Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Tutorial
Module Offerings
5521USST-SEP-PAR
Aims
To provide a foundation in engineering mathematics for application to the solution of engineering problems
Learning Outcomes
1.
Solve linear, first order, constant coefficient ordinary differential equations by the method of integrating factor and apply to the modelling of engineering problems
2.
Solve linear, second order, constant coefficient ordinary differential equations and apply to the modelling of engineering problems
3.
Find first and second order partial derivatives for functions of several variables and apply to engineering problems using optimisation and errors
4.
Use eigenvectors and eigenvalues in the solution of engineering problems
5.
Solve simultaneous homogeneous ordinary differential equations with constant coefficients and apply to the solution of a two degree of freedom system
6.
Use Laplace transforms in the solution of engineering problems involving ordinary differential equations
7.
Use Fourier series in the solution of engineering problems
8.
Find numerical solutions of ordinary differential equations
9.
Apply symbolic mathematical software eg. Mathcad in the solution to problems involving topics on the syllabus.
Module Content
Outline Syllabus:
The solution of first order ODE's by the integrating factor method.
The solution of second order ODE's by the method of undetermined coefficients. Application to single degree of freedom oscillating systems.
Functions of several variables. Partial differentiation with application to optimisation and error estimation.
Eigenvalues and eigenvectors. By manual calculation for low order matrices. Use of software for matrices of larger order.
Solution of two first and second order, homogeneous simultaneous ODE's with constant coefficients. Application to normal modes for a two degree of freedom system.
Laplace transforms. Concepts. Use of tables. The inverse transform. Application to the solution of ODE's. Transfer functions and stability.
Periodic functions. Fourier series for functions of any period. Harmonics.
Numerical solution of ODE's. Euler’s method and application of software.
The use of a symbolic mathematical package eg Mathcad in the solution of problems involving the above topics.
The solution of first order ODE's by the integrating factor method.
The solution of second order ODE's by the method of undetermined coefficients. Application to single degree of freedom oscillating systems.
Functions of several variables. Partial differentiation with application to optimisation and error estimation.
Eigenvalues and eigenvectors. By manual calculation for low order matrices. Use of software for matrices of larger order.
Solution of two first and second order, homogeneous simultaneous ODE's with constant coefficients. Application to normal modes for a two degree of freedom system.
Laplace transforms. Concepts. Use of tables. The inverse transform. Application to the solution of ODE's. Transfer functions and stability.
Periodic functions. Fourier series for functions of any period. Harmonics.
Numerical solution of ODE's. Euler’s method and application of software.
The use of a symbolic mathematical package eg Mathcad in the solution of problems involving the above topics.
Additional Information:
UNESCO Sustainable Development Goals
Quality Education
Gender Equality
Industry, Innovation and Infrastructure
Partnerships for the Goals
UK SPEC AHEP 4
CEng.
M1 Apply a comprehensive knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Much of the knowledge will be at the forefront of the particular subject of study and informed by a critical awareness of new developments and the wider context of engineering.
M2 Formulate and analyse complex problems to reach substantiated conclusions. This will involve evaluating available data using first principles of mathematics, statistics, natural science and engineering principles, and using engineering judgment to work with information that may be uncertain or incomplete, discussing the limitations of the techniques employed.
M3 Select and apply appropriate computational and analytical techniques to model complex problems, discussing the limitations of the techniques employed.
IEng.
B1 Apply knowledge of mathematics, statistics, natural science and engineering
principles to broadly-defined problems. Some of the knowledge will be informed by current developments in the subject of study.
B2 Analyse broadly-defined problems reaching substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles.
B3 Select and apply appropriate computational and analytical techniques to model broadly-defined problems, recognising the limitations of the techniques employed.
UNESCO Sustainable Development Goals
Quality Education
Gender Equality
Industry, Innovation and Infrastructure
Partnerships for the Goals
UK SPEC AHEP 4
CEng.
M1 Apply a comprehensive knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Much of the knowledge will be at the forefront of the particular subject of study and informed by a critical awareness of new developments and the wider context of engineering.
M2 Formulate and analyse complex problems to reach substantiated conclusions. This will involve evaluating available data using first principles of mathematics, statistics, natural science and engineering principles, and using engineering judgment to work with information that may be uncertain or incomplete, discussing the limitations of the techniques employed.
M3 Select and apply appropriate computational and analytical techniques to model complex problems, discussing the limitations of the techniques employed.
IEng.
B1 Apply knowledge of mathematics, statistics, natural science and engineering
principles to broadly-defined problems. Some of the knowledge will be informed by current developments in the subject of study.
B2 Analyse broadly-defined problems reaching substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles.
B3 Select and apply appropriate computational and analytical techniques to model broadly-defined problems, recognising the limitations of the techniques employed.