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Book

Bird's Comprehensive Engineering Mathematics

Book

Bird's Comprehensive Engineering Mathematics

DOI link for Bird's Comprehensive Engineering Mathematics

Bird's Comprehensive Engineering Mathematics book

Bird's Comprehensive Engineering Mathematics

DOI link for Bird's Comprehensive Engineering Mathematics

Bird's Comprehensive Engineering Mathematics book

ByJohn Bird
Edition 2nd Edition
First Published 2018
eBook Published 19 June 2018
Pub. Location London
Imprint Routledge
DOI https://doi.org/10.1201/9781351232876
Pages 1226
eBook ISBN 9781351232876
Subjects Engineering & Technology
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Bird, J. (2018). Bird's Comprehensive Engineering Mathematics (2nd ed.). CRC Press. https://doi.org/10.1201/9781351232876

ABSTRACT

Studying engineering, whether it is mechanical, electrical or civil, relies heavily on an understanding of mathematics. This textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them in real-life engineering problems.

It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher.

Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures is presented, before real world practical situations and problem solving demonstrate how the theory is applied.

Focusing on learning through practice, it contains simple explanations, supported by 1600 worked problems and over 3600 further problems contained within 384 exercises throughout the text. In addition, 35 Revision tests together with 9 Multiple-choice tests are included at regular intervals for further strengthening of knowledge.

An interactive companion website provides material for students and lecturers, including detailed solutions to all 3600 further problems. 

