620-211 Mathematics 2 (Advanced)

Note

1. 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).
2. In some cases (e.g. students from the MUPHAS Mathematics program), direct entry into this subject may be possible.
3. High-achieving students from 620-142 (1997 Handbook 618-142) should ask the Head of Department about taking this subject as an alternative to 620-200.

Credit Points

Coordinator

Prerequisites

620-111 (1997 Handbook 618-111) or invitation by the Head of Department.

Semester

Contact

Subject Description

This subject gives a sophisticated treatment of core material in single- and multi-variable calculus and linear algebra. This advanced perspective is especially suited to students planning higher-level studies in Mathematics and Statistics.

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, dimension, Rⁿ and Cⁿ; inner products in real and complex spaces; linear transformations, matrix of a linear transformation, change of basis; eigenvectors and eigenvalues, diagonalisation of real symmetric matrices, applications - including applications to geometry; symmetry groups of matrices of R² and R³. 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.

Assessment

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