620-112 Mathematics 1B (Advanced)

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).

Credit Points

Coordinator

Prerequisites

Mathematics and Statistics 620-111 (1997 Handbook 618-111) with a grade of H3 or better, or 620-121 with a grade of H2A or better, or invitation by the Head of Department.

Semester

Contact

Subject Description

This subject gives a more sophisticated treatment of core material in single-and multi-variable calculus and linear algebra than in 620-122. The 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, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.