9th Edition

Bird's Higher Engineering Mathematics

By John Bird Copyright 2021
    934 Pages 603 B/W Illustrations
    by Routledge

    934 Pages 603 B/W Illustrations
    by Routledge

    Higher Engineering Mathematics has helped thousands of students to succeed in their exams by developing problem-solving skills, It is supported by over 600 practical engineering examples and applications which relate theory to practice. The extensive and thorough topic coverage makes this a solid text for undergraduate and upper-level vocational courses. Its companion website provides resources for both students and lecturers, including lists of essential formulae, ands full solutions to all 2,000 further questions contained in the 277 practice exercises; and illustrations and answers to revision tests for adopting course instructors.

    Section A Number and algebra

    1 Algebra

    2 Partial fractions

    3 Logarithms

    4 Exponential functions

    5 The binomial series

    6.Solving equations by iterative methods

    7 Boolean algebra and logic circuits

    Section B Geometry and trigonometry

    8 Introduction to trigonometry

    9 Cartesian and polar co-ordinates

    10 The circle and its properties

    11 Trigonometric waveforms

    12 Hyperbolic functions

    13 Trigonometric identities and equations

    14 The relationship between trigonometric and hyperbolic functions

    15 Compound angles

    Section C Graphs

    16 Functions and their curves

    17 Irregular areas, volumes and mean values of waveforms

    Section D Complex numbers

    18 Complex numbers

    19 De Moivre’s theorem

    Section E Matrices and determinants

    20 The theory of matrices and determinants

    21 Applications of matrices and determinants

    Section F Vector geometry

    22 Vectors

    23 Methods of adding alternating waveforms

    24 Scalar and vector products

    Section G Differential calculus

    25 Methods of differentiation

    26 Some applications of differentiation

    27 Differentiation of parametric equations

    28 Differentiation of implicit functions

    29 Logarithmic differentiation

    30 Differentiation of hyperbolic functions

    31 Differentiation of inverse trigonometric and hyperbolic functions

    32 Partial differentiation

    33 Total differentials, rates of change and small changes

    34 Maxima, minima and saddle points for functions of two variables

    Section H Integral calculus

    35 Standard integration

    36 Some applications of integration

    37 Maclaurin’s series

    38 Integration using algebraic substitutions

    39 Integration using trigonometric and hyperbolic substitutions

    40 Integration using partial fractions

    41 The t = tan θ/2

    42 Integration by parts

    43 Reduction formulae

    44 Double and triple integrals

    45 Numerical integration

    Section I Differential equations

    46 Introduction to differential equations

    47 Homogeneous first order differential equations

    48 Linear first order differential equations

    49 Numerical methods for first order differential equations

    50 First order differential equations (1)

    51 First order differential equations (2)

    52 Power series methods of solving ordinary differential equations

    53 An introduction to partial differential equations

    Section J Laplace transforms

    54 Introduction to Laplace transforms

    55 Properties of Laplace transforms

    56 Inverse Laplace transforms

    57 The Laplace transform of the Heaviside function

    58 The solution of differential equations using Laplace transforms

    59 The solution of simultaneous differential equations using Laplace transforms

    Section K Fourier series

    60 Fourier series for periodic functions of period 2π

    61 Fourier series for a non-periodic function over period 2π

    62 Even and odd functions and half-range Fourier series

    63 Fourier series over any range

    64 A numerical method of harmonic analysis

    65 The complex or exponential form of a Fourier series

    Section L Z-transforms

    66 An introduction to z-transforms

    Section M Statistics and probability

    67 Presentation of statistical data

    68 Mean, median, mode and standard deviation

    69 Probability

    70 The binomial and Poisson distributions

    71 The normal distribution

    72 Linear correlation

    73 Linear regression

    74 Sampling and estimation theories

    75 Significance testing

    76 Chi-square and distribution-free tests

    Essential formulae

    Answers to Practice Exercises


    John Bird, BSc (Hons), CEng, CMath, CSci, FIMA, FIET, FCollT, is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with Examiner responsibilities for Advanced Mathematics with City and Guilds and examining for the International Baccalaureate Organisation. He has over 45 years’ experience of successfully teaching, lecturing, instructing, training, educating and planning of trainee engineers study programmes. He is the author of 146 textbooks on engineering, science and mathematical subjects, with worldwide sales of over one million copies. He is a chartered engineer, a chartered mathematician, a chartered scientist and a Fellow of three professional institutions. He has recently retired from lecturing at the Defence College of Marine Engineering in the Defence College of Technical Training at H.M.S. Sultan, Gosport, Hampshire, UK, one of the largest engineering training establishments in Europe.