Course Descriptions - Undergraduate Calendar 2023-2024

The concepts included are limits, derivatives, antiderivatives and definite integrals. These concepts will be applied to solve problems of rates of change, maximum and minimum, curve sketching and areas. The classes of functions used to develop these concepts and applications are: polynomial, rational, trigonometric, exponential, and logarithmic.

For studies at other universities under approved exchange agreements.

An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Topics will be chosen from linear equations, systems of linear equations, linear inequalities, functions, set theory, permutations and combinations, binomial theorem, probability theory. [Offered: F,W]

An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models studied will involve polynomial, rational, exponential, and logarithmic functions. The major concepts introduced to solve problems are rate of change, optimization, growth and decay, and integration. [Offered: F,W]

Systems of linear equations. Matrix algebra. Determinants. Introduction to vector spaces. Applications. [Offered: F,W,S]

Vectors in 2- and 3-space and their geometry. Linear equations, matrices, and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]

Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]

Functions: review of polynomials, exponential, logarithmic, trigonometric. Operations on functions, curve sketching. Trigonometric identities, inverse functions. Derivatives, rules of differentiation. Mean Value Theorem, Newton's Method. Indeterminate forms and L'Hopital's rule, applications. Integrals, approximations, Riemann definite integral, Fundamental Theorems. Applications of the integral. [Offered: F]

Functions of engineering importance; review of polynomial, exponential, and logarithmic functions; trigonometric functions and identities. Inverse functions (logarithmic and trigonometric). Limits and continuity. Derivatives, rules of differentiation; derivatives of elementary functions. Applications of the derivative, max-min problems, Mean Value Theorem. Antiderivatives, the Riemann definite integral, Fundamental Theorems. Methods of integration, approximation, applications, improper integrals. [Offered: F]

Methods of integration: by parts, trigonometric substitutions, partial fractions; engineering applications, approximation of integrals, improper integrals. Linear and separable first order differential equations, applications. Parametric curves and polar coordinates, arc length and area. Infinite sequences and series, convergence tests, power series and applications. Taylor polynomials and series, Taylor's Remainder Theorem, applications. [Offered: W,S]

Elementary approximation methods: interpolation; Taylor polynomials and remainder; Newton's method, Landau order symbol, applications. Infinite series: Taylor series and Taylor's Remainder Theorem, geometric series, convergence test, power series, applications. Functions of several variables: partial derivatives, linear approximation and differential, gradient and directional derivative, optimization and Lagrange multipliers. Vector-valued functions: parametric representation of curves, tangent and normal vectors, line integrals and applications. [Offered: W,S]

Review of trigonometry and basic algebra. Introduction to vectors in 2- and 3-space: sums, addition, dot products, cross products and angles between vectors. Solving linear systems in two and three variables. Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties. Intuitive discussion of limits and continuity. Derivatives of elementary functions, derivative rules; applications to curve sketching, optimization. Relationships between distance, velocity, and acceleration. The definite integral, antiderivatives, the Fundamental Theorem of Calculus; change of variable and integration by parts; applications to area, centre of mass. [Offered: F]

Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties and inverses. Intuitive discussion of limits and continuity. Definition and interpretation of the derivative, derivatives of elementary functions, derivative rules and applications. Riemann sums and other approximations to the definite integral. Fundamental theorems and antiderivatives; change of variable. Applications to area, rates, average value. [Offered: F,W,S; online: F,W,S]

Transforming and evaluating integrals; application to volumes and arc length; improper integrals. Separable and linear first order differential equations and applications. Introduction to sequences. Convergence of series; Taylor polynomials, Taylor's Remainder theorem, Taylor series and applications. Parametric/vector representation of curves; particle motion and arc length. Polar coordinates in the plane. [Offered: F,W,S; online: F,W,S]

An introduction to the language of mathematics and proof techniques through a study of the basic algebraic systems of mathematics: the integers, the integers modulo n, the rational numbers, the real numbers, the complex numbers and polynomials. [Offered: F,W,S]

Systems of linear equations, matrix algebra, elementary matrices, computational issues. Real n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations, and matrix representations. Determinants, eigenvalues and diagonalization, applications. [Offered: F,W,S; online: F,W,S]

Absolute values and inequalities. Sequences and their limits. Introduction to series. Limits of functions and continuity. The Intermediate Value theorem and approximate solutions to equations. Derivatives, linear approximation, and Newton's method. The Mean Value theorem and error bounds. Applications of the Mean Value theorem, Taylor polynomials and Taylor's theorem, Big-O notation. Suitable topics are illustrated using computer software. [Offered: F,W,S; online: F,W,S]

Introduction to the Riemann integral and approximations. Antiderivatives and the fundamental theorem of calculus. Change of variables, methods of integration. Applications of the integral. Improper integrals. Linear and separable differential equations and applications. Tests for convergence for series. Binomial series, functions defined as power series and Taylor series. Vector (parametric) curves in R2. Suitable topics are illustrated using computer software. [Offered: F,W,S; online: F,W,S]

MATH 145 is an advanced-level version of MATH 135. [Offered: F]

MATH 146 is an advanced-level version of MATH 136.

