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 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 |

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 |

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 |

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 |

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 |

Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application. |
Continuous | 10% | 1 to 4 |

## Prescribed and Recommended readings

#### 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 *

- 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

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

9. Additional Applications

#### Topic 4

*Introduction of Numerical Methods for Integration and Differentiation*

- The trapezoidal Rule
- Euler’s method
- Euler-Cauchy 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. 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*

- 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 Z-Scores
- 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