Description
The aim of this unit is to develop students’ skills in the mathematical principles and theories that underpin the engineering curriculum. Students will be introduced to mathematical methods and statistical techniques in order to analyse and solve problems within an engineering context.
On successful completion of this unit students will be able to employ mathematical methods within a variety of contextualised examples, interpret data using statistical techniques, and use analytical and computational methods to evaluate and solve engineering problems.
Learning Outcomes
By the end of this unit students will be able to:
1. Identify the relevance of mathematical methods to a variety of conceptualised
engineering examples.
Mathematical concepts:
Dimensional analysis
Arithmetic and geometric progressions
Functions:
Exponential, logarithmic, trigonometric and hyperbolic functions
2. Investigate applications of statistical techniques to interpret, organise and
present data.
Summary of data:
Mean and standard deviation of grouped data
Pearson’s correlation coefficient
Linear regression
Charts, graphs and tables to present data
Probability theory:
Binomial and normal distribution
3. Use analytical and computational methods for solving problems by relating
sinusoidal wave and vector functions to their respective engineering applications.
Sinusoidal waves:
Sine waves and their applications
Trigonometric and hyperbolic identities
Vector functions:
Vector notation and properties
Representing quantities in vector form
Vectors in three dimensions
4. Examine how differential and integral calculus can be used to solve engineering
problems.
Differential calculus:
Definitions and concepts
Definition of a function and of a derivative, graphical representation of a function, notation of derivatives, limits and continuity, derivatives; rates of change, increasing and decreasing functions and turning points
Differentiation of functions
Differentiation of functions including:
– standard functions/results
– using the chain, product and quotient rules
– second order and higher derivatives
Types of function: polynomial, logarithmic, exponential and trigonometric (sine, cosine and tangent), inverse trigonometric and hyperbolic functions
Integral calculus:
Definite and indefinite integration
Integrating to determine area
Integration of functions including:
• common/standard functions
• using substitution
• by parts
Exponential growth and decay
Types of function: algebraic including partial fractions and trigonometric (sine,
cosine and tangent) functions
Engineering problems involving calculus:
Including: stress and strain, torsion, motion, dynamic systems, oscillating systems, force systems, heat energy and thermodynamic systems, fluid flow, AC theory, electrical signals, information systems, transmission systems, electrical machines, electronics