MATH 147 is an advanced-level version of MATH 137. [Offered: F]

MATH 148 is an advanced-level version of MATH 138.

A course in problem solving in which intriguing and difficult problems are solved. Problems are taken mainly from the elementary parts of applied mathematics, computer science, statistics and actuarial science, pure mathematics, and combinatorics and optimization. Material relevant to the problems is taught in depth.

Multivariable functions and partial derivatives. Gradients. Optimization including Lagrange multipliers. Polar coordinates. Multiple integrals. Surface integrals on spheres and cylinders. Introduction to Fourier Series. [Offered: F,W,S]

Fourier series. Ordinary differential equations. Laplace transform. Applications to linear electrical systems. [Offered: F,W]

Triple integrals, cylindrical and spherical polar coordinates. Divergence and curl, applications. Surface integrals, Green's, Gauss' and Stokes' theorems, applications. Complex functions, analytic functions, contour integrals, Cauchy's integral formula, Laurent series, residues. [Offered: F,S]

Laplace transform methods for: solving linear ordinary differential equations, classical signals, and systems. Transfer functions, poles, and zeros; system stability. Frequency response of linear systems and its log-scale representation (Bode plot). Fourier series. Applications in areas of interest for software engineers and computer scientists. Brief introduction to Fourier transforms in the context of signals and systems.

Systems of linear equations; their representation with matrices and vectors; their generalization to linear transformations on abstract vector spaces; and the description of these linear transformations through quantitative characteristics such as the determinant, the characteristic polynomial, eigenvalues and eigenvectors, the rank, and singular values. [Offered: F,W]

Curves and surfaces in R3. Multivariable functions, partial derivatives, the chain rule, gradients. Optimization, Lagrange Multipliers. Double and triple integrals, change of variable. Vector fields, divergence and curl. Vector integral calculus: Green's theorem, the Divergence theorem and Stokes' theorem. Applications in engineering are emphasized. [Offered: F,W]

First order equations, second order linear equations with constant coefficients, series solutions, the Laplace transform method, systems of linear differential equations. Applications in engineering are emphasized. [Offered: F,S]

Vector spaces. Linear transformations and matrices. Inner products. Eigenvalues and eigenvectors. Diagonalization. Applications. [Offered: F,S; online: W]

Directional derivative and the chain rule for multivariable functions. Optimization, Lagrange multipliers. Double and triple integrals on simple domains; transformations and Jacobians; change of variable in multiple integrals. Vector fields, divergence and curl. Vector integral calculus: Line and surface integrals, Green's Theorem, Stokes' Theorem, Gauss' Theorem, conservative vector fields. [Offered: F]

First-order equations, second-order linear equations with constant coefficients, series solutions and special functions, the Laplace transform method. Applications in physics and chemistry are emphasized. [Offered: F,W; online: W,S]

Introduction to graph theory: colourings, connectivity, Eulerian tours, planarity. Introduction to combinatorial analysis: elementary counting, generating series, binary strings. [Offered: F]

Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Inner products, angles and orthogonality, orthogonal diagonalization, singular value decomposition, applications. [Offered: F,W,S]

Calculus of functions of several variables. Limits, continuity, differentiability, the chain rule. The gradient vector and the directional derivative. Taylor's formula. Optimization problems. Mappings and the Jacobian. Multiple integrals in various co-ordinate systems.

Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees. [Offered: F,W,S]

MATH 245 is an advanced-level version of MATH 235. [Offered: F,S]

Topology of real n-dimensional space: completeness, closed and open sets, connectivity, compact sets, continuity, uniform continuity. Differential calculus on multivariable functions: partial differentiability, differentiability, chain rule, Taylor polynomials, extreme value problems. Riemann integration: Jordan content, integrability criteria, Fubini's theorem, change of variables. Local properties of continuously differentiable functions: open mapping theorem, inverse function theorem, implicit function theorem. [Offered: F,W,S]

MATH 249 is an advanced-level version of MATH 239. [Offered: F,W]