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/Co-requisites BSC101C 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.

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:

1. Apply the principles of differential and integral calculus

2. Derive equations from graphs of trigonometric functions

3. Evaluate the concepts of analytical geometry

4. Apply concepts related to statistics and probability

Professional Development

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

1. Fostering personal and professional skills and attributes in order to:

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

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

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

4. Develop initiative and engagement in lifelong learning and professional development.

5. Enhance collaboration outcomes and performance in dynamic team roles.

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

7. Professionally utilise and manage information.

8. Enhance technologist literacy and apply contextualised technologist skills.

2. Enhance investigatory and research capabilities in order to:

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

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

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

4. Solve basic and open-ended engineering technologist problems.

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

3. Develop engineering application abilities in order to:

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

2. Apply engineering technologist techniques, tool and resources.

3. Apply systematic technologist synthesis and design processes.

4. 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 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.

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 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  1.2  1.3  1.4   1.5  1.6  2.1    2.2   2.3    2.4  3.1  3.2    3.3  3.4   3.5  3.6  Unit Learning Outcomes LO1    LO2    LO3    LO4   

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 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: Multi-choice 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: Multi-choice 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, self-assessment/reflection, case study analysis, application. Continuous 5% 1 to 4

Suggested Textbook

• Bird, J. Engineering Mathematics, 7th edn, John Wiley & Sons, ISBN-13: 978- 0415662802.

Reference Materials

• Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, John Wiley & Sons, ISBN-13: 978-0470458365.

• Kreyszig, A 2012, Advanced Engineering Mathematics Student Solutions Manual, 10th edn, John Wiley & Sons, ISBN-13: 978-1118007402

• 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 part-time 24-week units, where one topic is delivered every two weeks.

Topic 1

Differentiation 1

1. Domain and range

2. Limits and Continuity

3. Derivatives by Definition

4. Derivatives of Powers of x

5. Sketching curves

6. Gradient and Tangent to a Curve

7. Maxima, Minima and Points of Inflection

8. Mean Value Theorem

9. Functions from Derivatives

Topic 2

Differentiation 2

1. The Product Rule

2. The Chain Rule

3. The Quotient Rule

4. Parametric equations

5. Derivatives of Other Functions

6. Higher Derivatives and Graphs of Derivatives

7. Partial Differentiation

Topic 3

Differentiation 3

1. Rules of Differentiation/Derivatives Summary

2. Applications of Derivatives

3. Rates of Change

4. Minimum and maximum value problems

5. ODEs

6. Initial Value Problem

7. Application Examples

8. Second order differential equations

Topic 4

Integration 1

1. Integration process and Estimation

2. Substitution Method

3. Reimann Sums

4. The Fundamental Theorem of Calculus

5. Definite Integrals

6. Standard Integrals

Topic 5

Integration 2

1. Integration Rules and Techniques

2. Integration with trigonometric substitutions

3. Integration with partial fractions

4. Integration by parts

1. Double and Triple Integrals

2. Numerical Integration

Topic 6

Integration 3

1. Applications of Integration

2. Areas and Arc Length

3. Volumes of Solids of Revolution

4. Centroids

5. Theorem of Pappus

6. Second Moments of Area

7. Parallel Axis Theorem

8. Perpendicular Axis Theorem

Topic 7

Analytical Geometry 1

1. Angles and Lines

2. Triangles

4. Polygons

5. Circle Properties

6. Irregular Areas

7. Solid Figures

8. Straight Lines and Equations

9. Circle Equations

10. Parabolas, Ellipses and Hyperbolas

Topic 8

Analytical Geometry 2

1. Planes and spaces

2. Other coordinate systems

3. Vector space

4. Parametric equations

5. Spheres

6. Conic sections

7. Transformations in space

8. Geometric intersections

9. Volumes by integration

Topic 9

Introduction to Probability

1. Terminology and Definitions

2. Possible outcomes

3. Independent and dependent events

4. Probability Scale

5. Theoretical Probability

6. Probability Rules

7. Factorial

8. Permutations and Combinations

9. Pascal’s triangle

10. Continuous random variables

11. Probability of occurrence and not occurring

12. Probability density function

Topic 10

Statistics and Standard Deviation

1. Data and data averages

2. Mean

3. Variance

4. Elementary probability

5. Laws of probability

6. Standard Deviation

7. Coefficient of Variation

Topic 11

Distributions and Data

1. Normal Distribution and Z-Scores

2. Chebyshev’s Theorem

3. Histograms

4. Correlation and Scatterplots

5. Correlation Coefficient and Regression Equation

6. Utility and Validity

Topic 12

Sets

1. Sets and subsets

2. Union

3. Intersection

4. Differences

5. Product

6. Algebra

7. Power set

8. Exam revision