MAT-10041 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

Programme/Approved Electives for 2024/25

Available as a Free Standing Elective

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2024/25

Many physical problems are governed by ordinary or partial differential equations, the solution of which can help us understand their properties and characteristics. For instance, the oscillation frequency of a pendulum, the transfer time for sending a spaceship from the Earth to Mars, and the population evolution of a fish species in a lake can all be determined by solving ordinary differential equations. This module, which is a prerequisite for a number of other modules in the second and third years, will introduce some of the basic techniques for solving ordinary differential equations, familiarize students with partial differentiations, and explain how double integrals can be evaluated and used to compute areas and volumes.

The aim of this module is to introduce students to the solution of ordinary differential equations, and to Taylor series, elements of multi-variable calculus, including partial differentiation, double integration, and some of their applications.

Intended Learning Outcomes

recognize the type of ordinary differential equations (linear or nonlinear, constant or variable coefficients, order): 1,3
classify and solve several types of first-order ordinary differential equations (variable separable, linear and others which may be reduced to these): 1,3
study number and power series for convergence; expand a function of one variable as Taylor series: 2
calculate partial derivatives, and find local maxima/minima, and restricted maxima/minima using the method of Lagrange multipliers, apply chain rule to multi-variable functions: 2,3
evaluate double integrals and use them to find areas and volumes; change of variables under double integral, including polar coordinates: 3
solve first- and second-order, homogeneous linear ordinary differential equations with constant coefficients, as well as corresponding inhomogeneous ordinary differential equations with the right hand side of special form by the method of undetermined coefficients: 1,3

Study hours

36 hours lectures
12 hours examples classes
24 hours coursework preparation
78 hours private study

School Rules

None

Description of Module Assessment