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/Corequisites  Nil 
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 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:
 Perform simple trigonometric calculations and apply vector principles
Bloom’s Level 3  Perform calculations involving complex numbers
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 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: Multichoice 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  midsemester test Type: Multichoice 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: Multichoice 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: Examination 
Final Week  40%  1  6 
Attendance / Tutorial Participation Example: Presentation, discussion, group work, exercises, selfassessment/reflection, case study analysis, application. 
Continuous  5%   
Prescribed and Recommended readings
Suggested Textbook
 J. Bird, Higher Engineering Mathematics, 9th ed. Routledge, 2021  ISBN: 9780367643737
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 parttime 24week units, where one topic is delivered every two weeks.
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
 Reimann 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
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/vectorcalculator.html
Hardware
 Hardware: N/A