Higher engineering mathematics / John Bird.

Previous edition: Amsterdam: Newnes, 2010.

Includes index.

45.Integration by parts -- 46.Reduction formulae -- 47.Double and triple integrals -- 48.Numerical integration -- Section I.Differential equations -- 49.Solution of first-order differential equations by separation of variables -- 50.Homogeneous first-order differential equations -- 51.Linear first-order differential equations -- 52.Numerical methods for first-order differential equations -- 53.Second-order differential equations of the form -- 54.Power series methods of solving ordinary differential equations -- 56.An introduction to partial differential equations -- Section J.Statistics and probability -- 57.Presentation of statistics data -- 58.Mean, median, mode and standard deviaiton -- 59.Probability -- 60.The binomial and Poisson distribution -- 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 K.Laplace transforms -- 67.Introduction to Laplace transfomrs -- 68.Properties of Laplace transforms -- 69.Inverse Laplace transforms -- 70.The Laplace transform of the Heavisde function -- 71.The solution of differential equations using Laplace transform -- 72.The solutions of simultaneous differential equations using Laplace transforms -- Section L.Fourier series -- 73.Fourier series for periodic functions of period 2 -- 74.Fourier series for a non-periodic function over range 2 -- 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 fomr of a Fourier series.

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 interative 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.Trignometric 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 -- 26.Vectors -- 27.Methods of adding alternating waveforms -- 28.Scalar and vector products -- Section G.Diffenential calculus -- 29.Methods of differentiation -- 30.Some applications of differentiation -- 31.Differentiation of parametric equations -- 32.Differentiation of implicit functions -- 33.Logarithmic differentiation -- 34.Differentiation of hyperbolic functions -- 35.Differentiation of inverse trigonometric and hyperbolic functions -- 36.Partial differentiation -- 37.Total differential, rates of change and small changes -- 38.Maxima, minima and and saddle points for functions of two variables -- Section H.Integral calculus -- 39.Standard integration -- 40.Some application of integration -- 41.Integration using algebraic substitutions -- 42.Integration using trigonometric and hyperbolic substitutions -- 43.Integration using partial fractions -- 44.The t=tan substitution.

John Bird's approach, based on numerous worked examples and interactive problems, is ideal for students from a wide range of academic backgrounds. This edition has been extended with new topics to maximise the book's applicability for first year engineering degree students, and those following Foundation Degrees.