Higher Engineering Mathematics

Preface; Algebra; Partial fractions; Logarithms; Exponential functions; Hyperbolic functions; Arithmetic and geometric progressions; The binomial series; Maclaurin's series; Solving equations by iterative methods; Binary; octal and hexadecimal; Introduction to trigonometry; Cartesian and polar co-ordinates; The circle and its properties; Trigonometric waveforms; Trigonometric identities and equations; The relationship between trigonometric and hyperbolic functions; Compound angles; Functions and their curves; Irregular areas; volumes and mean values of waveforms; Complex numbers; De Moivre's theorem; The theory of matrices and determinants; The solution of simultaneous equations by matrices and determinants; Vectors; Methods of adding alternating waveforms; Scalar and vector products; Methods of differentiation; Some applications of differentiation; Differentiation of parametric equations; Differentiation of implicit functions; Logarithmic differentiation; Differentiation of hyperbolic functions; Differentiation of inverse trigonometric and hyperbolic functions; Partial differentiation; Total differential; rates of change and small changes; Maxima; minima and saddle points for functions of two variables; Standard integration; Some applications of integration; Integration using algebraic substitutions; Integration using trigonometric and hyperbolic substitutions; Integration using partial fractions; The t = __substitution; Integration by parts; Reduction formulae; Numerical integration; Solution of first order differential equations by separation of variables; Homogeneous first order differential equations; Linear first order differential equations; Numerical methods for first order differential equations; Second order differential equations of the form __; Second order differential equations of the form __; Power series methods of solving ordinary differential equations; An introduction to partial differential equations; Presentation of statistical data; Measures of central tendency and dispersion; Probability; The binomial and Poisson distributions; The normal distribution; Linear correlation; Linear regression; Introduction to Laplace transforms; Properties of Laplace transforms; Inverse Laplace transforms; The solution of differential equations using Laplace transforms; The solution of simultaneous differential equations using Laplace transforms; Fourier series for periodic functions of period 2p ; Fourier series for a non-periodic function over range 2p ; Even and odd functions and half-range Fourier series; Fourier series over any range; A numerical method of harmonic analysis; The complex or exponential form of a Fourier series; Essential formulae; Index