Engineering Mathematics 1

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Description

Mathematical models are used to understand, predict and optimise engineering systems. Many of these systems are deterministic and are modelled using differential equations. Others are random in nature and are analysed using probability theory and statistics. This course provides an introduction to differential equations and their solutions and to probability and statistics, and relates the theory to physical systems and simple real world applications.

Objective

To introduce students to the mathematical modelling of physical systems using differential equations and the methods used to solve these equations. To develop the ability to recognise and use the appropriate techniques for the statistical analysis of a variety of experimental and observational studies. At the end of this course, students will have the ability to solve a broad range of ordinary differential equations and some important second-order linear partial differential equations. Students will have the ability to describe and analyse data in certain common situations and to use simple probability models.

Content

Topics covered are: Ordinary differential equations, including first and second order equations and series solutions; Fourier series; partial differential equations, including the heat equation, the wave equation, Laplace's equation and separation of variables; probability and statistical methods, including sampling and probability, descriptive statistics, random variables and probability distributions, mean and variance, linear combinations of random variables, statistical inference for means and proportions and linear regression.