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.

This subject develops problem-solving skills (especially through tutorial exercises) including facing unfamiliar problems, identifying relevant strategies and the ability to generalise mathematical arguments.

Topics covered: Matrices: matrix algebra, rank, inverses, applications to linear systems. Determinants: definitions, evaluation, applications. Vectors: dot and cross products, scalar triple product. Vector geometry: problems involving intersecting lines and planes, volumes and areas. Linear transformations: transformation matrices, orthogonal matrices, geometrical applications. Single variables: polynomial, rational, trigonometric, exponential, logarithmic and hyperbolic functions and their inverses; implicit differentiation. Multivariable calculus: partial derivatives, chain rules for functions of several variables, directional derivatives, tangent planes, extrema for functions of several variables. Complex numbers: cartesian and polar form, De Moivre's theorem, roots of equations, complex exponential function and applications to derivatives and integrals.

Up to 24 pages of written assignments, class tests totalling not more than 1.5 hours and a 3-hour end-of-semester written examination.