# Engineering Institute of Technology

Unit Name | ENGINEERING MATHEMATICS I |

Unit Code | BSC101C |

Unit Duration | 1 Term (2 Terms for 24 week delivery*) |

Award | Bachelor of Science (Engineering) Duration 3 years |

Year Level | One |

Unit Creator/Reviewer | |

Core/Elective | Core |

Pre/Co-requisites | Nil |

Credit Points | 3 Total Course Credit Points 81 (27 x 3) |

Mode of Delivery | Online or on-campus. |

Unit Workload | (Total student workload including “contact hours” = 10 hours per week; 5 hours per week for 24 week delivery) Pre-recordings / Lecture – 1.5 hours (0.75 hours for 24 week delivery) Tutorial – 1.5 hours (0.75 hours for 24 week delivery) Guided labs / Group work / Assessments – 2 hours (1 hour for 24 week delivery) Personal Study recommended – 5 hours (2.5 hours for 24 week delivery) |

This unit may be delivered over 24 weeks (2 Terms) because the nature of the content is deemed suitable (from a pedagogical perspective) for a longer duration than the standard 12 week (1 Term). In addition, these 24-week duration Units require half the student workload hours, 5 hours per week, which allows the total load to be kept at 15 hours per week when combined with a typical 10 hours per week, 12-week Unit. EIT has extensive data to demonstrate that if the load is higher than 15 hours per week the attrition rate for part time students dramatically increases.

## Unit Description and General Aims

This unit introduces the student to core mathematical concepts, processes and techniques necessary to support subsequent studies in Engineering. These concepts include, but are not limited to, the properties and engineering applications of linear, quadratic, logarithmic and exponential functions. The unit commences with linear equations and goes on to cover varied subjects including inequalities, functions, trigonometry, sequences, series, variation, ratio, proportion, algebraic functions, trigonometric ratios, trigonometric functions and applications. It rounds off with an introduction to differentiation and integration, followed by vectors, complex numbers and matrices. The topics in this unit are structured in such a manner that the student will be able to solve problems related to engineering applications by using these mathematical techniques.

## Learning Outcomes

On successful completion of this Unit, students are expected to be able to:

Detail mathematical concepts related to linear and absolute value inequalities

Solve linear and quadratic equations

Comprehend and apply the basics of functions and logarithms

Perform simple trigonometric calculations

Evaluate concepts related to sequences, series, variation, ratio and proportion

Solve algebraic equations

Use trigonometric ratios to solve mathematical problems

Apply vector principles

Perform calculations involving complex numbers

Use matrices and determinants to solve mathematical problems

## Professional Development

Completing this unit may add to students professional development/competencies by:

Fostering personal and professional skills and attributes in order to:

Conduct work in a professionally diligent, accountable and ethical manner.

Effectively use oral and written communication in personal and professional domains.

Foster applicable creative thinking, critical thinking and problem solving skills.

Develop initiative and engagement in lifelong learning and professional development.

Enhance collaboration outcomes and performance in dynamic team roles.

Effectively plan, organise, self-manage and manage others.

Professionally utilise and manage information.

Enhance technologist literacy and apply contextualised technologist skills.

Enhance investigatory and research capabilities in order to:

Develop an understanding of systematic, fundamental scientific, mathematic principles, numerical analysis techniques and statistics applicable to technologists.

Access, evaluate and analyse information on technologist processes, procedures, investigations and the discernment of technologist knowledge development.

Foster an in-depth understanding of specialist bodies of knowledge, computer science, engineering design practice and contextual factors applicable to technologists.

Solve basic and open-ended engineering technologist problems.

Understand the scope, principles, norms, accountabilities and bounds associated with sustainable engineering practice.

Develop engineering application abilities in order to:

Apply established engineering methods to broadly-defined technologist problem solving.

Apply engineering technologist techniques, tool and resources.

Apply systematic technologist synthesis and design processes.

Systematically conduct and manage technologist projects, work assignments, testing and experimentation.

Engineers Australia

The Australian Engineering Stage 1 Competency Standards for Engineering Technologists, approved as of 2013. This table is referenced in the mapping of graduate attributes to learning outcomes and via the learning outcomes to student assessment.

