Last Updated S012019

BSC101C

Unit Name Engineering Mathematics I
Unit Code BSC101C
Unit Duration 1 Term (2 Terms for 24 week delivery)
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 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:

  1. Detail mathematical concepts related to linear and absolute value inequalities
    Bloom’s Level 3
  2. Solve linear and quadratic equations
    Bloom’s Level 3
  3. Comprehend and apply the basics of functions and logarithms
    Bloom’s Level 3
  4. Perform simple trigonometric calculations
    Bloom’s Level 3
  5. Evaluate concepts related to sequences, series, variation, ratio and proportion
    Bloom’s Level 4
  6. Solve algebraic equations
    Bloom’s Level 3
  7. Use trigonometric ratios to solve mathematical problems
    Bloom’s Level 3
  8. Apply vector principles
    Bloom’s Level 3
  9. Perform calculations involving complex numbers
    Bloom’s Level 3
  10. Use matrices and determinants to solve mathematical problems
    Bloom’s Level 3
  11. Apply the principles of differential and integral calculus
    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, 4, 6, 7, 8

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% 9, 11

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% 5, 11

Assessment 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 - 11

Attendance / Tutorial Participation

Example: Presentation, discussion, group work, exercises, self-assessment/reflection, case study analysis, application.

Continuous 5% 1 - 11

 

Prescribed and Recommended readings

Suggested Textbook

  • J. Bird, Higher Engineering Mathematics, 7th ed. John Wiley & Sons, 2010. ISBN-13: 978-0415662802.

 

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

 

Topic 12

Exam revision