ABSTRACT

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.

part Section A|86 pages

Number and algebra

chapter Chapter 1|15 pages

Algebra

chapter Chapter 2|7 pages

Partial fractions

chapter Chapter 3|8 pages

Logarithms

chapter Chapter 4|16 pages

Exponential functions

chapter Chapter 5|9 pages

The binomial series

chapter Chapter 6|8 pages

Solving equations by iterative methods

chapter Chapter 7|22 pages

Boolean algebra and logic circuits

part Section B|102 pages

Geometry and trigonometry

chapter Chapter 8|23 pages

Introduction to trigonometry

chapter Chapter 9|6 pages

Cartesian and polar co-ordinates

chapter Chapter 10|15 pages

The circle and its properties

chapter Chapter 11|19 pages

Trigonometric waveforms

chapter Chapter 12|10 pages

Hyperbolic functions

chapter Chapter 13|8 pages

Trigonometric identities and equations

chapter Chapter 15|16 pages

Compound angles

part Section C|36 pages

Graphs

chapter Chapter 16|23 pages

Functions and their curves

chapter Chapter 17|12 pages

Irregular areas, volumes and mean values of waveforms

part Section D|26 pages

Complex numbers

chapter Chapter 18|15 pages

Complex numbers

chapter Chapter 19|10 pages

De Moivre's theorem

part Section E|32 pages

Matrices and determinants

chapter Chapter 20|13 pages

The theory of matrices and determinants

chapter Chapter 21|18 pages

Applications of matrices and determinants

part Section F|42 pages

Vector geometry

chapter Chapter 22|17 pages

Vectors

chapter Chapter 23|11 pages

Methods of adding alternating waveforms

chapter Chapter 24|13 pages

Scalar and vector products

part Section G|96 pages

Differential calculus

chapter Chapter 25|14 pages

Methods of differentiation

chapter Chapter 26|23 pages

Some applications of differentiation

chapter Chapter 27|6 pages

Differentiation of parametric equations

chapter Chapter 28|6 pages

Differentiation of implicit functions

chapter Chapter 29|7 pages

Logarithmic differentiation

chapter Chapter 30|4 pages

Differentiation of hyperbolic functions

chapter Chapter 32|7 pages

Partial differentiation

chapter Chapter 33|7 pages

Total differential, rates of change and small changes

part Section H|102 pages

Integral calculus

chapter Chapter 35|9 pages

Standard integration

chapter Chapter 36|19 pages

Some applications of integration

chapter Chapter 37|11 pages

Maclaurin's series and limiting values

chapter Chapter 38|6 pages

Integration using algebraic substitutions

chapter Chapter 40|6 pages

Integration using partial fractions

chapter Chapter 41|6 pages

The t = tan ⁡ θ 2 substitution

chapter Chapter 42|6 pages

Integration by parts

chapter Chapter 43|9 pages

Reduction formulae

chapter Chapter 44|6 pages

Double and triple integrals

chapter Chapter 45|11 pages

Numerical integration

part Section I|94 pages

Graphs

part Section J|44 pages

Laplace transforms

chapter Chapter 54|7 pages

Introduction to Laplace transforms

chapter Chapter 55|7 pages

Properties of Laplace transforms

chapter Chapter 56|8 pages

Inverse Laplace transforms

chapter Chapter 57|8 pages

The Laplace transform of the Heaviside function

part Section K|50 pages

Laplace transforms

chapter Chapter 60|8 pages

Fourier series for periodic functions of period 2π

chapter Chapter 62|8 pages

Even and odd functions and half-range Fourier series

chapter Chapter 63|6 pages

Fourier series over any range

chapter Chapter 64|8 pages

A numerical method of harmonic analysis

chapter Chapter 65|13 pages

The complex or exponential form of a Fourier series

part Section L|18 pages

Z–Transforms

chapter Chapter 66|17 pages

An introduction to z-transforms

part Section M|117 pages

Statistics and probability

chapter Chapter 67|13 pages

Presentation of statistical data

chapter Chapter 68|8 pages

Mean, median, mode and standard deviation

chapter Chapter 69|13 pages

Probability

chapter Chapter 70|7 pages

The binomial and Poisson distributions

chapter Chapter 71|9 pages

The normal distribution

chapter Chapter 72|5 pages

Linear correlation

chapter Chapter 73|7 pages

Linear regression

chapter Chapter 74|13 pages

Sampling and estimation theories

chapter Chapter 75|17 pages

Significance testing

chapter Chapter 76|24 pages

Chi-square and distribution-free tests