Unit 02 – Engineering Maths

The mathematics that is delivered in this unit is that which is directly applicable to the engineering industry, and it will help to increase students’ knowledge of the broad underlying principles within this discipline.

This Module includes:

  • 3 Workbooks
  • 3 Assignments
  • 3 Worked Solutions
  • 38 Videos
  • 1 Software

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

Additional information

Workbooks

3

Assignments

3

Worked Solutions

3

Tutorial Videos

38 tutorial videos available, included in the cost.

Introduction to Dimensions (13:48)
Transposition of Formulae (14:53)
Revision of Indices (22:24)
Dimensions of Resistance (09:48)
Dimensions of Frequency (08:26)
Simultaneous Equations (24:24)
Deriving Equations (19:20)
Arithmetic and Geometric Series (16:01)
Exponential Functions (21:16)
Graphical and Polar signals (12:35)
Sinusoids and Radian Measure (13:03)
Hyperbolic Functions (13:02)
Hyperbolic Identities (07:17)
Graph Simulator – Beginner (23:17)
Graph Simulator – Intermediate (15:12)
Graph Simulator – Advanced (12:46)

Sinusoids and Radians (13:22)
Compound Angle Identities – Concept (16:33)
Compound Angle Identities – Example 1 (21:22)
Compound Angle Identities – Example 2 (24:52)
Vector Quantities (19:25)
Vector (Cross) Product and Scalar(Dot) Product (31:08)
Plotting Vectors with Software (13:54)

Rate of Change and Derivative (16:56)
Polynomial Differentiation (23:47)
Turning Points (10:12)
Sinusoidal Differentiation (17:51)
Exponential Differentiation (14:50)
Logarithmic Differentiation (23:02)
Hyperbolic Differentiation (10:38)
Function of a Function (24:29)
The Product Rule (19:28)
The Quotient Rule (13:53)
Maxima, Minima and Points of Inflexion (16:39)
Hyperbolic Integration (24:08)
Integration by Substitution (08:20)
Integration by Parts (36:07)
Definite Integrals (18:38)

Software

1

Workbook Sample

Video Sample