620-122 Mathematics 1B

Note

Students may gain credit for only one of 620-112, 620-122, 620-200, 620-211 (1997 Handbook 618-112, 618-222, 618-200, 618-211). Students unable to take this subject in semester 2 should seek advice from the Director of First-year Studies about the suitability of taking either 620-200 or 620-211 in semester 1 of the following year.

Credit Points

Coordinator

Prerequisites

620-111 or 620-121 (1997 Handbook: 618-111 or 618-121).

Semester

Contact

Subject Description

This subject gives a solid grounding in key areas of mathematics needed by in modern science and technology, and is the gateway to all mathematical developments since 1900. Little of the material here has been seen at school, and the level of understanding required represents a distinct advance on the minimum necessary in previous subjects.

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadratics and conics, rotation matrices, diagonal, real-symmetric and orthogonal matrices. 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; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment

Up to 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.