Last Updated S012019

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 BSC104C
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 4

3. Evaluate complex integration

    Bloom’s Level 4

4. Use Conformal mapping for solving engineering problems

    Bloom’s Level 6

5. Find solutions for linear systems using numerical methods

    Bloom’s Level 6

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, numerical methods

Questions predominantly related to conformal mapping, interpolation, numeric integration and differentiation, tridiagonalization and QR− factorization

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

O’Neil, J 2003, Advanced Engineering Mathematics, 5th Edn, ISBN 0-534-40077-9

Second Textbook

Bird, J 2014, Higher Engineering Mathematics, 7th Edn, Routledge, ISBN-13: 978-0415662826

Reference

Kreyszig, A 2012, Advanced Engineering Mathematics Student Solutions Manual, 10th edn, John Wiley $ Sons, 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. Linear Regression
3. Numeric integration

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