Stage 1 Competencies and Elements of Competency | |

1. | Knowledge and Skill Base |

1.1 | Systematic, theory based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the technology domain. |

1.2 | Conceptual understanding of the, mathematics, numerical analysis, statistics, and computer and information sciences which underpin the technology domain. |

1.3 | In-depth understanding of specialist bodies of knowledge within the technology domain. |

1.4 | Discernment of knowledge development within the technology domain. |

1.5 | Knowledge of engineering design practice and contextual factors impacting the technology domain. |

1.6 | Understanding of the scope, principles, norms, accountabilities and bounds of sustainable engineering practice in the technology domain. |

2. | Engineering Application Ability |

2.1 | Application of established engineering methods to broadly-defined problem solving within the technology domain. |

2.2 | Application of engineering techniques, tools and resources within the technology domain. |

2.3 | Application of systematic synthesis and design processes within the technology domain. |

2.4 | Application of systematic approaches to the conduct and management of projects within the technology domain. |

3. | Professional and Personal Attributes |

3.1 | Ethical conduct and professional accountability. |

3.2 | Effective oral and written communication in professional and lay domains. |

3.3 | Creative, innovative and pro-active demeanour. |

3.4 | Professional use and management of information. |

3.5 | Orderly management of self and professional conduct. |

3.6 | Effective team membership and team leadership. |

Graduate Attributes

Successfully completing this Unit will contribute to the recognition of attainment of the following graduate attributes aligned to the AQF Level 7 criteria, Engineers Australia Stage 1 Competency Standards for Engineering Technologists and the Sydney Accord:

Graduate Attributes (Knowledge, Skills, Abilities, Professional and Personal Development) | EA Stage 1 Competencies | Learning Outcomes |

A. Knowledge of Science and Engineering Fundamentals | ||

A1. Breadth of knowledge of engineering and systematic, theory-based understanding of underlying principles, and depth of knowledge across one or more engineering sub- disciplines | 1.1, 1.3 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |

A2. Knowledge of mathematical, statistical and computer sciences appropriate for engineering technology | 1.2 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |

A3. Discernment of knowledge development within the technology domain | 1.4 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |

A4. Knowledge of engineering design practice and contextual factors impacting the technology domain | 1.5 | |

B. Problem Solving, Critical Analysis and Judgement | ||

B1. Ability to research, synthesise, evaluate and innovatively apply theoretical concepts, knowledge and approaches across diverse engineering technology contexts to effectively solve engineering problems | 1.4, 2.1, 2.3 | |

B2. Technical and project management skills to design complex systems and solutions in line with developments in engineering technology professional practice | 2.1, 2.2, 2.3, 3.2 | |

C. Effective Communication | ||

C1. Cognitive and technical skills to investigate, analyse and organise information and ideas and to communicate those ideas clearly and fluently, in both written and spoken forms appropriate to the audience | 3.2 | |

C2. Ability to engage effectively and appropriately across a diverse range of cultures | 3.2 | |

D. Design and Project Management | ||

D1. Apply systematic synthesis and design processes within the technology domain | 2.1, 2.2, 2.3 | |

D2. Apply systematic approaches to the conduct and management of projects within the technology domain | 2.4 | |

E. Accountability, Professional and Ethical Conduct | ||

E1. Innovation in applying engineering technology, having regard to ethics and impacts including economic; social; environmental and sustainability | 1.6, 3.1, 3.4 | |

E2. Professional conduct, understanding and accountability in professional practice across diverse circumstances including team work, leadership and independent work | 3.3, 3.4, 3.5, 3.6 |

Unit Competency and Learning Outcome Map

This table details the mapping of the unit graduate attributes to the unit learning outcomes and the Australian Engineering Stage 1 Competency Standards for the Engineering Technologist.

Graduate Attributes | |||||||||||||

A1 | A2 | A3 | A4 | B1 | B2 | C1 | C2 | D1 | D2 | E1 | E2 | ||

Engineers Australia Stage 1 Competency Standards for Engineering Technologist | 1.1 | | |||||||||||

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## Student assessment

Assessment Type | When assessed | Weighting (% of total unit marks) | Learning Outcomes Assessed |

Assessment 1 Type: Multi-choice test / Group work / Short answer questions Example Topics: Arithmetic, Variation, Ratio and Proportion, Algebra, Simple Equations, Graphs, Simultaneous Equations, Trigonometry, Geometry, Quadratic equations Students may be asked to provide solutions to simple problems on various topics. | Week 4 (Week 8 for 24 week delivery) | 15% | 2, 5, 6 |

