620-162 Introductory Mathematics B

Note

Credit Points

Coordinator

Prerequisites

620-161

Semester

Contact

Subject Description

This subject introduces difference equations, complex numbers, the manipulation of matrices and extends integration skills and the treatment of differential equations. Students should develop the ability to solve simple difference equations, to use complex numbers, use matrices in selected applications, use integral calculus to solve simple differential equations. The subject develops the fundamental concepts in linear algebra and calculus with a view to applications in biology and environmental science.

Iteration:Iteration, spreadsheets, the notion of convergence.Difference equations:First and second order difference equations, solution by iteration, general solution for linear difference equations.First order systems:Applications to finance and discrete-time population models.Complex numbers:the algebra of complex numbers, the complex plane, polar form, complex exponentials. Matrices: matrix operations, vectors as special matrices, inverses, row-reduction, rank; eigenvectors and eigenvalues of matrices. Applications of matrices to topics such as Markov chains, game theory, age-structured population models. Calculus: antiderivatives and the definite integral; integrals involving polynomials, exponential, logarithmic, trigonometric and hyperbolic functions. Differential equations: separable first order, linear constant coefficient equations and first order systems, applications to population models and biosystems. Simple numerical solution of differential equations.

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.