Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Practical
Module Offerings
5321CIT-SEP-PAR
Aims
To provide a foundation in engineering mathematics for application to the solution of engineering problems
Learning Outcomes
1.
Solve linear, first and second order, constant coefficient ordinary differential equations by the method of integrating factor and apply to the modelling of engineering problems.
2.
Find first and second order partial derivatives for functions of several variables and apply to engineering problems using optimisation and errors.
3.
Use eigenvectors and eigenvalues in the solution of engineering problems.
4.
Solve simultaneous homogeneous ordinary differential equations with constant coefficients and apply to the solution of a two degree of freedom system.
5.
Use Laplace transforms in the solution of engineering problems involving ordinary differential equations. Use Fourier series in the solution of engineering problems.
6.
Find numerical solutions of ordinary differential equations and apply symbolic mathematical software e.g. MATLAB in the solution to problems involving topics on the syllabus.
Module Content
Outline Syllabus:1. The solution of first order ODE's by the integrating factor method
2. The solution of second order ODE's by the method of undetermined coefficients
3. Application to single degree of freedom oscillating systems
4. Functions of several variables. Partial differentiation with application to optimization and error estimation
5. Eigenvalues and eigenvectors. By manual calculation for low order matrices. Use of software for matrices of larger order
6. Solution of two first and second order, homogeneous simultaneous ODE's with constant coefficients. Application to normal modes for a two degree of freedom
7. Laplace transforms. Concepts. Use of tables. The inverse transform. Application to the solution of ODE's. Transfer functions and stability
8. Periodic functions. Fourier series for functions of any period. Harmonics.
9. Numerical solution of ODE's. Euler's method and application of software.
10. The use of a symbolic mathematical package e.g. MATLAB in the solution of problems involving the above topics.
Additional Information:This module provides a basis in advanced engineering mathematics for level five students in mechanical and electrical engineering.
For each topic area of the syllabus, relevant commands will be given for application of a symbolic algebra package, e.g. Mathcad to harder problems.
Reports are 2500 maximum word count.
Examinations are 2 hour duration.