**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.

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 include first order ODE's of various types, higher order ODE's and methods of solving them, initial and boundary value problems, applications to mass-spring systems and electrical RLC circuits, Laplace transforms and their use for solving differential equations, systems of linear ODE's, orthogonal functions and Fourier series.

**Antirequisite(s):** Applied Mathematics 2402A, the former Applied Mathematics 2411, 2413, 2415.

**Prerequisite(s):** Applied Mathematics 1411A/B and 1413.

**Pre-or Corequisite(s):**

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

Introduction to first order differential equations, linear second and higher order differential equations with applications, complex numbers including Euler's formula, series solutions, Bessel and Legendre equations, existence and uniqueness, introduction to systems of linear differential equations.

**Antirequisite(s):** The former Differential Equations 2402A.

**Prerequisite(s):** A minimum mark of 60% in Calculus 1301A/B, or a minimum mark of 55% in Calculus 1501A/B or Applied Mathematics 1413.

**Pre-or Corequisite(s):** Mathematics 1600A/B or the former Linear Algebra 1600A/B.

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

Topics include: Fourier series, integrals and transforms; boundary value problems in cartesian coordinates; separation of variables; Fourier and Laplace methods of solution.

**Antirequisite(s):** Applied Mathematics 3415A/B.

**Prerequisite(s):** Applied Mathematics 2413.

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

Topics Include: numerical methods; introduction to complex analysis; complex integration; boundary value problems in cartesian coordinates; separation of variables; Fourier series and transform methods of solution.

**Antirequisite(s):** Applied Mathematics 3413A/B.

**Prerequisite(s):** Applied Mathematics 2415.

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

*New for September 2015.*

Basic introduction to C++, review of numerical methods applicable to problems in linear algebra and differential equations, introduction to the concept of object-oriented programming techniques, applications to scientific computation. Grade is based upon two projects and a presentation.

**Prerequisite(s):** Calculus 1301A/B, 1501A/B, Applied Mathematics 1201B or 1413.

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

Offered in alternate years with Applied Mathematics 4615F/G.

An introduction to mathematical biology. Case studies from neuroscience,immunology, medical imaging, cell biology, molecular evolution and ecology will give an overview of this diverse field, illustrating standard mathematical approaches such as compartmental analysis and evolutionary game theory.

**Prerequisite(s):** One of Calculus 2302A/B, 2402A/B, 2502A/B; plus one of Mathematics 1600A/B or the former Linear Algebra 1600A/B, or Applied Mathematics 1411A/B.

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

Functions of a complex variable, analytic functions, integration in the complex plane, Taylor and Laurent series, analytic continuation, Cauchy's theorem, evaluation of integrals using residue theory, applications to Laplace transforms, conformal mapping and its applications.

**Antirequisite(s):** Mathematics 3124A/B.

**Prerequisite(s):** Calculus 2303A/B or 2503A/B.

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

Boundary value problems for Laplace, heat, and wave equations; derivation of equations; separation of variables; Fourier series; Sturm-Liouville Theory; eigenfunction expansions; cylindrical and spherical problems; Legendre and Bessel functions; spherical harmonics; Fourier and Laplace transforms.

**Prerequisite(s):** (i) Mathematics 1600A/B or the former Linear Algebra 1600A/B; Applied Mathematics 2402A or the former Differential Equations 2402A; Calculus 2303A/B or 2503A/B; or (ii) Calculus 2402A/B and Applied Mathematics 2503A/B. In each course a minimum mark of 60% is required.

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

Strengths and limitations of computer algebra systems (CAS); complexity of exact computations versus possible instability of numerical computations; selecta from Groebner bases, resultants, fractional derivatives, Risch integration algorithm, special functions including the Lambert W function. The emphasis is on preparing the student to use CAS in mathematics, science, and engineering.

**Prerequisite(s):** Applied Mathematics 2413, 2415 or 2813B.

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

Offered in alternate years with Applied Mathematics 4611F/G.

The student will work on a project under faculty supervision. The project may involve an extension, or more detailed coverage, of material presented in other courses. Credit for the course will involve a written as well as oral presentation.

**Prerequisite(s):** Registration in the fourth year of a program in Applied Mathematics.

**Extra Information:** 0.5 course.

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.

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

**Prerequisite(s):** One or more of Ontario Secondary School MCV4U, Mathematics 0110A/B.**Extra Information:** 4 lecture hours, 0.5 course.

Functions of multiple variables and their differential calculus. The gradient and the Hessian. Constrained and unconstrained optimization of scalar-valued functions of many variables: Lagrange multipliers. Multidimensional Taylor series. Integrating scalar-valued functions of several variables: Jacobian transformations. Pointwise and uniform convergence. Power series.

**Antirequisite(s):** Calculus 2302A/B, Calculus 2502A/B.

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