Version  1.0 
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/Corequisites  BSC101 
Credit Points  3 
Mode of Delivery  Online or oncampus. 
Unit Workload  (Total student workload including “contact hours” = 10 hours per week; 5 hours per week for 24 week delivery) 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 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: Multichoice test / Extended answer questions / Short answer questions Example Topic: Topics 1 to 4 
Due after Topic 4  20%  1 
Assessment 3 Type: Multichoice 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 
Tutorial attendance + Participation

Continuous  5%  All 
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 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  ISBN13: 9780367643737
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, ISBN13: 9780470458365.
 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, Midordinate Rule, and Simpson's Rule
 Euler’s method, EulerCauchy method and the RungeKutta 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 ZScores
 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