BENG401 

Module Name Engineering Mathematics I 
 Module Code BENG401  
Level Four 
 Credits 15 

  

  

Module Description and General Aims 

This module 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 module 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 module 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 Module, students are expected to be able to: 

  1. Perform trigonometric calculations and calculations involving complex numbers and apply vector principles 
    Bloom’s Level 3 
  1. Apply vector principles 
    Bloom’s Level 3 
  1. Apply the principles of differential and integral calculus 
    Bloom’s Level 3 
  1. Evaluate concepts related to sequences, series and sets 
    Bloom’s Level 4 
  1. Comprehend and apply the basics of functions and logarithms 
    Bloom’s Level 3 
  1. Use matrices to solve mathematical problems 
    Bloom’s Level 3 
  1. Conduct basic probability analysis.  
    Bloom’s Level 3 

  

Student Assessment 

Assessment Type When assessed Weighting (% of total module 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: 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  
Attendance / Tutorial Participation 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 module. An overall final module score of 50% or above must be achieved to pass the module 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 

Module Content 

One topic is delivered per contact week. 

Topic 1: Trigonometric Functions and Formulae 

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

Topic 2: Vectors and Scalars 

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

Topic 3: Complex numbers 

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

Topic 4: Differentiation 1 

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

Topic 5: Differentiation 2 

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

Topic 6: Integration 

  1. Integration process and Estimation 
  1. Substitution Method 
  1. Reimann Sums 
  1. The Fundamental Theorem of Calculus 
  1. Definite Integrals 
  1. Standard Integrals 

Topic 7: Sequences and Series 

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

Topic 8: Sets 

  1. Sets and subsets 
  1. Union 
  1. Intersection 
  1. Differences 
  1. Product 
  1. Algebra 
  1. Power set 

Topic 9: Logarithms and exponentials 

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

Topic 10: Matrices, determinants and multivariable functions 1 

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

Topic 11: Matrices, determinants and multivariable functions 2 

  1. Matrix form trigonometric identities 
  1. Cramer’s rule 
  1. Using the inverse matrix to solve simultaneous equations 
  1. Gaussian elimination 

Topic 12: Introduction to Probability 

  1. Terminology and Definitions 
  1. Possible outcomes 
  1. Independent and dependent events 
  1. Probability Scale 
  1. Theoretical Probability 
  1. Probability Rules 
  1. Factorial 
  1. Permutations and Combinations 
  1. Continuous random variables 
  1. Probability of occurrence and not occurring 
  1. Probability density function 
  1. Exam revision 

  

Software/Hardware Used 

Software 

  • Software: Desmos online calculator 
  • Version: N/A 

Hardware 

  • Hardware: N/A