Higher Engineering Mathematics

John Bird (BSc(Hons), CMath, CEng, CSci, FITE, FIMA, 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 and examining, and is the author of over 130 textbooks on engineering and mathematical subjects with worldwide sales of one million copies. He is currently lecturing at the Defence School of Marine Engineering in the Defence College of Technical Training at HMS Sultan, Gosport, Hampshire, UK.

Preface


Syllabus guidance


Section A Number and algebra


1 Algebra


2 Partial fractions


3 Logarithms


4 Exponential functions


5 Inequalities


6 Arithmetic and geometric progressions


7 The binomial series


8 Maclaurin’s series


9 Solving equations by iterative methods


10 Binary, octal and hexadecimal numbers


11 Boolean algebra and logic circuits


Section B Geometry and trigonometry


12 Introduction to trigonometry


13 Cartesian and polar co-ordinates


14 The circle and its properties


15 Trigonometric waveforms


16 Hyperbolic functions


17 Trigonometric identities and equations


18 The relationship between trigonometric and


hyperbolic functions


19 Compound angles


Section C Graphs


20 Functions and their curves


21 Irregular areas, volumes and mean values of waveforms


Section D Complex numbers


22 Complex numbers


23 De Moivre’s theorem


Section E Matrices and determinants


24 The theory of matrices and determinants


25 Applications of matrices and determinants


Section F Vector geometry 303


26 Vectors


27 Methods of adding alternating waveforms


28 Scalar and vector products


Section G Introduction to calculus


29 Methods of differentiation


30 Some applications of differentiation


31 Standard integration


32 Some applications of integration


33 Introduction to differential equations


Section H Further differential calculus


34 Differentiation of parametric equations


35 Differentiation of implicit functions


36 Logarithmic differentiation


37 Differentiation of hyperbolic functions


38 Differentiation of inverse trigonometric and hyperbolic functions


39 Partial differentiation


40 Total differential, rates of change and small changes


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


Section I Further integral calculus


42 Integration using algebraic substitutions


43 Integration using trigonometric and hyperbolic substitutions


44 Integration using partial fractions


45 The t = tan θ/2


46 Integration by parts


47 Reduction formulae


48 Double and triple integrals


49 Numerical integration


Section J Further differential equations


50 Homogeneous first order differential equations


51 Linear first order differential equations


52 Numerical methods for first order differential equations


53 First order differential equations of the form


54 First order differential equations of the form


55 Power series methods of solving ordinary differential equations


56 An introduction to partial differential equations


Section K Statistics and probability


57 Presentation of statistical data


58 Mean, median, mode and standard deviation


59 Probability


60 The binomial and Poisson distributions


61 The normal distribution


62 Linear correlation


63 Linear regression


64 Sampling and estimation theories


65 Significance testing


66 Chi-square and distribution-free tests


Section L Laplace transforms


67 Introduction to Laplace transforms


68 Properties of Laplace transforms


69 Inverse Laplace transforms


70 The Laplace transform of the Heaviside function


71 The solution of differential equations using Laplace transforms


72 The solution of simultaneous differential equations using Laplace transforms


Section M Fourier series


73 Fourier series for periodic functions of period 2π


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


75 Even and odd functions and half-range Fourier series


76 Fourier series over any range


77 A numerical method of harmonic analysis


78 The complex or exponential form of a Fourier series


Section N Z-transforms


79 An introduction to z-transforms


Essential formulae


Answers to Practice Exercises


Index