| Last Updated | S022020 |
BSC202C
| Unit Name | Engineering Mathematics 3 |
| Unit Code | BSC202C |
| Unit Duration | 1 Semester |
| Award |
Bachelor of Science (Engineering) Duration 3 years |
| Year Level | Two |
| Unit Creator / Reviewer |
| Core/Elective: | Core |
| Pre/Co-requisites | BSC106 |
| 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 Tutorial – 1.5 hours Guided labs / Group work / Assessments – 2 hours Personal Study recommended – 5 hours |
Unit Description and General Aims
This unit builds on the fundamentals discussed in Mathematics units 1 and 2 by providing the student with a sound understanding of advanced engineering mathematical concepts involving vector calculus, Laplace and Fourier transform, complex numeric functions and statistics. Students will be able to solve problems related to engineering applications by applying these techniques. The topics in the unit are so structured that the student is able to achieve proficiency in all three phases of problem-solving viz. modelling, solving the model by applying a suitable mathematical model, and interpreting the results.
Learning Outcomes
On successful completion of this Unit, students are expected to be able to:
1. Apply Laplace and Fourier transforms
Bloom’s Level 3
2. Acquire knowledge of vector calculus concepts needed to solve problems across all engineering disciplines
Bloom’s Level 3
3. Evaluate complex integration
Bloom’s Level 3
4. Use Conformal mapping for solving engineering problems
Bloom’s Level 3
5. Find solutions for linear systems using numerical methods
Bloom’s Level 4
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: Laplace transforms, Fourier series Students may complete a quiz with MCQ type answers and solve some simple equations to demonstrate a good understanding of the fundamental concepts. |
Due after Topic 3 | 10% | 1 |
|
Assessment 2 - mid-semester test Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Fourier transforms, Fourier integral, FFT Students will provide solutions to problems on vector differential and integral calculus and complex integration to show evidence of their understanding of the concepts involved or complete a practical. |
Due after Topic 6 | 30% | 1, 2 |
|
Assessment 3 Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Vector differential and integral calculus Students will provide solutions to simple problems related to conformal mapping and use numeric methods to solve problems |
Due after Topic 9 | 10% | 2, 3, 4 |
|
Assessment 4 Type: Examination Example Topic: All topics An examination where the student will complete a quiz with MCQ type answers and perform simple calculations and provide solutions to mathematical problems to be completed in 3 hours |
Final Week | 45% | 1 to 5 |
|
Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application. |
Continuous | 5% | 1 to 5 |
Prescribed and Recommended Readings
Textbook
P. O'Neil, Advanced Engineering Mathematics, SI Edition, 8th Edition. Cengage, 2018. ISBN 9781337274524
Second Textbook
J. Bird, Higher Engineering Mathematics, 9th Edition. Routledge, 2021. ISBN: 9780367643737
Reference
A. Kreyszig, Advanced Engineering Mathematics Student Solutions Manual, 10th Edition. John Wiley & Sons, 2012. ISBN-13: 978-1118007402
Journal, website
http://www.elsevier.com/physical-sciences/mathematics/mathematics-journals
Notes and Reference texts
Open Textbook Library: http://open.umn.edu/opentextbooks/
Knovel library: http://app.knovel.com
IDC Technologies
Other material advised during the lectures
Unit Content
Topic 1
Laplace Transforms 1
1. Laplace Transform and inverse
2. Elementary functions
3. Transforms of derivatives ad integrals
4. Initial and final value theorems
5. Laplace transform in a solution of initial value problems
Topic 2
Laplace Transforms 2
1. Unit step function
2. Short impulses, Dirac's delta function
3. Shifting theorems
4. Convolution
5. Differential equations with polynomial coefficients
6. Transfer function
Topic 3
Fourier Series, Integrals and Transforms 1
1. Fourier series
2. Functions having points of discontinuity
3. Convergence of Fourier series
4. Even and Odd functions
Topic 4
Fourier Series, Integrals and Transforms 2
1. Fourier cosine and sine series
2. Integration and differentiation of Fourier series
3. Phase angle form of Fourier series
4. Complex Fourier series
Topic 5
Fourier Series, Integrals and Transforms 3
1. Fourier integral
2. Fourier cosine and sine integral
3. Complex Fourier integral
4. Fourier transform
5. Fourier Cosine and Sine Transforms
6. Finite Fourier cosine and sine transform
7. Discrete and Fast Fourier transforms
8. Frequency response of a system
Topic 6
Vector Differential Calculus
1. Vectors in 2−space and 3−space
2. Velocity, acceleration and Curvature
3. Curves, Arc length
4. Streamlines
5. Gradient of a scalar field and directional derivatives
6. Divergence and curl of a vector field
Topic 7
Vector Integral Calculus
1. Path independence of line integrals
2. Green's Theorem in the plane
3. Independence of path
4. Surface integrals
5. Triple integrals, Divergence theorem of Gauss
6. Stokes' theorem
Topic 8
Complex Integration
1. Line integral in the complex plane
2. Properties of complex integrals
3. Cauchy's integral theorem
4. Consequences of Cauchy’s theorem
5. Deformation theorem
6. Cauchy's integral formula
Topic 9
Conformal Mapping
1. Functions as mapping
2. Linear fractional transformation
3. Special linear fractional transformations
4. Conformal mapping by other functions
5. Modelling and use of conformal mapping
Topic 10
Numerical Methods 1
1. Solution of the equation by iteration
2. Regression
3. Numeric integration review
Topic 11
Numerical Methods 2
1. Eigenvalues and eigenvectors
2. Matrix Eigenvalues
3. Tridiagonalization
4. Orthogonal & symmetric matrices
Topic 12
Numerical Methods 3
1. Numeric methods for First−Order ODEs
2. Power series methods of solving ODEs
3. Exam revision
Software/Hardware Used
Software
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Software: Python Jupyter Notebook or Google Colab
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Version: N/A
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Instructions: N/A
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Additional resources or files: N/A
Hardware
- N/A
