620-182 Mathematics 1S

Note

This subject is not available to students enrolled in any Bachelor of Science course. Combined Science/Engineering students are required to take Science Mathematics.

Credit Points

Coordinator

Prerequisites

620-181 (1997 Handbook 618-181).

Semester

Contact

Subject Description

This subject gives a solid grounding in key areas of mathematics needed in modern science and technology.

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), Mean Value Theorem and applications, Newton's method for root-finding, approximate integration, Taylor polynomials. Multivariable calculus: functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals and applications. Systems of differential equations: systems of first-order differential equations; linear systems; eigenvalues and eigenvectors; solutions for distinct, repeated and complex eigenvalues; inhomogeneous systems; application to phase plane; equilibrium points and their stability; second-order systems, application to systems of mechanical or electrical oscillators; longitudinal and transverse oscillations.

Assessment

Up to 35 pages of written assignments, four hours of end-of-semester written examination (one hour of which will be a written examination on differential equations) and class tests totalling not more than 1.5 hours.