**NOTE:** The following course descriptions are for ease of student use and the official course descriptions including any and all requisites are found in the academic calendar.

Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predator-prey dynamics, age-structured populations.

**Antirequisite(s):** The former Calculus 1201A/B.

**Prerequisite(s):** One or more of Calculus 1000A/B, 1100A/B, 1500A/B or Mathematics 1225A/B.

**Extra Information:** 3 lecture hours, 1 tutorial hour, 0.5 course.

Matrix operations, systems of linear equations, linear spaces and transformations, determinants, eigenvalues and eigenvectors, applications of interest to Engineers including diagonalization of matrices, quadratic forms, orthogonal transformations.

**Prerequisite(s):** Ontario Secondary School MHF4U or MCV4U, or Mathematics 0110A/B.

**Extra Information:** 3 lecture hours, 1 tutorial hour, 0.5 course. For students in Engineering only.

*New for September 2015.*

Topics covered include a review of orthogonal expansions of functions and Fourier series and transforms, multiple integration with methods of evaluation in different systems of coordinates, vector fields, line integrals, surface and flux integrals, the Green, Gauss and Stokes theorems with applications.

**Antirequisite(s):** Calculus 2302A/B, 2303A/B, 2502A/B, 2503A/B, Applied Mathematics 2277B, the former Applied Mathematics 2411, 2413, 2415.**Prerequisite(s):** Applied Mathematics 2270A/B.

**Extra Information:** 3 lecture hours, 1 tutorial hour, 0.5 course. Restricted to students in the Faculty of Engineering.

*New for September 2015.*

This course provides a survey of the applied mathematics methods of special interest to chemical and civilengineering students. Topics covered include a review of orthogonal expansions of functions and Fourier series, partial differential equations and Fourier series solutions, boundary value problems, the wave, diffusion and Laplace equations, multiple integration with methods of evaluation in different systems of coordinates, vector fields, line integrals, surface and flux integrals, the Green, Gauss and Stokes theorems with applications.

**Antirequisite(s):** Calculus 2302A/B, 2303A/B, 2502A/B, 2503A/B, Applied Mathematics 2276B, the former Applied Mathematics 2411, 2413, 2415.**Prerequisite(s):** Applied Mathematics 2270A/B.

**Extra Information:** 3 lecture hours, 1 tutorial hour, 0.5 course. Restricted to students in the Faculty of Engineering.

Vector space examples. Inner products, orthogonal sets including Legendre polynomials, trigonometric functions, wavelets. Projections, least squares, normal equations, Fourier approximations. Eigenvalue problems, diagonalization, defective matrices. Coupled difference and differential equations; applications such as predator-prey, business competition, coupled oscillators. Singular value decomposition, image approximations. Linear transformations, graphics.

**Prerequisite(s):** Applied Mathematics 1413 or Calculus 1301A/B or 1501A/B and a minimum mark of 60% in Mathematics 1600A/B or the former Linear Algebra 1600A/B, or Applied Mathematics 1411A/B.

**Extra Information:** 3 lecture hours, 0.5 course.

Introduction to numerical analysis; polynomial interpolation, numerical integration, matrix computations, linear systems, nonlinear equations and optimization, the initial value problem. Assignments using a computer and the software package, Matlab, are an important component of this course.

**Antirequisite(s):** Applied Mathematics 2413, the former Applied Mathematics 2813B.

**Prerequisite(s):** A minimum mark of 55% in Mathematics 1600A/B or the former Linear Algebra 1600A/B.**Pre- or Corequisite(s):** Calculus 2302A/B, 2402A/B or 2502A/B. ** Extra Information:** 3 lecture hours, 1 laboratory hour, 0.5 course.

Existence and uniqueness of solutions, phase space, singular points, stability, periodic attractors, Poincaré-Bendixson theorem, examples from physics, biology and engineering, frequency (phase) locking, parametric resonance, Floquet theory, stability of periodic solutions, strange attractors and chaos, Lyapunov exponents, chaos in nature, fractals.

**Prerequisite(s):** Applied Mathematics 2402A or the former Differential Equations 2402A; Calculus 2303A/B or 2503A/B and Mathematics 1600A/B or the former Linear Algebra 1600A/B.

**Extra Information:** 3 lecture hours, 0.5 course.

Fourier, Laplace and Hankel transforms with applications to partial differential equations; integral equations; and signal processing and imaging; asymptotic methods with application to integrals and differential equations.

**Prerequisite(s):** Applied Mathematics 3815A/B.

**Corequisite(s):** Applied Mathematics 3811A/B.

**Extra Information:** 3 lecture hours, 0.5 course.

Offered in alternate years.

Review of limits and derivatives of exponential, logarithmic and rational functions. Trigonometric functions and their inverses. The derivatives of the trig functions and their inverses. L'Hospital's rules. The definite integral. Fundamental theorem of Calculus. Simple substitution. Applications including areas of regions and volumes of solids of revolution. 4 lecture hours, 0.5 course.

**Antirequisite(s):** Calculus 1100A/B, Calculus 1500A/B, Applied Mathematics 1413

**Prerequisite(s):** One or more of Ontario Secondary School MCV4U, Mathematics 0110A/B

For students requiring the equivalent of a full course in calculus at a less rigorous level than Calculus 1501A/B. Integration by parts, partial fractions, integral tables, geometric series, harmonic series, Taylor series with applications, arc length of parametric and polar curves, first order linear and separable differential equations with applications. 4 lecture hours, 0.5 course.

**Antirequisite(s):** Calculus 1501A/B, Applied Mathematics 1413.

**Prerequisite(s):** A minimum mark of 55% in one of Calculus 1000A/B, 1100A/B or 1500A/B.

Integral calculus of functions of several variables: double, triple and iterated integrals; applications; surface area. Vector integral calculus: vector fields; line integrals in the plane; Green's theorem; independence of path; simply connected and multiply connected domains; parametric surfaces and their areas; divergence and Stokes' theorem. 3 lecture hours, 0.5 course.

**Antirequisite(s):** Calculus 2503A/B.

**Prerequisite(s):** Calculus 2502A/B or Calculus 2302A/B.

Integral calculus of functions of several variables: multiple integrals; Leibnitz' rule; arc length; surface area; Green's theorem; independence of path; simply connected and multiply connected domains; three dimensional theory and applications; divergence theorem; Stokes' theorem. 3 lecture hours, 0.5 course.

**Antirequisite(s):** Calculus 2303A/B.

**Prerequisite(s):** A minimum mark of 60% in Calculus 2502A/B.