Teaching Responsibility
LJMU Schools involved in Delivery:
Civil Engineering and Built Environment
Learning Methods
Lecture
Tutorial
Workshop
Module Offerings
4200CIV-SEP-CTY
Aims
To develop knowledge and understanding of the mathematics underpinning engineering, and to apply these techniques within an engineering context.
Learning Outcomes
1.
Use basic algebraic manipulations, matrices and mathematical functions proficiently in the analysis and solution of engineering problems
2.
Use and apply mathematical software to the solution of engineering mathematics problems
3.
Apply differential and integral calculus proficiently in the analysis and solution of engineering problems
4.
Communicate effectively through the clear presentation of mathematical equations and formulae.
Module Content
Outline Syllabus:Revision of basic algebraic techniques: substitution, simplification, factorisation, indices, evaluation and transposition of formulae, fractions and partial fractions. Linear and quadratic equations, linear simultaneous equations.
Revision of elementary coordinate geometry: Distance between two points.
Trigonometry: Angular measurement (radians and degrees, minutes and seconds), Sine and cosine rules. Trigonometric identities and equations.
Applications: Surveying; Forces
Exponential function: Properties and graph. Natural logarithm as inverse of exponential function, graph and properties. Definitions and calculation of hyperbolic functions including inverse functions.
Revision of differential calculus of one variable: Gradient of curve, derivatives of standard functions, linearity, derivatives of composite functions, products and quotients.
Applications: Stationary points. Rates of change.
Revision of integral calculus as inverse of differentiation. Standard integrals, linearity, integration of composite functions. Numerical integration.
Applications: Centroids
Functions: Notation, types of function, composite and inverse, graphs.
Complex numbers: Complex arithmetic, complex conjugate, Argand diagram.
Rectangular, polar forms. Magnitude and phase. Basic use of Euler’s formula.
Roots: Numerical techniques, including the Newton-Raphson method.
Applications: Solving cubic equations.
Basic vector algebra including Cartesian components and products. Differentiation of vectors. Applications: Forces
Basic matrix manipulation including the inverse matrix.
Applications: Solution of systems of linear equations.
1st order differential equations.
Module Overview:
This module develops your knowledge and understanding of the mathematics underpinning engineering. It develops your ability to apply these techniques within an engineering context. Laboratory sessions enable you to use and apply mathematical software to the solution of engineering mathematics problems.
This module develops your knowledge and understanding of the mathematics underpinning engineering. It develops your ability to apply these techniques within an engineering context. Laboratory sessions enable you to use and apply mathematical software to the solution of engineering mathematics problems.
Additional Information:This module provides a foundation in engineering mathematics for use in the analysis and solution of engineering problems.
Where this module is part of a Degree Apprenticeship programme, the knowledge learning outcomes are K2, the skills learning outcomes are S3.