Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Module Offerings
5503NCCG-APR-PAR
5503NCCG-JAN-PAR
5503NCCG-SEP-PAR
5503NCCG-SEP_NS-PAR
Aims
The module will prepare students to analyse and model engineering situations using mathematical techniques. Among the topics included in this module are: number theory, complex numbers, matrix theory, linear equations, numerical integration, numerical differentiation, and graphical representations of curves for estimation within an engineering context. Finally, students will expand their knowledge of calculus to discover how to model and solve engineering problems using first and second order differential equations. On successful completion of this module students will be able to use applications of number theory in practical engineering situations, solve systems of linear equations relevant to engineering applications using matrix methods, approximate solutions of contextualised examples with graphical and numerical methods, and review models of engineering systems using ordinary differential equations.
Learning Outcomes
1.
Use applications of number theory in practical engineering situations
2.
Solve systems of linear equations relevant to engineering applications using matrix methods
3.
Approximate solutions of contextualised examples with graphical and numerical methods.
4.
Review models of engineering systems using ordinary differential equations.
Module Content
Outline Syllabus:Number theory: types of numbers (Natural, Integer, Rational, Real, Complex), the modulus, argument and conjugate of complex numbers, polar and exponential forms of complex numbers, the use of de Moivre’s Theorem in engineering, complex number applications
Matrix methods: introduction to matrices and matrix notation, the process for addition, subtraction and multiplication of matrices, the determinant of a matrix, using the inverse of a square matrix to solve linear equations, Gaussian elimination to solve systems of linear equations.
Graphical and numerical methods: standard curves of common functions, including quadratic, cubic, logarithm and exponential curves, systematic curve sketching knowing the equation of the curve, using sketches to approximate solutions of equations, numerical analysis using a variety of formal methods.
Differential equations: formation and solutions of first-order differential equations, applications of first-order differential equations, formation and solutions of second-order differential equations, applications of second-order differential equations, Laplace transform solutions of linear ordinary differential equations, applications of Laplace transforms