Bird s Engineering Mathematics 9th Edition by John Bird ISBN 0367643782 9780367643782

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ISBN 10: 0367643782
ISBN 13: 9780367643782
Author: John Bird

Bird s Engineering Mathematics 9th Edition Table of contents:

Section 1 Number and algebra

Chapter 1 Revision of fractions, decimals and percentages

1.1 Fractions

1.2 Ratio and proportion

1.3 Decimals

1.4 Percentages

Percentage absorption

Chapter 2 Indices, engineering notation and metric conversions

2.1 Indices

Reciprocal

Square root

Laws of indices

2.2 Standard form

2.3 Engineering notation and common prefixes

2.4 Metric conversions

Length in metric units

Areas in metric units

Volumes in metric units

2.5 Metric – US/imperial conversions

Temperature

Chapter 3 Binary, octal and hexadecimal numbers

3.1 Introduction

3.2 Binary numbers

3.3 Octal numbers

3.4 Hexadecimal numbers

Chapter 4 Calculations and evaluation of formulae

4.1 Errors and approximations

4.2 Use of calculator

4.3 Conversion tables and charts

4.4 Evaluation of formulae

Revision Test 1 Fractions, decimals, percentages, indices, numbering systems and calculations

Chapter 5 Algebra

5.1 Basic operations

5.2 Laws of indices

5.3 Brackets and factorisation

5.4 Fundamental laws and precedence

5.5 Direct and inverse proportionality

Chapter 6 Further algebra

6.1 Polynomial division

6.2 The factor theorem

6.3 The remainder theorem

Chapter 7 Partial fractions

7.1 Introduction to partial fractions

7.2 Partial fractions with linear factors

7.3 Partial fractions with repeated linear factors

7.4 Partial fractions with quadratic factors

Chapter 8 Solving simple equations

8.1 Expressions, equations and identities

8.2 Worked problems on simple equations

8.3 Further worked problems on simple equations

8.4 Practical problems involving simple equations

8.5 Further practical problems involving simple equations

Revision Test 2 Algebra, partial fractions and simple equations

Chapter 9 Transposition of formulae

9.1 Introduction to transposition of formulae

9.2 Worked problems on transposition of formulae

9.3 Further worked problems on transposition of formulae

9.4 Harder worked problems on transposition of formulae

Chapter 10 Solving simultaneous equations

10.1 Introduction to simultaneous equations

10.2 Worked problems on simultaneous equations in two unknowns

10.3 Further worked problems on simultaneous equations

10.4 More difficult worked problems on simultaneous equations

10.5 Practical problems involving simultaneous equations

Chapter 11 Solving quadratic equations

11.1 Introduction to quadratic equations

11.2 Solution of quadratic equations by factorisation

11.3 Solution of quadratic equations by ‘completing the square’

11.4 Solution of quadratic equations by formula

11.5 Practical problems involving quadratic equations

11.6 The solution of linear and quadratic equations simultaneously

Chapter 12 Inequalities

12.1. Introduction in inequalities

Some simple rules

12.2. Simple inequalities

12.3. Inequalities involving a modulus

12.4. Inequalities involving quotients

12.5. Inequalities involving square functions

12.6. Quadratic inequalities

Chapter 13 Logarithms

13.1. Introduction to logarithms

What is a logarithm?

Common logarithms

Napierian logarithms

13.2. Laws of logarithms

13.3. Indicial equations

13.4. Graphs of logarithmic functions

Revision Test 3 Simultaneous and quadratic equations, transposition of formulae, inequalities and logarithms