Assessment 2 Type: Multi-choice test / Group work / Short answer questions Example Topics: Sequences and Series, Logarithms exponentials and Inequalities, Trigonometric Functions and Formulae Students may complete a quiz with MCQ type answers or solve some simple problems or solve problems using software. | Week 7 (Week 14 for 24 week delivery) | 20% | 1, 3, 5, 7 |

Assessment 3 Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Short problems on basic differentiation and integration and vectors | Week 10 (Week 20 for 24 week delivery) | 20% | 8 |

Assessment 4 Type: Examination Example Topic: All topics An examination with a mix of detailed report type questions and/or simple numerical problems to be completed in 3 hours | Final Week | 40% | 1 to 10 |

Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application. | Continuous | 5% | 1 to 10 |

## Prescribed and Recommended readings

### Suggested Textbook

Bird, J. Basic Engineering Mathematics, 6th edn, John Wiley & Sons, ISBN-13: 978-0- 415-66278-9.

### Reference Materials

Kreyszig, A 2012,

*Advanced Engineering Mathematics Student Solutions Manual*, 10th edn, John Wiley & Sons, ISBN-13: 978-1118007402Peer reviewed Journals

Knovel library: http://app.knovel.com

IDC Technologies publications

Other material and online collections as advised during the lectures

## Unit Content

One topic is delivered per contact week, with the exception of part-time 24-week units, where one topic is delivered every two weeks.

### Topic 1

Basic Mathematics Review 1 (Mathematics Equation Editor Tools)

(Arithmetic, Variation, Ratio and Proportion)

BODMAS

Scientific notation, engineering notation

Ratios

Rates

Scale Diagrams

Direct Variation

Inverse Variation

(Algebra, Simple Equations, Graphs, Simultaneous Equations)

Indices, Brackets, Factorization

Solving simple linear equations

Graphing – axes, straight lines, gradients, proportionality

Simultaneous equations

### Topic 2

Basic Mathematics Review 2 (Introductory Trigonometry)

Angles

Triangles

Pythagoras

Sine, cosine, tan

Trigonometric Ratios

Elevation and Depression

Non Right Angle Triangles

Circle – properties, arc length, equation

Graphing circles and the unit circle

Radians

Trigonometric Identities

(Introductory Geometry)

Common shapes

Area of common and complex shapes

Common 3D shapes

Volume of common and complex 3D shapes

### Topic 3

Quadratic equations

Quadratic equations

Quadratic graphs

Factorization

Completing the square

Solving by formula

Practical problems

### Topic 4

Sequences and Series

Sums vs sequences

Simple series (progression)

Arithmetic progression

Geometric progression

Pascal’s triangle

Permutation and combination

Binomial theorem

Graphing progressions

Power series

### Topic 5

Logarithms exponentials and Inequalities

Logarithmic expression

Laws of logarithms

Natural (Naperian, hyperbolic) logarithms

Exponential functions

Graphing exponential functions

Logarithmic Equations

Application of Logarithms and exponential functions

Change of base

Inequalities and absolute values

### Topic 6

Trigonometric Functions and Formulae

Trigonometric graphs

Period, amplitude, cycle, frequency

Lag and lead (phase displacement)

Trigonometric identities and formulae

Cartesian and polar coordinates

### Topic 7

Introduction to differentiation

Basic principles of differentiation

Notation

Gradient curves

Differentiation of simple trigonometric functions

Differentiation of simple function

Rate of change

### Topic 8

Introduction to integration

Basic principles integration

Standard integrals

Area under a curve – calculation and graph

### Topic 9

Vectors and Scalars

Vectors and Scalars

Vector notation

Resolving vectors

Relative velocity

Vector Definitions and Components

Operations with Vectors

Vector Applications

Laws of Sines and Cosines

### Topic 10

Complex Numbers

Imaginary numbers

Arithmetic of complex numbers

The Argand diagram and polar form of a complex number

The exponential form of a complex number

De Moivre's theorem

Solving equations and finding roots of complex numbers

Phasors

### Topic 11

Matrices, determinants and multivariable functions 1

Introduction to matrices

Multiplication of matrices

Determinants

The inverse of a matrix

Multivariable functions

Multivariable calculus

Vector valued functions

Parameterization

### Topic 12

Matrices, determinants and multivariable functions 2

Matrix form trigonometric identities

Cramer's rule

Using the inverse matrix to solve simultaneous equations

Gaussian elimination

lterative techniques

Exam revision