Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Module Offerings
4315CIT-SEP-PAR
Aims
To provide a foundation in engineering mathematics for its application to the solution of engineering problems
Learning Outcomes
1.
Use basic algebraic manipulations and mathematical functions in the solution of engineering problems.
2.
Use basic trigonometry to describe engineering waves in mechanical and electrical systems.
3.
Use exponentials and logarithms to solve relevant engineering problems.
4.
Apply complex numbers in the solution of engineering problems.
5.
Use and apply mathematical software to the solution of engineering mathematics.
Module Content
Outline Syllabus:1. Revision of basic algebraic techniques: Representation of numbers, Rules of arithmetic, Modulus and intervals. Substitution, simplification, factorization, indices, evaluation and transposition of formulae, fractions and partial fractions. Number and accuracy.
2. Geometry: Coordinates, Straight lines, Circles, Conics.
3. Introduction of the use of a mathematical software, e.g. MATLAB.
4.Functions: Notation, types of function, composite and inverse, graphs.
5. Linear and quadratic functions: Linear functions, Least squares fit, Quadratic functions
6.Polynomial functions: Factorization, Nested multiplication and synthetic division, Roots of polynomial functions
7. Rational functions: Partial fractions, Asymptotes, Parametric representation
8.Circular functions: Angles and circular measure. Trigonometric ratios for right-angled triangles. Sine and cosine rules. Trigonometric functions and their graphs, simple trigonometric identities and equations. Engineering waves in mechanical and electrical problems.
9. Exponential function: Properties and graph. Natural logarithm as inverse of
exponential function, graph and properties. Definitions and calculation of hyperbolic functions including inverse functions.
10. Complex numbers: Complex arithmetic, complex conjugate, Argand diagram. Rectangular, polar forms. Magnitude and phase. Very basic treatment of Euler's formula.
11. Vector Algebra: Basic definition and properties, Scalar product and vector product, Vector treatment of the geometry of lines and planes, Engineering
application.
Additional Information:This module provides a foundation in pre-calculus for level four students in
mechanical and electrical engineering, to enable them to apply this to the solution of engineering problems.
For each topic area of the syllabus, relevant commands will be given for application of a symbolic algebra package, e.g. Matlab to harder problems.
Examinations are 2 hour duration.