Chapter 14 Exponential functions

14.1 Introduction to exponential functions

14.2 The power series for ex

14.3 Graphs of exponential functions

14.4 Napierian logarithms

14.5 Laws of growth and decay

Chapter 15 Number sequences

15.1. Arithmetic progressions

15.2. Worked problems on arithmetic progressions

15.3. Further worked problems on arithmetic progressions

15.4. Geometric progressions

15.5. Worked problems on geometric progressions

15.6. Further worked problems on geometric progressions

15.7. Combinations and permutations

Chapter 16 The binomial series

16.1. Pascal’s triangle

16.2. The binomial series

16.3. Worked problems on the binomial series

16.4. Further worked problems on the binomial series

16.5. Practical problems involving the binomial theorem

Revision Test 4 Exponential functions, number sequences, and the binomial series

Section 2 Trigonometry

Chapter 17 Introduction to trigonometry

17.1 Trigonometry

17.2 The theorem of Pythagoras

17.3 Trigonometric ratios of acute angles

17.4 Fractional and surd forms of trigonometric ratios

17.5 Evaluating trigonometric ratios of any angles

17.6 Solution of right-angled triangles

17.7 Angle of elevation and depression

17.8 Trigonometric approximations for small angles

Chapter 18 Trigonometric waveforms

18.1. Graphs of trigonometric functions

18.2. Angles of any magnitude

18.3. The production of a sine and cosine wave

18.4. Sine and cosine curves

Graphs of sine and cosine waveforms

Periodic functions and period

Amplitude

Lagging and leading angles

18.5. Sinusoidal form A sin (ωt ± α)

18.6. Waveform harmonics

Chapter 19 Cartesian and polar co-ordinates

19.1. Introduction

19.2. Changing from Cartesian into polar co-ordinates

19.3. Changing from polar into Cartesian co-ordinates

19.4. Use of Pol/Rec functions on calculators

Revision Test 5 Trigonometry

Chapter 20 Triangles and some practical applications

20.1 Sine and cosine rules

Sine rule

Cosine rule

20.2 Area of any triangle

20.3 Worked problems on the solution of triangles and their areas

20.4 Further worked problems on the solution of triangles and their areas

20.5 Practical situations involving trigonometry

20.6 Further practical situations involving trigonometry

Chapter 21 Trigonometric identities and equations

21.1 Trigonometric identities

21.2 Worked problems on trigonometric identities

21.3 Trigonometric equations

21.4 Worked problems (i) on trigonometric equations

21.5 Worked problems (ii) on trigonometric equations

21.6 Worked problems (iii) on trigonometric equations

21.7 Worked problems (iv) on trigonometric equations

Chapter 22 Compound angles

22.1 Compound angle formulae

22.2 Conversion of a sinωt  + b cosωt into R sin(ωt +α)

22.3 Double angles

22.4 Changing products of sines and cosines into sums or differences

22.5 Changing sums or differences of sines and cosines into products

Revision Test 6 Further trigonometry

Section 3 Areas and volumes

Chapter 23 Areas of common shapes

23.1 Introduction

23.2 Properties of quadrilaterals

Polygon

23.3 Areas of common shapes

23.4 Worked problems on areas of common shapes

23.5 Further worked problems on areas of plane figures

23.6 Worked problems on areas of composite figures

23.7 Areas of similar shapes

Chapter 24 The circle and its properties

24.1. Introduction

24.2. Properties of circles

24.3. Radians and degrees

24.4. Arc length and area of circles and sectors

Arc length

Area of circle

Area of sector

24.5. Worked problems on arc length and area of circles and sectors

24.6. The equation of a circle

Chapter 25 Volumes and surface areas of common solids

25.1. Introduction

25.2. Volumes and surface areas of regular solids

25.3. Worked problems on volumes and surface areas of regular solids

25.4 Further worked problems on volumes and surface areas of regular solids

25.5 Volumes and surface areas of frusta of pyramids and cones

Method 1

Method 2

Method 1

Method 2

25.6 The frustum and zone of a sphere

25.7 Prismodal rule

25.8 Volumes of similar shapes

Chapter 26 Irregular areas and volumes and mean values of waveforms

26.1 Area of irregular figures

26.2 Volumes of irregular solids

26.3 The mean or average value of a waveform

Revision Test 7 Areas and volumes

