Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Seminar
Module Offerings
6601PMEC-JAN-PAR
Aims
To refresh and further develop the common mathematical skills necessary to support those students who require additional preparation in mathematics for progression to postgraduate programmes in Engineering and Computing.
Module Content
Outline Syllabus: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.
Introduction to vector calculus. Divergence, gradient and curl and their physical
meanings and applications.
Z transforms. Definition and properties. Inversion. Applications.
The use of a symbolic mathematical package e.g. Mathcad in the solution of problems
involving the above topics.
Additional Information:This module will provide students with the knowledge and skills required to study a postgraduate level programme in Engineering or Computing.
Assessments
Test
Exam