Higher Engineering Mathematics (Sixth Edition) - Copy

Algebra

Partial fractions

Logarithms

Exponential

Hyperbolic functions

Arithmetic and geometric progressions

The binomial series

8 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 =tan θ 2 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 a d2y dx2 +b dy dx +cy=0

Second order differential equations of the form a d2y dx2 +b dy dx +cy=f(x)

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 2π

Fourier series for a non-periodic function over range 2π

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