Section 4 Graphs

Chapter 27 Straight line graphs

27.1 Introduction to graphs

27.2 The straight line graph

27.3 Practical problems involving straight line graphs

Chapter 28 Reduction of non-linear laws to linear form

28.1 Determination of law

28.2 Determination of law involving logarithms

Chapter 29 Graphs with logarithmic scales

29.1 Logarithmic scales

29.2 Graphs of the form y = ax n

29.3 Graphs of the form y=ab x

29.4 Graphs of the form y =ae k x

Chapter 30 Graphical solution of equations

30.1 Graphical solution of simultaneous equations

30.2 Graphical solution of quadratic equations

30.3 Graphical solution of linear and quadratic equations simultaneously

30.4 Graphical solution of cubic equations

Chapter 31 Functions and their curves

31.1 Standard curves

31.2 Simple transformations

31.3 Periodic functions

31.4 Continuous and discontinuous functions

31.5 Even and odd functions

Even functions

Odd functions

31.6 Inverse functions

Inverse trigonometric functions

Revision Test 8 Graphs

Section 5 Graphs

Chapter 32 Complex numbers

32.1 Cartesian complex numbers

32.2 The Argand diagram

32.3 Addition and subtraction of complex numbers

32.4 Multiplication and division of complex numbers

32.5 Complex equations

32.6 The polar form of a complex number

Calculator

32.7 Multiplication and division in polar form

32.8 Applications of complex numbers

Chapter 33 De Moivre’s theorem

33.1 Introduction

33.2 Powers of complex numbers

33.3 Roots of complex numbers

Section 6 Vectors

Chapter 34 Vectors

34.1 Introduction

34.2 Scalars and vectors

34.3 Drawing a vector

Representing a vector

34.4 Addition of vectors by drawing

(a) Nose-to-tail method

(b) Parallelogram method

(a) ‘Nose-to tail’ method

(b) ‘Parallelogram’ method

34.5 Resolving vectors into horizontal and vertical components

34.6 Addition of vectors by calculation

34.7 Vector subtraction

34.8 Relative velocity

34.9 i, j and k notation

Chapter 35 Methods of adding alternating waveforms

35.1 Combination of two periodic functions

35.2 Plotting periodic functions

35.3 Determining resultant phasors by drawing

35.4 Determining resultant phasors by the sine and cosine rules

35.5 Determining resultant phasors by horizontal and vertical components

35.6 Determining resultant phasors by complex numbers

Revision Test 9 Complex numbers and vectors

Section 7 Differential calculus

Chapter 36 Introduction to differentiation

36.1. Introduction to calculus

36.2. Functional notation

36.3. The gradient of a curve

36.4. Differentiation from first principles

36.5. Differentiation of y = ax  n by the general rule

36.6. Differentiation of sine and cosine functions

36.7. Differentiation of e ax and ln ax

Chapter 37 Methods of differentiation

37.1. Differentiation of common functions

37.2. Differentiation of a product

37.3. Differentiation of a quotient

37.4. Function of a function

37.5. Successive differentiation

Chapter 38 Some applications of differentiation

38.1. Rates of change

38.2. Velocity and acceleration

38.3. Turning points

38.4. Practical problems involving maximum and minimum values

38.5. Points of inflexion

38.6. Tangents and normals

Tangents

Normals

38.7. Small changes

Chapter 39 Solving equations by Newton’s method

39.1 Introduction to iterative methods

39.2 The Newton–Raphson method

39.3 Worked problems on the Newton–Raphson method

Chapter 40 Maclaurin’s series

40.1 Introduction

40.2 Derivation of Maclaurin’s theorem

40.3 Conditions of Maclaurin’s series

40.4 Worked problems on Maclaurin’s series

Revision Test 10 Differentiation

Chapter 41 Differentiation of parametric equations

41.1 Introduction to parametric equations

41.2 Some common parametric equations

41.3 Differentiation in parameters

41.4 Further worked problems on differentiation of parametric equations

Chapter 42 Differentiation of implicit functions

42.1 Implicit functions

42.2 Differentiating implicit functions

42.3 Differentiating implicit functions containing products and quotients

42.4 Further implicit differentiation

Chapter 43 Logarithmic differentiation

43.1 Introduction to logarithmic differentiation

43.2 Laws of logarithms

43.3 Differentiation of logarithmic functions

