Note: This is the 2011–2012 edition of the eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or click here to jump to the newest eCalendar.
Program Requirements
Minor Adviser: Faculty Student Adviser in the Engineering Student Centre (Frank Dawson Adams Building, Room 22) AND an adviser designated by the Department of Mathematics and Statistics, normally beginning in the U2 year (please consult the Department of Mathematics and Statistics for this adviser). Selection of courses must be done in conjunction with the Minor advisers. Note: The Mathematics Minor is open to all students in the Faculty of Engineering (B.Eng., B.S.E., and B.Sc.(Arch.)). Engineering students must obtain a grade of C or better in courses approved for this Minor.Course Selection
At least 18 credits must be chosen from the Mathematics and Statistics courses approved for the Mathematics Major or Honours program, or from the following courses:

MATH 249 Honours Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable; CauchyRiemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Terms: Winter 2012
Instructors: Robert Seiringer (Winter)

MATH 363 Discrete Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Logic and combinatorics. Mathematical reasoning and methods of proof. Sets, relations, functions, partially ordered sets, lattices, Boolean algebra. Propositional and predicate calculi. Recurrences and graph theory.
Terms: Winter 2012
Instructors: Daniel Wise (Winter)

MATH 381 Complex Variables and Transforms (3 credits)
Overview
Mathematics & Statistics (Sci) : Analytic functions, CauchyRiemann equations, simple mappings, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent expansions, residue calculus. Properties of one and twosided Fourier and Laplace transforms, the complex inversion integral, relation between the Fourier and Laplace transforms, application of transform techniques to the solution of differential equations. The Ztransform and applications to difference equations.
Terms: Fall 2011, Winter 2012
Instructors: John A Toth (Fall) Michael Pichot (Winter)
Fall and Winter
(315)
Prerequisite: MATH 264
Restriction: Open only to students in the Faculty of Engineering.
The remaining credits may be chosen from mathematicallyallied courses.
The following courses cannot be used toward the Minor:

MATH 222 Calculus 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: James G Loveys, Mathew Donald Rogers (Fall) James G Loveys (Winter) Nicolás Fraiman (Summer)

MATH 223 Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Terms: Fall 2011, Winter 2012
Instructors: Wilbur Jonsson (Fall) Wilbur Jonsson (Winter)

MATH 247 Honours Applied Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Terms: Winter 2012
Instructors: Axel W Hundemer (Winter)

MATH 248 Honours Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2011
Instructors: Pengfei Guan (Fall)

MATH 262 Intermediate Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Series and power series, including Taylor's theorem. Brief review of vector geometry. Vector functions and curves. Partial differentiation and differential calculus for vector valued functions. Unconstrained and constrained extremal problems. Multiple integrals including surface area and change of variables.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Brian Seguin, Neville G F Sancho (Fall) Charles Roth (Winter) Jan Feys (Summer)

MATH 263 Ordinary Differential Equations for Engineers (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ODEs. Second and higher order linear ODEs. Series solutions at ordinary and regular singular points. Laplace transforms. Linear systems of differential equations with a short review of linear algebra.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: JianJun Xu, Patrick Reynolds (Fall) Matthew Roberts, JianJun Xu (Winter) Patrick Reynolds (Summer)

MATH 264 Advanced Calculus for Engineers (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of multiple integrals. Differential and integral calculus of vector fields including the theorems of Gauss, Green, and Stokes. Introduction to partial differential equations, separation of variables, SturmLiouville problems, and Fourier series.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Ivo Klemes, Neville G F Sancho (Fall) Heekyoung Hahn, Rustum Choksi (Winter) Sidney Trudeau (Summer)

MATH 270 Applied Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction. Review of basic linear algebra. Vector spaces. Eigenvalues and eigenvectors of matrices. Linear operators.
Terms: Fall 2011, Winter 2012
Instructors: Axel W Hundemer (Fall) Karol Palka (Winter)
Winter
(315)
Prerequisite: MATH 263

MATH 271 Linear Algebra and Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. SturmLiouville Theory and Applications. Fourier Transforms.
Terms: Fall 2011, Winter 2012
Instructors: Charles Roth (Fall) Charles Roth (Winter)

MATH 314 Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: Wilbur Jonsson (Fall) Ivo Klemes (Winter) Charles Roth (Summer)

MATH 315 Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2011, Winter 2012, Summer 2012
Instructors: JianJun Xu (Fall) JianJun Xu (Winter) Suresh Eswarathasan (Summer)

MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2012
Instructors: Gantumur Tsogtgerel (Winter)

MATH 325 Honours Ordinary Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Fall 2011, Winter 2012
Instructors: Charles Roth (Fall) Antony Raymond Humphries (Winter)