Version | 1.0 |

Unit Name | Engineering Mathematics I |

Unit Code | BSC101 |

Unit Duration | 1 Semester |

Award |
Bachelor of Science (Engineering) Duration 3 years |

Year Level | One |

Unit Creator / Reviewer | N/A |

Common/Elective: | Common |

Pre/Co-requisites | Nil |

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) 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 introduces the student to core mathematical concepts, processes and techniques necessary to support subsequent studies in Engineering. These concepts include, but are not limited to, the properties and engineering applications of linear, quadratic, logarithmic and exponential functions. The unit commences with fundamental concepts of trigonometry, vectors and complex numbers, and goes on to cover basic differential and integral calculus. It then moves to varied subjects including sequences, series, sets, logarithms and exponentials. It rounds off with using matrices to solve equations, followed by an introduction of probability. The topics in this unit are structured in such a manner that the student will be able to solve problems related to engineering applications by using these mathematical techniques.

## Learning Outcomes

- Perform trigonometric calculations and calculations involving complex numbers and apply vector
principles

Bloom's Level 3 - Apply vector principles

Bloom's Level 3 - Apply the principles of differential and integral calculus

Bloom's Level 3 - Evaluate concepts related to sequences, series and sets

Bloom's Level 4 - Comprehend and apply the basics of functions and logarithms

Bloom's Level 3 - Use matrices to solve mathematical problems

Bloom's Level 3 - Conduct basic probability analysis.

Bloom's Level 3

## Student assessment

Assessment Type | When assessed | Weighting (% of total unit marks) | Learning Outcomes Assessed |

Type: Weekly quizzes Topics: Topics 2 to 11 |
Weekly | 10% | 1 to 6 |

Type: Multi-choice test / Extended answer / Short answer questions Example Topics: Topics 1 to 4 Students may complete a quiz with MCQ type answers or solve some simple problems or solve problems using software. |
After Topic 4 | 20% | 1, 2, 3 |

Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Topics 5 to 8 |
After Topic 8 | 25% | 3, 4 |

Type: Examination Example Topic: All topics with an emphasis on Logarithms and Matrices 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 - 7 |

Example: Presentation, discussion, group work, exercises, self-assessment/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 achieved to pass the unit once all assessment, including the exam, has been completed.

## Prescribed and Recommended Readings

#### Suggested Textbook

- J. Bird,
*Higher Engineering Mathematics*, 9th ed. Routledge, 2021 - ISBN: 978-0367643737

#### Reference Materials

- Peer-reviewed Journals
- Knovel library: http://app.knovel.com
- IDC Technologies publications
- Other material and online collections as advised during lectures

## Unit Content

*One topic is delivered per contact week. *

#### Topic 1

*Trigonometric Functions and Formulae*

- Trigonometric graphs
- Period, amplitude, cycle, frequency
- Lag and lead (phase displacement)
- Trigonometric identities and formulae
- Cartesian and polar coordinates

#### Topic 2

*Vectors and Scalars*

- Vectors and Scalars
- Vector notation
- Resolving vectors
- Relative velocity
- Vector Definitions and Components
- Operations with Vectors
- Vector Applications
- Laws of Sines and Cosines

#### Topic 3

*Complex numbers*

- Imaginary numbers
- Arithmetic of complex numbers
- The Argand diagram and polar form of a complex number
- The exponential form of a complex number
- De Moivre's theorem
- Solving equations and finding roots of complex numbers
- Phasors

#### Topic 4

*Differentiation 1*

- Domain and range
- Limits and Continuity
- Derivatives by Definition
- Derivatives of Powers of x
- Sketching curves
- Gradient and Tangent to a Curve
- Maxima, Minima and Points of Inflection
- Mean Value Theorem
- Functions from Derivatives

#### Topic 5

*Differentiation 2*

- The Product Rule
- The Chain Rule
- The Quotient Rule
- Parametric equations
- Derivatives of Other Functions
- Higher Derivatives and Graphs of Derivatives
- Partial Differentiation

#### Topic 6

*Integration*

- Integration process and Estimation
- Substitution Method
- Riemann Sums
- The Fundamental Theorem of Calculus
- Definite Integrals
- Standard Integrals

#### Topic 7

*Sequences and Series*

- Sequences and Series
- Sums vs sequences
- Simple series (progression)
- Arithmetic progression
- Geometric progression
- Pascal’s triangle
- Permutation and combination
- Binomial theorem
- Graphing progressions
- Power series

#### Topic 8

*Sets*

- Sets and subsets
- Union
- Intersection
- Differences
- Product
- Algebra
- Power set

#### Topic 9

*Logarithms and exponentials*

- Logarithmic expression
- Laws of logarithms
- Natural (Naperian, hyperbolic) logarithms
- Exponential functions
- Graphing exponential functions
- Logarithmic Equations
- Application of Logarithms and exponential functions
- Change of base

#### Topic 10

*Matrices, determinants and multivariable functions 1*

- Introduction to matrices
- Multiplication of matrices
- Determinants
- The inverse of a matrix
- Multivariable functions
- Multivariable calculus
- Vector valued functions
- Parameterization

#### Topic 11

*Matrices, determinants and multivariable functions 2*

- Matrix form trigonometric identities
- Cramer's rule
- Using the inverse matrix to solve simultaneous equations
- Gaussian elimination

#### Topic 12

*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
- Exam revision

## Software/Hardware Used

#### Software

- Software: Desmos online calculator
- Version: N/A
- Instructions: https://www.desmos.com/scientific
- Additional resources or files: https://www.mathsisfun.com/algebra/vector-calculator.html

#### Hardware

- Hardware: N/A