Last Updated S022021

### BSC101C

 Unit Name Engineering Mathematics I
 Unit Code BSC101C
 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 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; 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 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 linear equations and goes on to cover varied subjects including inequalities, functions, trigonometry, sequences, series, variation, ratio, proportion, algebraic functions, trigonometric ratios, trigonometric functions and applications. It rounds off with an introduction to differentiation and integration, followed by vectors, complex numbers and matrices. 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

On successful completion of this Unit, students are expected to be able to:

1. Perform simple trigonometric calculations and apply vector principles
Bloom’s Level 3
2. Perform calculations involving complex numbers
Bloom’s Level 3
3. Apply the principles of differential and integral calculus
Bloom’s Level 3
4. Evaluate concepts related to sequences, series and sets
Bloom’s Level 4
5. Comprehend and apply the basics of functions and logarithms
Bloom’s Level 3
6. Use matrices and determinants to solve mathematical problems
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 Topics: Trigonometric Functions, Vectors and Scalars, Complex Numbers Students may be asked to provide solutions to simple problems on various topics. After Topic 3 10% 1, 2 Assessment 2 - mid-semester test Type: Multi-choice test / Extended answer / Short answer questions Example Topics: Topics 1 to 6 Students may complete a quiz with MCQ type answers or solve some simple problems or solve problems using software. After Topic 6 30% 1, 2, 3 Assessment 3 Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Short problems on basic Integration and Sequences and Series After Topic 9 15% 3, 4, 5 Assessment 4 Type: ExaminationExample Topic: All topics with an emphasis on Logarithms and MatricesAn examination with a mix of detailed report type questions and/or simple numerical problems to be completed in 3 hours Final Week 40% 1 - 6 Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application. Continuous 5% -

#### 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, with the exception of part-time 24-week units, where one topic is delivered every two weeks.

#### Topic 1

Trigonometric Functions and Formulae

1. Trigonometric graphs
2. Period, amplitude, cycle, frequency
3. Lag and lead (phase displacement)
4. Trigonometric identities and formulae
5. Cartesian and polar coordinates

#### Topic 2

Vectors and Scalars

1. Vectors and Scalars
2. Vector notation
3. Resolving vectors
4. Relative velocity
5. Vector Definitions and Components
6. Operations with Vectors
7. Vector Applications
8. Laws of Sines and Cosines

#### Topic 3

Complex numbers

1. Imaginary numbers
2. Arithmetic of complex numbers
3. The Argand diagram and polar form of a complex number
4. The exponential form of a complex number
5. De Moivre's theorem
6. Solving equations and finding roots of complex numbers
7. Phasors

#### Topic 4

Differentiation 1

1. Domain and range
2. Limits and Continuity
3. Derivatives by Definition
4. Derivatives of Powers of x
5. Sketching curves
6. Gradient and Tangent to a Curve
7. Maxima, Minima and Points of Inflection
8. Mean Value Theorem
9. Functions from Derivatives

#### Topic 5

Differentiation 2

1. The Product Rule
2. The Chain Rule
3. The Quotient Rule
4. Parametric equations
5. Derivatives of Other Functions
6. Higher Derivatives and Graphs of Derivatives
7. Partial Differentiation

#### Topic 6

Integration

1. Integration process and Estimation
2. Substitution Method
3. Reimann Sums
4. The Fundamental Theorem of Calculus
5. Definite Integrals
6. Standard Integrals

#### Topic 7

Sequences and Series

1. Sequences and Series
2. Sums vs sequences
3. Simple series (progression)
4. Arithmetic progression
5. Geometric progression
6. Pascal’s triangle
7. Permutation and combination
8. Binomial theorem
9. Graphing progressions
10. Power series

#### Topic 8

Sets

1. Sets and subsets
2. Union
3. Intersection
4. Differences
5. Product
6. Algebra
7. Power set

#### Topic 9

Logarithms and exponentials

1. Logarithmic expression
2. Laws of logarithms
3. Natural (Naperian, hyperbolic) logarithms
4. Exponential functions
5. Graphing exponential functions
6. Logarithmic Equations
7. Application of Logarithms and exponential functions
8. Change of base

#### Topic 10

Matrices, determinants and multivariable functions 1

1. Introduction to matrices
2. Multiplication of matrices
3. Determinants
4. The inverse of a matrix
5. Multivariable functions
6. Multivariable calculus
7. Vector valued functions
8. Parameterization

#### Topic 11

Matrices, determinants and multivariable functions 2

1. Matrix form trigonometric identities
2. Cramer's rule
3. Using the inverse matrix to solve simultaneous equations
4. Gaussian elimination

Exam revision

## Software/Hardware Used

#### Hardware

• Hardware: N/A