Prerequisites: One of Mathematics 353, Applied Mathematics 309, Mathematics 331; or consent of the Division. Familiarity with a computer programming language is strongly advised.
Note: Credit for both Applied Mathematics 413 and 407 will not be allowed.
Applied Mathematics 415 H(3-1T)
Mathematical Methods
Mathematical analysis of linear systems. Fourier and Laplace transforms, applications and numerical methods. Functions of a complex variable and applications.
Prerequisites: One of Applied Mathematics 311, 307, Mathematics 331, 353, or Applied Mathematics 309.
Note: Credit for both Applied Mathematics 415 and 433 will not be allowed for Applied Mathematics and General Mathematics programs.
Applied Mathematics 425 H(3-1T)
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.
Prerequisites: Mathematics 311; and Mathematics 353 or Applied Mathematics 309 or Mathematics 331.
Applied Mathematics 433 H(3-1T)
Mathematical Methods in Physics
Complex analysis and residue integrals. Fourier analysis. Laplace transforms. Vector spaces. Eigenvalues and eigenvectors. Extensive physical applications.
Prerequisites: One of Applied Mathematics 307 or 311 or Physics 341; one of Applied Mathematics 309 or Mathematics 353 or 331.
Note: Credit for both Applied Mathematics 415 and 433 will not be allowed for Applied Mathematics and General Mathematics programs.
Applied Mathematics 451 H(3-1T)
Introduction to Mathematical Modelling
Mathematical formulation, solution and interpretation of real-world problems chosen from various areas. Students may consult the division for typical problem areas for any given year.
Prerequisites: Mathematics 311 or Applied Mathematics 311; and Mathematics 353 or Applied Mathematics 309 or Mathematics 331; or consent of the Division.
Applied Mathematics 481 H(3-1T)
Introduction to Mathematical Finance
Introduction to financial markets and derivatives, asset price random walks, Black-Scholes option pricing model, American options and other generalizations.
Applied Mathematics 483 H(3-1T)
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.
Prerequisites: Applied Mathematics 481 and 491.
Corequisites: Applied Mathematics 493.
Applied Mathematics 491 H(3-1T)
Numerical Analysis I
Interpolation and approximation, numerical integration, numerical methods for the solution of nonlinear equations, systems of linear equations and the eigenvalue problem.
Prerequisites: Mathematics 311, 349, and 353 or Applied Mathematics 309, and Computer Science 231 or 215; or consent of the Division.
Note: Not open to students with credit in Computer Science 491.
Applied Mathematics 493 H(3-1T)
Numerical Analysis II
Numerical differentiation, numerical solution of ordinary and partial differential equations.
Prerequisites: Mathematics 311, 353, Applied Mathematics 311, 413, and 491 or Computer Science 491.
Corequisites: Applied Mathematics 371.
Applied Mathematics 501 H(3-0)
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.
Prerequisites: Consent of the Division.
MAY BE REPEATED FOR CREDIT
Applied Mathematics 503 H(3-1T)
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.
Prerequisites: Applied Mathematics 491 or Computer Science 491.
Corequisites: Applied Mathematics 371.
Applied Mathematics 505 H(3-0)
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.
Prerequisites: Pure Mathematics 445; and one of Applied Mathematics 311 or 307; or consent of the Division.
Applied Mathematics 507 H(3-0)
Introduction to Relativity Theory
Mathematical theories of space and time. Special Relativity. Electro-dynamics. General Relativity.
Prerequisites: Applied Mathematics 505 and consent of the Division.
Applied Mathematics 509 H(3-0)
Analytical Dynamics
Symplectic geometry, Hamilton's equation, Hamilton-Jacobi theory, constraints and reduction.
Prerequisites: Applied Mathematics 505 and consent of the Division.
Applied Mathematics 581 H(3-0)
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.
Prerequisites: Applied Mathematics 483 and Statistics 407.
Corequisites: Statistics 409.
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 H(3-0)
Topics in Applied Mathematics
Topics will be chosen according to the interests of instructors and students.
Prerequisites: Consent of the Division.
MAY BE REPEATED FOR CREDIT
Applied Mathematics 605 H(3-0)
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.
Prerequisites: Applied Mathematics 411 and Pure Mathematics 445 or equivalents.
Applied Mathematics 613 H(3-0)
Partial Differential Equations II
Fundamental solutions, integral equations, eigenvalue problems, non-linear problems.
Prerequisites: Consent of the Division.
Applied Mathematics 617 H(3-0)
(formerly Pure Mathematics 617)
Analysis IV
Analysis in abstract spaces. Function spaces.
Prerequisites: Pure Mathematics 545.
Applied Mathematics 621 Q(2S-0)
Research Seminar
Reports on studies of the literature or of current research.
Note: 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
Applied Mathematics 643 H(3-0)
Perturbation Theory
Perturbation problems for ordinary differential equations, matrices and more general operators. Applications. Methods will be motivated by discussion of physical problems.
Prerequisites: Familiarity with complex variables, linear algebra and differential equations.
Applied Mathematics 671 H(3-0)
Numerical Linear Algebra
Iterative and elimination methods for linear systems of equations, determination of eigenvalues, linear and convex programming.
Prerequisites: Applied Mathematics 441 or Mathematics 411; and Applied Mathematics 491.
Applied Mathematics 673 H(3-0)
Approximation Theory
Existence, uniqueness of minimal solutions, Haar systems, characterization by alternation, Remez algorithm, monotone operators, spline approximation.
Prerequisites: Applied Mathematics 491 and Pure Mathematics 435.
Applied Mathematics 677 H(3-0)
Numerical Solution of Partial Differential Equations
Explicit and implicit methods for PDE, difference equations.
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.