Last Updated  S012019 
BSC104C
Unit Name  Engineering Mathematics 2 
Unit Code  BSC104C 
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  BSC101C 
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; 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. 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. This is followed by 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 differential and integral calculus
Bloom’s Level 3  Derive equations from graphs of trigonometric functions
Bloom’s Level 4  Evaluate the concepts of analytical geometry
Bloom’s Level 4  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: Multichoice test / Group work / Short answer questions Example Topic: Differentiation basics 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, 2 
Assessment 2  midsemester test Type: Multichoice test / Extended answer questions/ Short answer questions Example Topic: Topics 1 to 6 Students may be asked to provide solutions to simple problems on various topics. 
Due after Topic 6 
20%  1, 2 
Assessment 3 Type: Multichoice test / Group work / Short answer questions / Practical Example Topic: Analytical geometry Students may complete a quiz with MCQ type answers or solve some simple problems or use software to complete a practical. 
Due after Topic 9 
20%  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%  1 to 4 
Tutorial attendance + Weekly homework 5% for tutorial attendance and 5% for weekly homework submission. Weekly homework will be discussed and assigned during live tutorials. 
Continuous  10%  1 to 4 
Prescribed and Recommended readings
Suggested Textbook
 Bird, J. Higher Engineering Mathematics, 7th edn, John Wiley & Sons, ISBN13: 9780415662802.
Reference Materials
 Bird, J. Engineering Mathematics, 5th edn, John Wiley & Sons, ISBN9780750685559
 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
1. Integration Rules and Techniques
2. Integration with trigonometric substitutions
3. Integration with partial fractions
4. Integration by parts
5. Double and Triple Integrals
Topic 3
Integration 2
1. Applications of Integration
2. Areas and Arc Length
3. Volumes of Solids of Revolution
4. Centroids
5. Theorem of Pappus
6. Second Moments of Area
7. Parallel Axis Theorem
8. Perpendicular Axis Theorem
9. Additional Applications
Topic 4
Introduction of Numerical Methods for Integration and Differentiation
 The trapezoidal Rule, Midordinate Rule, and Simpson's Rule
 Euler’s method
 EulerCauchy method
 Comparisons between numerical and analytical methods
Topic 5
Analytical Geometry 1
1. Angles and Lines
2. Triangles
3. Quadrilaterals
4. Polygons
5. Circle Properties
6. Irregular Areas
7. Solid Figures
8. Straight Lines and Equations
9. Circle Equations
10. Parabolas, Ellipses and Hyperbolas
Topic 6
Analytical Geometry 2
1. Planes and spaces
2. Other coordinate systems
3. Parametric equations
4. Spheres
5. Conic sections
6. Transformations in space
7. Geometric intersections
8. 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
Introduction to Probability
 Terminology and Definitions
 Possible outcomes
 Independent and dependent events
 Probability Scale
 Theoretical Probability
 Probability Rules
 Factorial
 Permutations and Combinations
 Continuous random variables
 Probability of occurrence and not occurring
 Probability density function
Topic 9
Statistics and Standard Deviation
 Data and data averages
 Mean
 Variance
 Elementary probability
 Laws of probability
 Standard Deviation
 Coefficient of Variation
Topic 10
Distributions and Data
 Normal Distribution and ZScores
 Chebyshev’s Theorem
 Histograms
 Correlation and Scatterplots
 Correlation Coefficient and the Regression Equation
 Utility and Validity
Topic 11
Mathematical Induction Proofs
 Notation
 Axioms
 Sums, Series and Sequences
 Binomial theorem
 De Moivre theorem
 Taylor series
 Inequalities
 Convergence and continuity
 Divisibility and geometry
Topic 12
 Strong induction
 Smallest counterexample
 Exam revision / Dummy practice exam
Software/Hardware Used
Software

Software: N/A

Version: N/A

Instructions: N/A

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