Engineering Mathematics, 7th Edition

A practical introduction to the core mathematics required for engineering study and practice

Now in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.

John Bird’s approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for a range of Level 2 and 3 engineering courses.

This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,800 further questions contained within the practice exercises, and biographical information on the 24 famous mathematicians and engineers referenced throughout the book.

The companion website for this title can be accessed from www.routledge.com/cw/bird

Table of Contents

Section 1 Number and algebra
Chapter 1 Revision of fractions, decimals and percentages
Chapter 2 Indices, standard form and engineering notation
Chapter 3 Binary, octal and hexadecimal numbers
Chapter 4 Calculations and evaluation of formulae
Chapter 5 Algebra
Chapter 6 Further algebra
Chapter 7 Partial fractions
Chapter 8 Solving simple equations
Chapter 9 Solving simultaneous equations
Chapter 10 Transposition of formulae
Chapter 11 Solving quadratic equations
Chapter 12 Inequalities
Chapter 13 Logarithms
Chapter 14 Exponential functions
Chapter 15 Number sequences
Chapter 16 The binomial series
Chapter 17 Solving equations by iterative methods

Section 2 Areas and volumes
Chapter 18 Areas of common shapes
Chapter 19 The circle
Chapter 20 Volumes and surface areas of common solids
Chapter 21 Irregular areas and volumes and mean values of waveforms

Section 3 Trigonometry
Chapter 22 Introduction to trigonometry
Chapter 23 Trigonometric waveforms
Chapter 24 Cartesian and polar co-ordinates
Chapter 25 Triangles and some practical applications
Chapter 26 Trigonometric identities and equations
Chapter 27 Compound angles

Section 4 Graphs
Chapter 28 Straight line graphs
Chapter 29 Reduction of non-linear laws to linear form
Chapter 30 Graphs with logarithmic scales
Chapter 31 Graphical solution of equations
Chapter 32 Functions and their curves

Section 5 Complex numbers
Chapter 33 Complex numbers
Chapter 34 De Moivre’s theorem

Section 6 Vectors
Chapter 35 Vectors
Chapter 36 Methods of adding alternating waveforms

Section 7 Statistics
Chapter 37 Presentation of statistical data
Chapter 38 Mean, median, mode and standard deviation
Chapter 39 Probability
Chapter 40 The binomial and Poisson distribution
Chapter 41 The normal distribution
Chapter 42 Linear correlation
Chapter 43 Linear regression
Chapter 44 Sampling and estimation theories

Section 8 Differential calculus
Chapter 45 Introduction to differentiation
Chapter 46 Methods of differentiation
Chapter 47 Some applications of differentiation
Chapter 48 Differentiation of parametric equations
Chapter 49 Differentiation of implicit functions
Chapter 50 Logarithmic differentiation

Section 9 Integral calculus
Chapter 51 Standard integration
Chapter 52 Integration using algebraic substitutions
Chapter 53 Integration using trigonometric substitutions
Chapter 54 Integration using partial fractions
Chapter 55 The t = tanθ/2 substitution
Chapter 56 Integration by parts
Chapter 57 Numerical integration
Chapter 58 Areas under and between curves
Chapter 59 Mean and root mean square values
Chapter 60 Volumes of solids of revolution
Chapter 61 Centroids of simple shapes
Chapter 62 Second moments of area

Section 10 Further number and algebra
Chapter 63 Boolean algebra and logic circuits
Chapter 64 The theory of matrices and determinants
Chapter 65 The solution of simultaneous equations by matrices and determinants
Chapter Section 11 Differential equations
Chapter 66 Introduction to differential equations