Version | 1.1 |
Unit Name | Engineering Mathematics 2 |
Unit Code | BSC106 |
Unit Duration | 1 Semester |
Award |
Bachelor of Science (Engineering) Duration 3 years |
Year Level | One |
Unit Creator / Reviewer | N/A |
Core/Elective: | Core |
Pre/Co-requisites | BSC101 |
Credit Points | 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 Tutorial – 1.5 hours Guided labs / Group work / Assessments – 2 hours Personal Study recommended – 5 hours |
Unit Description and General Aims
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 including vector calculus and complex analysis. 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. Further, 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 calculus and make use of numerical methods.
Bloom's Level 3 - Evaluate the concepts of analytical geometry
Bloom's Level 4 - Acquire knowledge of vector spaces and perform vector calculus by applying various theorems.
Bloom's Level 4 - Evaluate complex integration
Bloom's Level 3 - Apply concepts related to statistics and probability
Bloom's Level 3
Student assessment
Assessment Type | When assessed | Weighting (% of total unit marks) | Learning Outcomes Assessed |
Assessment 1 Type: Weekly quizzes Topics: Topics 2 to 11 |
Weekly | 10% | All |
Assessment 2 Type: Multi-choice test / Extended answer questions / Short answer questions Example Topic: Topics 1 to 4 |
Due after Topic 4 | 25% | 1 |
Assessment 3 Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Topics 5 to 8 Students may complete a quiz with MCQ type answers or solve some simple problems or use software to complete a practical. |
Due after Topic 8 | 25% | 2 and 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% | All |
Overall Requirements: Students must achieve a result of 50% or above in the exam itself to pass the exam and must pass the exam to be able to pass the unit. An overall final unit score of 50% or above must be achieved to pass the unit once all assessment, including the exam, has been completed.
Prescribed and Recommended Readings
Suggested Textbooks
- J. Bird, Higher Engineering Mathematics, 9th Edition. Routledge, 2021 - ISBN-13: 978-0367643737
Reference Materials
- P. O'Neil, Advanced Engineering Mathematics, SI Edition, 8th Edition. Cengage, 2018. ISBN 9781337274524
- Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, John Wiley & Sons, ISBN-13: 978-0470458365.
- Knovel library: http://app.knovel.com
- IDC Technologies publications
- Other material and online collections as advised during the lectures and in the Reading Guide.
Unit Content
Topic 1
Differentiation
- 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 2
Integration 1
- Integration Rules and Techniques
- Integration with trigonometric substitutions
- Integration with partial fractions
- Integration by parts
- Double and Triple Integrals
Topic 3
Integration 2
- 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 4
Numerical Methods
- The trapezoidal Rule, Mid-ordinate Rule, and Simpson's Rule
- Euler’s method, Euler-Cauchy method and the Runge-Kutta method
- Solution of equations by iteration
Topic 5
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 6
Analytical Geometry 2
- Planes and spaces
- Other coordinate systems
- Parametric equations
- Spheres
- Conic sections
- Transformations in space
- Geometric intersections
- Volumes by integration
Topic 7
Vector Spaces
- Linear combination and spans
- Linear dependence and independence
- Subspaces
- Vector dot and cross product
- Null space and column space
- Linear transformations
Topic 8
Vector Differential Calculus
- Vectors in 2−space and 3−space
- Velocity, acceleration and Curvature
- Curves, Arc length
- Streamlines
- Gradient of a scalar field and directional derivatives
- Divergence and curl of a vector field
Topic 9
Vector Integral Calculus
- Path independence of line integrals
- Green's Theorem in the plane
- Independence of path
- Surface integrals
- Triple integrals, Divergence theorem of Gauss
- Stokes' theorem
Topic 10
Complex Integration
- Line integral in the complex plane
- Properties of complex integrals
- Cauchy's integral theorem
- Consequences of Cauchy’s theorem
- Deformation theorem
- Cauchy's integral formula
Topic 11
Statistics and Standard Deviation
- Data and data averages
- Mean
- Variance
- Elementary probability
- Laws of probability
- Standard Deviation
- Coefficient of Variation
Topic 12
Distributions and Data
- Normal Distribution and Z-Scores
- Chebyshev’s Theorem
- Histograms
- Correlation and Scatterplots
- Correlation Coefficient and Regression Equation
- Utility and Validity
Software/Hardware Used
Software
- Software: N/A
- Version: N/A
- Instructions: N/A
- Additional resources or files: N/A
Hardware
- N/A