Version  1.0 
Unit Name  Engineering Mathematics 3 
Unit Code  BSC202 
Unit Duration  1 Semester 
Award 
Bachelor of Science (Engineering) Duration 3 years 
Year Level  Two 
Unit Creator / Reviewer  N/A 
Core/Elective:  Core 
Pre/Corequisites  BSC106 
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) Prerecordings / 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 solving differential equations, advanced matrix applications, Laplace, z, Fourier transforms, and conformal mapping. 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 problemsolving viz. modelling, solving the model by applying a suitable mathematical model, and interpreting the results.
Learning Outcomes
 Solving differential equations by assessing and applying various analytical and numerical methods.
Bloom's Level 4  Apply matrices in solving linear systems.
Bloom's Level 3  Apply Laplace, Fourier and z transforms, and evaluate their applications in engineering contexts.
Bloom's Level 4  Conduct conformal mappings and make use of them in engineering.
Bloom's Level 3
Student Assessment
Assessment Type  When assessed  Weighting (% of total unit marks)  Learning Outcomes Assessed 
Assessment 1 Type: Weekly quizzes Example Topics: Topics 2 to 11 Description: Students are required to complete a quiz after viewing the lecture recordings and prior to the live tutorial of each topic. 
Prior to Each Tutorial  10%  All 
Assessment 2 Type: Multichoice test / Group work / Short answer questions / Practical Example Topics: Topics 1 to 4 Students may be required to provide solutions to problems on differential equations and matrices to show evidence of their understanding of the concepts involved or complete a practical. 
Due after Topic 4  20%  1, 2 
Assessment 3 Type: Multichoice test / Group work / Short answer questions / Practical Example Topic: Topics 5 to 8 Students may be required to provide solutions to problems related to Laplace, ztransforms, and Fourier series. 
Due after Topic 8  25%  3 
Assessment 4 Type: Examination An examination where the student will complete a quiz with MCQ type answers and perform calculations and provide solutions to mathematical problems to be completed in 3 hours. 
Final Week  40%  1 to 4 
Attendance / Tutorial Participation Description: Presentation, discussion, group work, exercises, selfassessment/reflection, case study analysis, application. 
Continuous  5%   
Overall Requirements: Students must achieve a result of 40% 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
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, 7th Edition. Routledge, 2014. ISBN13: 9780415662826
Reference
 A. Kreyszig, Advanced Engineering Mathematics Student Solutions Manual, 10th Edition. John Wiley & Sons, 2012. ISBN13: 9781118007402
Journal, website
 http://www.elsevier.com/physicalsciences/mathematics/mathematicsjournals
 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
Differential Equations 1
 Definition
 The Solutions of equations of some simple forms
 Homegeneous firstorder differential equations and their solutions
 Linear firstorder differential equations and their solutions
Topic 2
Differential Equations 2
 Secondorder differential equations
 The Solutions of homogeneous secondorder differential equations
 The Solutions of nonhomogeneous secondorder differential equations
 An introduction to partial differential equations
Topic 3
Differential Equations 3
 Power series Solutions
 Frobenius Solutions
 Euler Lagrange equation
 Lagrangian equation
Topic 4
Applications of Matrices
 Eigenvalues and eigenvectors
 Diagonalization
 Special Matrices
 Linear systems and their solutions using matrices
Topic 5
Laplace Transforms 1
 Laplace Transform and inverse Laplace Transforms
 Laplace Transforms of Elementary functions
 Transforms of derivatives and integrals
 Initial and final value theorems
 Laplace transform in a solution of initial value problems
Topic 6
Laplace Transforms 2
 Unit step function
 Dirac's delta function
 Shifting theorems
 Convolution
 Differential equations with polynomial coefficients
Topic 7
ztransforms
 Definition
 Some properties of ztransforms
 Inverse ztransforms
 Using ztransforms to solve difference equations
Topic 8
Fourier Series, Integrals and Transforms 1
 Fourier series
 Functions having points of discontinuity
 Even and Odd functions
 Convergence of Fourier series
Topic 9
Fourier Series, Integrals and Transforms 2
 Fourier cosine and sine series
 Integration and differentiation of Fourier series
 Phase angle form of Fourier series
 Complex Fourier series
Topic 10
Fourier Series, Integrals and Transforms 3
 Fourier integral
 Complex Fourier integral
 Fourier transform
 Discrete and Fast Fourier transforms
 Fourier Transform in signal analysis using engineering tools
Topic 11
Conformal Mappings
 Definition
 Bilinear transformation
 Special bilinear transformations
 Construction of conformal mappings
Topic 12
Exam Revision
 Mathematical induction proofs
 Unit revision
Software/Hardware Used
Software

Software: Python Jupyter Notebook or Google Colab

Version: N/A

Instructions: N/A

Additional resources or files: N/A
Hardware
 N/A