620-140 Intermediate Mathematics

Students transferring from another tertiary institution should talk with the Director of First Year Studies in Mathematics and Statistics to ascertain which of the subjects 620-140 or 620-141 is more suitable for them. In 620-140 some basic knowledge of linear equations, row operations on matrices and elementary partial derivatives is assumed.

Students may only gain credit for one of [00]620-111, 620-121, 620-140, 620-141.

620-161 or equivalent.

This subject introduces vectors, matrices and linear transformations, the concepts of vector geometry, the properties of basic functions of calculus, complex numbers and elementary complex functions. Students should develop the ability to employ vector methods in geometrical problems, apply linear transformation ideas in geometrical situations, differentiate the basic functions of calculus and use calculus methods to solve optimisation problems including problems which involve functions of more than one variable. This subject develops the fundamental concepts in linear algebra, calculus and complex numbers necessary for further studies in mathematics.

The following topics are covered:

• matrices: matrix algebra, rank, inverses and applications to linear systems;

• determinants: definitions, evaluation and applications;

• vectors: dot and cross products and scalar triple product;

• vector geometry: problems involving intersecting lines and planes, volumes and areas;

• linear transformations: transformation matrices, orthogonal matrices and geometrical applications;

• single variables: polynomial, rational, trigonometric, exponential, logarithmic and hyperbolic functions and their inverses, and implicit differentiation;

• multivariable calculus: partial derivatives, chain rules for functions of several variables, directional derivatives, tangent planes, and extrema for functions of several variables; and

• complex numbers: Cartesian and polar form, De Moivre's theorem, roots of equations, complex exponential function and applications to derivatives and integrals.

Up to 36 pages of written assignments during semester (10%), a 45-minute written mid-semester test (0% or 10%) and a 3-hour written examination at the end of semester (80% or 90%). The relative weighting of the examination and mid-semester test will be chosen so as to maximise the student's final mark.