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/Co-requisites BSC101C
 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 hoursTutorial – 1.5 hoursGuided labs / Group work / Assessments – 2 hoursPersonal 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:

1. Apply the principles of differential and integral calculus
Bloom’s Level 3
2. Derive equations from graphs of trigonometric functions
Bloom’s Level 4
3. Evaluate the concepts of analytical geometry
Bloom’s Level 4
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: Multi-choice 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 - mid-semester test Type: Multi-choice 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 25% 1, 2 Assessment 3 Type: Multi-choice 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 15% 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 Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application. Continuous 10% 1 to 4

#### Suggested Textbook

• Bird, J. Engineering Mathematics, 7th edn, John Wiley & Sons, ISBN-13: 978-0415662802.

#### Reference Materials

• Bird, J. Engineering Mathematics, 5th edn, John Wiley & Sons, ISBN-978-0-75-068555-9
• Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, John Wiley & Sons, ISBN-13: 978-0470458365.
• 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

1. Rules of Differentiation/Derivatives Summary
2. Applications of Derivatives
3. Rates of Change
4. Minimum and maximum value problems
5. ODEs
6. Initial Value Problem
7. Application Examples
8. 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
6. Numerical Integration

#### 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

#### Topic 4

Introduction of Numerical Methods for Integration and Differentiation

1. The trapezoidal Rule
2. Euler’s method
3. Euler-Cauchy method
4. Comparisons between numerical and analytical methods

#### Topic 5

Analytical Geometry 1

1. Angles and Lines
2. Triangles
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. Vector space
4. Parametric equations
5. Spheres
6. Conic sections
7. Transformations in space
8. Geometric intersections
9. Volumes by integration

#### Topic 7

Vector Spaces

1. Linear combination and spans
2. Linear dependence and independence
3. Subspaces
4. Vector dot and cross product
5. Null space and column space
6. Linear transformations

#### Topic 8

Introduction to Probability

1. Terminology and Definitions
2. Possible outcomes
3. Independent and dependent events
4. Probability Scale
5. Theoretical Probability
6. Probability Rules
7. Factorial
8. Permutations and Combinations
9. Continuous random variables
10. Probability of occurrence and not occurring
11. Probability density function

#### Topic 9

Statistics and Standard Deviation

1. Data and data averages
2. Mean
3. Variance
4. Elementary probability
5. Laws of probability
6. Standard Deviation
7. Coefficient of Variation

#### Topic 10

Distributions and Data

1.  Normal Distribution and Z-Scores
2. Chebyshev’s Theorem
3. Histograms
4. Correlation and Scatterplots
5. Correlation Coefficient and the Regression Equation
6. Utility and Validity

#### Topic 11

Mathematical Induction Proofs

1. Notation
2. Axioms
3. Sums, Series and Sequences
4. Binomial theorem
5. De Moivre theorem
6. Taylor series
7. Inequalities
8. Convergence and continuity
9. Divisibility and geometry

#### Topic 12

1. Strong induction
2. Smallest counterexample
3. Exam revision / Dummy practice exam

## Software/Hardware Used

#### Software

• Software: N/A

• Version: N/A

• Instructions:  N/A

• Additional resources or files: N/A

• N/A