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Program Requirements
Minor Adviser: Faculty Student Adviser in the McGill Engineering Student Centre (Student Affairs Office) (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 2015
Instructors: Gantumur Tsogtgerel (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 2015
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 2014, Winter 2015
Instructors: Niky Kamran (Fall) Pengfei Guan (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 2014, Winter 2015, Summer 2015
Instructors: Michael Brandenbursky, JianJun Xu (Fall) Gantumur Tsogtgerel (Winter) Suresh Eswarathasan (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 2014, Winter 2015
Instructors: Stephan Ehlen (Fall) Tiago Miguel Saldanha Salvador (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 2015
Instructors: Piotr Przytycki (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 2014
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 2014, Winter 2015, Summer 2015
Instructors: Neville G F Sancho, Dmitry Jakobson, Yiyan Xu (Fall) JianJun Xu (Winter) Yariv Barsheshat (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 2014, Winter 2015, Summer 2015
Instructors: Nathan Grieve, Jacques Claude Hurtubise (Fall) Nathan Grieve, JeanChristophe Nave (Winter) Patrick Munroe (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 2014, Winter 2015, Summer 2015
Instructors: Ivo Klemes, Neville G F Sancho (Fall) John A Toth, Renato Calleja Castillo (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 2014, Winter 2015
Instructors: JianJun Xu (Fall) Stephen W Drury (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 2014, Winter 2015
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. Fourier series with applications.
Terms: Fall 2014, Winter 2015
Instructors: Ivo Klemes (Fall) Neville G F Sancho (Winter)

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 2014, Winter 2015, Summer 2015
Instructors: Charles Roth (Fall) JianJun Xu (Winter) Krista Reimer (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 2015
Instructors: Peter Bartello (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 2014, Winter 2015
Instructors: Antony Raymond Humphries (Fall) Charles Roth (Winter)