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Program Requirements

Minor Adviser: Faculty Student Adviser in the ³ÉÈËVRÊÓƵ 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)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Functions of a complex variable; Cauchy-Riemann 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; Schwarz-Christoffel transformation; Poisson's integral formulas; applications.

  Terms: Winter 2015

  Instructors: Tsogtgerel, Gantumur (Winter)

  • Winter

  • Prerequisite: MATH 248.

  • Restriction: Intended for Honours Physics and Engineering students

  • Restriction: Not open to students who have taken or are taking MATH 316

• MATH 363 Discrete Mathematics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  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: Wise, Daniel (Winter)

  • (3-0-6)

  • Prerequisites: MATH 263, MATH 264.

  • Restriction: Open only to students in the Faculty of Engineering.

• MATH 381 Complex Variables and Transforms (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  Overview

  Mathematics & Statistics (Sci) : Analytic functions, Cauchy-Riemann equations, simple mappings, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent expansions, residue calculus. Properties of one and two-sided 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 Z-transform and applications to difference equations.

  Terms: Fall 2014, Winter 2015

  Instructors: Kamran, Niky (Fall) Guan, Pengfei (Winter)

  • Fall and Winter

  • (3-1-5)

  • Prerequisite: MATH 264

  • Restriction: Open only to students in the Faculty of Engineering.

The remaining credits may be chosen from mathematically-allied courses.

The following courses cannot be used toward the Minor:

• MATH 222 Calculus 3 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Brandenbursky, Michael; Xu, Jian-Jun (Fall) Tsogtgerel, Gantumur (Winter) Eswarathasan, Suresh (Summer)

  • Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133

  • Restriction: Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227

• MATH 223 Linear Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Ehlen, Stephan (Fall) Saldanha Salvador, Tiago Miguel (Winter)

  • Fall and Winter

  • Prerequisite: MATH 133 or equivalent

  • Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs

• MATH 247 Honours Applied Linear Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Przytycki, Piotr (Winter)

  • Winter

  • Prerequisite: MATH 133 or equivalent.

  • Restriction: Intended for Honours Physics and Engineering students

  • Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251

• MATH 248 Honours Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Guan, Pengfei (Fall)

  • Fall and Winter and Summer

  • Prerequisites: MATH 133 and MATH 222 or consent of Department.

  • Restriction: Intended for Honours Mathematics, Physics and Engineering students

  • Restriction: Not open to students who have taken or are taking MATH 314

• MATH 262 Intermediate Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  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: Sancho, Neville G F; Jakobson, Dmitry; Xu, Yiyan (Fall) Xu, Jian-Jun (Winter) Barsheshat, Yariv (Summer)

  • (3-1-5)

  • Prerequisites: MATH 141, MATH 133 or equivalent.

  • Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 151, MATH 152, OR MATH 222.

• MATH 263 Ordinary Differential Equations for Engineers (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  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: Grieve, Nathan; Hurtubise, Jacques Claude (Fall) Grieve, Nathan; Nave, Jean-Christophe (Winter) Munroe, Patrick (Summer)

  • (3-1-5)

  • Corequisite: MATH 262.

  • Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 315 or MATH 325.

• MATH 264 Advanced Calculus for Engineers (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  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, Sturm-Liouville problems, and Fourier series.

  Terms: Fall 2014, Winter 2015, Summer 2015

  Instructors: Klemes, Ivo; Sancho, Neville G F (Fall) Toth, John A; Calleja Castillo, Renato (Winter) Trudeau, Sidney (Summer)

  • (3-1-5)

  • Prerequisite: MATH 262 or MATH 151 or MATH 152 or equivalent.

  • Corequisite: MATH 263

  • Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 319 or MATH 375.

• MATH 270 Applied Linear Algebra (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  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: Xu, Jian-Jun (Fall) Drury, Stephen W (Winter)

  • Winter

  • (3-1-5)

  • Prerequisite: MATH 263

• MATH 271 Linear Algebra and Partial Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Engineering)

  Overview

  Mathematics & Statistics (Sci) : Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms.

  Terms: Fall 2014, Winter 2015

  Instructors: Roth, Charles (Fall) Roth, Charles (Winter)

  • Fall and Winter

  • (3-1-5)

  • Prerequisites: MATH 263, MATH 264.

  • Not open to students who have taken MATH 266.

• MATH 314 Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Klemes, Ivo (Fall) Sancho, Neville G F (Winter)

  • Prerequisites: MATH 133, MATH 222

  • Restriction: Not open to students who have taken or are taking MATH 248

• MATH 315 Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Roth, Charles (Fall) Xu, Jian-Jun (Winter) Reimer, Krista (Summer)

  • Prerequisite: MATH 222.

  • Corequisite: MATH 133.

  • Restriction: Not open to students who have taken or are taking MATH 325.

• MATH 319 Introduction to Partial Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

  Terms: Winter 2015

  Instructors: Bartello, Peter (Winter)

  • Winter

  • Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315

• MATH 325 Honours Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Humphries, Antony Raymond (Fall) Roth, Charles (Winter)

  • Fall and Winter

  • (3-0-6)

  • Prerequisite: MATH 222.

  • Restriction: Intended for Honours Mathematics, Physics and Engineering programs.

  • Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315