Engineering Institute of Technology
Unit Name  ENGINEERING MATHEMATICS 2 
Unit Code  BSC104C 
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/Corequisites  BSC101C 
Credit Points  3
Total Course Credit Points 81 (27 x 3) 
Mode of Delivery  Online or oncampus. 
Unit Workload  (Total student workload including “contact hours” = 10 hours per week; 5 hours per week for 24 week delivery) Prerecordings / 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 24week 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, 12week 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.
This unit is intended at expanding the scope of engineering mathematics learning further, by introducing the student to the principles and applications of differential and integral calculus. The derivative and integration rules and techniques are brought out clearly, so as to enable the student to solve simple as well as complex engineering problems, using calculus. This is followed by a detailed overview of the concepts related to analytical geometry, probability and statistics and sets, so that the student will be able to use these mathematical techniques to effectively deal with problems in engineering application areas.
Learning Outcomes
On successful completion of this Unit, students are expected to be able to:
Apply the principles of differential and integral calculus
Derive equations from graphs of trigonometric functions
Evaluate the concepts of analytical geometry
Apply concepts related to statistics and probability
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, selfmanage 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 indepth understanding of specialist bodies of knowledge, computer science, engineering design practice and contextual factors applicable to technologists.
Solve basic and openended 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 broadlydefined 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.
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  Indepth 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 broadlydefined 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 proactive 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. 
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, theorybased understanding of underlying principles, and depth of knowledge across one or more engineering sub disciplines 
1.1, 1.3 
1, 2, 3, 4 
A2. Knowledge of mathematical, statistical and computer sciences appropriate for engineering technology 
1.2 
1, 2, 3, 4 
A3. Discernment of knowledge development within the technology domain  1.4  1, 2, 3, 4 
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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3.1 









 
 
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Unit Learning Outcomes  LO1    









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Student assessment
Assessment Type  When assessed  Weighting (% of total unit marks)  Learning Outcomes Assessed 
Assessment 1 Type: Multichoice test / Group work / Short answer questions Example Topic: Differentiation basics Students may complete a quiz with MCQ type answers and solve some simple equations to demonstrate a good understanding of the fundamental concepts 
Week 4 (Week 8 for 24 week delivery) 
15% 
1, 2 
Assessment 2 Type: Multichoice test / Group work / Short answer questions / Practical Example Topic: Derivative applications, integration basics Students may be asked to provide solutions to simple problems on various topics. 
Week 7 (Week 14 for 24 week delivery) 
20% 
1, 2 
Assessment 3 Type: Multichoice test / Group work / Short answer questions / Practical Example Topic: Analytical geometry Students may complete a quiz with MCQ type answers or solve some simple problems or use software to complete a practical. 
Week 9 (Week 18 for 24 week delivery) 
20% 
3 
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 4 
Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, selfassessment/reflection, case study analysis, application.  Continuous  5%  1 to 4 
Prescribed and recommended readings
Suggested Textbook
Bird, J. Engineering Mathematics, 7th edn, John Wiley & Sons, ISBN13: 978 0415662802.
Reference Materials
Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, John Wiley & Sons, ISBN13: 9780470458365.
Kreyszig, A 2012, Advanced Engineering Mathematics Student Solutions Manual, 10th edn, John Wiley & Sons, ISBN13: 9781118007402
Peer 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 parttime 24week units, where one topic is delivered every two weeks.
Topic 1
Differentiation 1
Domain and range
Limits and Continuity
Derivatives by Definition
Derivatives of Powers of x
Sketching curves
Gradient and Tangent to a Curve
Maxima, Minima and Points of Inflection
Mean Value Theorem
Functions from Derivatives
Topic 2
Differentiation 2
The Product Rule
The Chain Rule
The Quotient Rule
Parametric equations
Derivatives of Other Functions
Higher Derivatives and Graphs of Derivatives
Partial Differentiation
Topic 3
Differentiation 3
Rules of Differentiation/Derivatives Summary
Applications of Derivatives
Rates of Change
Minimum and maximum value problems
ODEs
Initial Value Problem
Application Examples
Second order differential equations
Topic 4
Integration 1
Integration process and Estimation
Substitution Method
Reimann Sums
The Fundamental Theorem of Calculus
Definite Integrals
Standard Integrals
Topic 5
Integration 2
Integration Rules and Techniques
Integration with trigonometric substitutions
Integration with partial fractions
Integration by parts
Double and Triple Integrals
Numerical Integration
Topic 6
Integration 3
Applications of Integration
Areas and Arc Length
Volumes of Solids of Revolution
Centroids
Theorem of Pappus
Second Moments of Area
Parallel Axis Theorem
Perpendicular Axis Theorem
Additional Applications
Topic 7
Analytical Geometry 1
Angles and Lines
Triangles
Quadrilaterals
Polygons
Circle Properties
Irregular Areas
Solid Figures
Straight Lines and Equations
Circle Equations
Parabolas, Ellipses and Hyperbolas
Topic 8
Analytical Geometry 2
Planes and spaces
Other coordinate systems
Vector space
Parametric equations
Spheres
Conic sections
Transformations in space
Geometric intersections
Volumes by integration
Topic 9
Introduction to Probability
Terminology and Definitions
Possible outcomes
Independent and dependent events
Probability Scale
Theoretical Probability
Probability Rules
Factorial
Permutations and Combinations
Pascal’s triangle
Continuous random variables
Probability of occurrence and not occurring
Probability density function
Topic 10
Statistics and Standard Deviation
Data and data averages
Mean
Variance
Elementary probability
Laws of probability
Standard Deviation
Coefficient of Variation
Topic 11
Distributions and Data
Normal Distribution and ZScores
Chebyshev’s Theorem
Histograms
Correlation and Scatterplots
Correlation Coefficient and Regression Equation
Utility and Validity
Topic 12
Sets
Sets and subsets
Union
Intersection
Differences
Product
Algebra
Power set
Exam revision