TABLE OF CONTENTS

part A|167 pages

Number and algebra

chapter 1|8 pages

Basic arithmetic

chapter 2|8 pages

Fractions

chapter 3|6 pages

Decimals

chapter 4|12 pages

Using a calculator

chapter 5|8 pages

Percentages

chapter 6|9 pages

Ratio and proportion

chapter 7|7 pages

Powers, roots and laws of indices

chapter 8|17 pages

Units, prefixes and engineering notation

chapter 9|8 pages

Basic algebra

chapter 10|8 pages

Further algebra

chapter 11|10 pages

Solving simple equations

chapter 12|8 pages

Transposing formulae

chapter 13|13 pages

Solving simultaneous equations

chapter 14|12 pages

Solving quadratic equations

chapter 15|8 pages

Logarithms

chapter 16|12 pages

Exponential functions

chapter 17|10 pages

Inequalities

part B|105 pages

Further number and algebra

chapter 18|7 pages

Polynomial division and the factor and remainder theorems

chapter 19|7 pages

Partial fractions

chapter 20|11 pages

Number sequences

chapter 21|9 pages

The binomial series

chapter 22|11 pages

Maclaurin’s series

chapter 23|11 pages

Solving equations by iterative methods

chapter 24|11 pages

Hyperbolic functions

chapter 25|11 pages

Binary, octal and hexadecimal numbers

chapter 26|25 pages

Boolean algebra and logic circuits

part C|58 pages

Areas and volumes

chapter 27|12 pages

Areas of common shapes

chapter 28|14 pages

The circle and its properties

chapter 29|22 pages

Volumes and surface areas of common solids

chapter 30|8 pages

Irregular areas and volumes, and mean values

part D|82 pages

Graphs

chapter 31|19 pages

Straight line graphs

chapter 32|9 pages

Graphs reducing non-linear laws to linear form

chapter 33|9 pages

Graphs with logarithmic scales

chapter 34|4 pages

Polar curves

chapter 35|9 pages

Graphical solution of equations

chapter 36|29 pages

Functions and their curves

part E|100 pages

Geometry and trigonometry

chapter 37|16 pages

Angles and triangles

chapter 38|20 pages

Introduction to trigonometry

chapter 39|15 pages

Trigonometric waveforms

chapter 40|5 pages

Cartesian and polar co-ordinates

chapter 41|10 pages

Non-right-angled triangles and some practical applications

chapter 42|7 pages

Trigonometric identities and equations

chapter 43|4 pages

The relationship between trigonometric and hyperbolic functions

chapter 44|21 pages

Compound angles

part F|26 pages

Complex numbers

chapter 45|13 pages

Complex numbers

chapter 46|11 pages

De Moivre’s theorem

part G|28 pages

Matrices and determinants

chapter 47|10 pages

The theory of matrices and determinants

chapter 48|16 pages

Applications of matrices and determinants

part H|39 pages

Vector geometry

chapter 49|14 pages

Vectors

chapter 50|11 pages

Methods of adding alternating waveforms

chapter 51|12 pages

Scalar and vector products

part I|97 pages

Differential calculus

chapter 52|10 pages

Introduction to differentiation

chapter 53|9 pages

Methods of differentiation

chapter 54|17 pages

Some applications of differentiation

chapter 55|6 pages

Differentiation of parametric equations

chapter 56|5 pages

Differentiation of implicit functions

chapter 57|6 pages

Logarithmic differentiation

chapter 58|3 pages

Differentiation of hyperbolic functions

chapter 59|11 pages

Differentiation of inverse trigonometric hyperbolic functions

chapter 60|6 pages

Partial differentiation

chapter 61|6 pages

Total differential, rates of change and small changes

chapter 62|16 pages

Maxima, minima and saddle points for functions of two variables

part J|110 pages

Integral calculus

chapter 63|7 pages

Standard integration

chapter 64|5 pages

Integration using algebraic substitutions

chapter 65|12 pages

Integration using trigonometric and hyperbolic substitutions

chapter 66|5 pages

Integration using partial fractions

chapter 67|5 pages

The t = t a n θ / 2 $ \boldsymbol{t} = tan \boldsymbol{\theta }/2 $ substitution

chapter 68|7 pages

Integration by parts

chapter 69|9 pages

Reduction formulae

chapter 70|4 pages

Double and triple integrals

chapter 71|10 pages

Numerical integration

chapter 72|9 pages

Areas under and between curves

chapter 73|5 pages

Mean and root mean square values

chapter 74|5 pages

Volumes of solids ofrevolution

chapter 75|9 pages

Centroids of simple shapes

chapter 76|16 pages

Second moments of area

part K|96 pages

Differential equations

chapter 77|8 pages

Solution of first-order differential equations by separation of variables

chapter 78|4 pages

Homogeneous first-order differential equations

chapter 79|5 pages

Linear first-order differential equations

chapter 80|18 pages

Numerical methods for first-order differential equations

chapter 81|7 pages

Second-order differential equations of the form a d 2 y d x 2 + b d y d x + cy = 0 $ {{{a}}\dfrac{\mathbf{d }^{\boldsymbol{2}}\mathbf {y} }{\mathbf{d }\mathbf {x} ^{\boldsymbol{2}}}\boldsymbol{+}{{b}}\dfrac{{\text{ d}}\mathbf {y} }{\mathbf{d }\mathbf {x} }\boldsymbol{+}{{cy}}\boldsymbol{=}\boldsymbol{0}} $

chapter 82|10 pages

Second-order differential equations of the form a d 2 y d x 2 + b d y d x + c y = f ( x ) $ {a \dfrac{\mathrm{d}^{2}y}{\mathrm{d} x^{2}} + b \dfrac{\mathrm{d} y}{\mathrm{d} x} + cy = f(x)} $

chapter 83|24 pages

Power series methods of solving ordinary differential equations

chapter 84|18 pages

An introduction to partial differential equations

part L|118 pages

Statistics and probability

chapter 85|12 pages

Presentation of statisticaldata

chapter 86|7 pages

Mean, median, mode and standard deviation

chapter 87|12 pages

Probability

chapter 88|7 pages

The binomial and Poisson distributions

chapter 89|8 pages

The normal distribution

chapter 90|5 pages

Linear correlation

chapter 91|7 pages

Linear regression

chapter 92|13 pages

Sampling and estimation theories

chapter 93|17 pages

Significance testing

chapter 94|28 pages

Chi-square and distribution-free tests

part M|40 pages

Laplace transforms

chapter 95|5 pages

Introduction to Laplace transforms

chapter 96|6 pages

Properties of Laplace transforms

chapter 97|7 pages

Inverse Laplace transforms

chapter 98|7 pages

The Laplace transform of the Heaviside function

chapter 99|5 pages

The solution of differential equations using Laplace transforms

chapter 100|8 pages

The solution of simultaneous differential equations using Laplace transforms

part N|50 pages

Fourier series

chapter 101|7 pages

Fourier series for periodic functions of period 2 π $ \pi $

chapter 102|6 pages

Fourier series for a non-periodic function overrange 2 π $ \pi $

chapter 103|7 pages

Even and odd functions and half-range Fourier series

chapter 104|6 pages

Fourier series over any range

chapter 105|7 pages

A numerical method of harmonic analysis

chapter 106|15 pages

The complex or exponential form of a Fourierseries

part O|17 pages

Z-transforms

chapter 107|15 pages

An introduction to z-transforms

chapter |52 pages

Answers to practice exercises

chapter |1 pages

Answers to multiple choice questions

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