The Basics

It is assumed that students taking Engineering Mathematics II already have some basic mathematical skills.

However, skills get rusty, and what we have learnt sometimes just disappears!

The material here should be used to review and revise your basic mathematical skills.

The material here was provided by Tony Hobson, formerly of School of Mathematical and Information Sciences, Coventry University. We thank him for making it available.

There is a full set of material covering a wide range of engineering mathematics at the "Just the Maths" web site at www.mis.coventry.ac.uk/jtm (this link appears broken). You may find parts of it useful for this course, or other engineering courses.

All material is provided as PDF files.

• UNIT 1.1 - ALGEBRA 1 - INTRODUCTION TO ALGEBRA
  • The Language of Algebra
  • The Laws of Algebra
  • Priorities in Calculations
  • Factors
  • Exercises
  • Answers to exercises (6 pages)
• UNIT 1.2 - ALGEBRA 2 - NUMBERWORK
  • Types of number
  • Decimal numbers
  • Use of electronic calculators
  • Scientific notation
  • Percentages
  • Ratio
  • Exercises
  • Answers to exercises (8 pages)
• UNIT 1.3 - ALGEBRA 3 - INDICES AND RADICALS (OR SURDS)
  • Indices
  • Radicals (or Surds)
  • Exercises
  • Answers to exercises (8 pages)
• UNIT 1.4 - ALGEBRA 4 - LOGARITHMS
  • Common logarithms
  • Logarithms in general
  • Useful Results
  • Properties of logarithms
  • Natural logarithms
  • Graphs of logarithmic and exponential functions
  • Logarithmic scales
  • Exercises
  • Answers to exercises (10 pages)
• UNIT 1.5 - ALGEBRA 5 - MANIPULATION OF ALGEBRAIC EXPRESSIONS
  • Simplification of expressions
  • Factorisation
  • Completing the square in a quadratic expression
  • Algebraic Fractions
  • Exercises
  • Answers to exercises (9 pages)
• UNIT 1.6 - ALGEBRA 6 - FORMULAE AND ALGEBRAIC EQUATIONS
  • Transposition of formulae
  • Solution of linear equations
  • Solution of quadratic equations
  • Exercises
  • Answers to exercises (7 pages)
• UNIT 1.7 - ALGEBRA 7 - SIMULTANEOUS LINEAR EQUATIONS
  • Two simultaneous linear equations in two unknowns
  • Three simultaneous linear equations in three unknowns
  • Ill-conditioned equations
  • Exercises
  • Answers to exercises (6 pages)
• UNIT 1.8 - ALGEBRA 8 - POLYNOMIALS
  • The factor theorem
  • Application to quadratic and cubic expressions
  • Cubic equations
  • Long division of polynomials
  • Exercises
  • Answers to exercises (8 pages)
• UNIT 1.9 - ALGEBRA 9 - THE THEORY OF PARTIAL FRACTIONS
  • Introduction
  • Standard types of partial fraction problem
  • Exercises
  • Answers to exercises (7 pages)
• UNIT 1.10 - ALGEBRA 10 - INEQUALITIES 1
  • Introduction
  • Algebraic rules for inequalities
  • Intervals
  • Exercises
  • Answers to exercises (5 pages)
• UNIT 1.11 - ALGEBRA 11 - INEQUALITIES 2
  • Recap on modulus, absolute value or numerical value
  • Interval inequalities
  • Exercises
  • Answers to exercises (5 pages)