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This subject introduces important mathematical methods required in engineering such as manipulating vector differential operators, computing multiple integrals and using integral theorems. A range of ordinary and partial differential equations are solved by a variety of methods and their solution behaviour is interpreted. The subject also introduces sequences and series including the concepts of convergence and divergence.
Topics include: Vector calculus, including Gauss’ and Stokes’ Theorems; sequences and series; Fourier series, Laplace transforms; systems of homogeneous ordinary differential equations, including phase plane and linearization for nonlinear systems; second order partial differential equations and separation of variables.
Intended learning outcomes
At the completion of this subject, students should be able to
- manipulate vector differential operators
- determine convergence and divergence of sequences and series
- solve ordinary differential equations using Laplace transforms
- sketch phase plane portraits for linear and nonlinear systems of ordinary differential equations
- represent suitable functions using Fourier series
- solve second order partial differential equations using separation of variables
- use MATLAB to perform simple numerical and symbolic calculations
In addition to learning specific mathematical skills, students will have the opportunity to develop generic skills that will assist them in any career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing tasks;
- computer skills: the ability to use mathematical computing packages.
Last updated: 1 March 2024