43.4 Differentiation of further logarithmic functions

43.5 Differentiation of [ f(x)] x

Revision Test 11 Further differentiation

Section 8 Integral calculus

Chapter 44 Standard integration

44.1 The process of integration

44.2 The general solution of integrals of the form ax n

44.3 Standard integrals

44.4 Definite integrals

Chapter 45 Integration using algebraic substitutions

45.1 Introduction

45.2 Algebraic substitutions

45.3 Worked problems on integration using algebraic substitutions

45.4 Further worked problems on integration using algebraic substitutions

45.5 Change of limits

Chapter 46 Integration using trigonometric substitutions

46.1 Introduction

46.2 Worked problems on integration of sin2 x, cos2 x, tan2 x and cot2 x

46.3 Worked problems on integration of powers of sines and cosines

46.4 Worked problems on integration of products of sines and cosines

Worked problems on integration using the sin θ substitution

Worked problems on integration using the tan θsubstitution

Revision Test 12 Integration

Chapter 47 Integration using partial fractions

47.1 Introduction

47.2 Integration using partial fractions with linear factors

47.3 Integration using partial fractions with repeated linear factors

47.4 Integration using partial fractions with quadratic factors

Chapter 48 The t=tan⁡θ2 substitution

48.1 Introduction

48.2 Worked problems on the t=tanθ2 substitution

48.3 Further worked problems on the t=tanθ2 substitution

Chapter 49 Integration by parts

49.1 Introduction

49.2 Worked problems on integration by parts

49.3 Further worked problems on integration by parts

Chapter 50 Numerical integration

50.1 Introduction

50.2 The trapezoidal rule

50.3 The mid-ordinate rule

50.4 Simpson’s rule

50.5 Accuracy of numerical integration

Revision Test 13 Further integration

Chapter 51 Areas under and between curves

51.1 Area under a curve

51.2 Worked problems on the area under a curve

51.3 Further worked problems on the area under a curve

51.4 The area between curves

Chapter 52 Mean and root mean square values

52.1 Mean or average values

52.2 Root mean square values

Chapter 53 Volumes of solids of revolution

53.1 Introduction

53.2 Worked problems on volumes of solids of revolution

53.3 Further worked problems on volumes of solids of revolution

Chapter 54: Centroids of simple shapes

54.1. Centroids

54.2. The first moment of area

54.3. Centroid of area between a curve and the x-axis

54.4 Centroid of area between a curve and the y-axis

54.5. Worked problems on centroids of simple shapes

54.6. Further worked problems on centroids of simple shapes

54.7. Theorem of Pappus

Chapter 55 Second moments of area

55.1 Second moments of area and radius of gyration

Radius of gyration

55.2 Second moment of area of regular sections

55.3 Parallel axis theorem

55.4 Perpendicular axis theorem

55.5 Summary of derived results

55.6 Worked problems on second moments of area of regular sections

55.7 Worked problems on second moments of area of composite areas

Revision Test 14 Boolean algebra, logic circuits, matrices and determinants

Section 9 Differential equations

Chapter 56 Introduction to differential equations

56.1 Family of curves

56.2 Differential equations

56.3 The solution of equations of the form dydx = f (x)

56.4 The solution of equations of the form d yd x = f (y)

56.5 The solution of equations of the form dydx = f (x) · f (y)

Revision Test 15 Differential equations

Section 10 Further number and algebra

Chapter 57 Boolean algebra and logic circuits

57.1 Boolean algebra and switching circuits

The or-function

The and-function

The not-function

57.2 Simplifying Boolean expressions

57.3 Laws and rules of Boolean algebra

57.4 De Morgan’s laws

57.5 Karnaugh maps

(i) Two-variable Karnaugh maps

(ii) Three-variable Karnaugh maps

(iii) Four-variable Karnaugh maps

57.6 Logic circuits

The and-gate

The or-gate

The invert-gate or not-gate

The nand-gate

The nor-gate

Combinational logic networks

57.7 Universal logic gates

Chapter 58 The theory of matrices and determinants

58.1 Matrix notation

58.2 Addition, subtraction and multiplication of matrices

58.3 The unit matrix

58.4 The determinant of a 2 by 2 matrix

58.5 The inverse or reciprocal of a 2 by 2 matrix

58.6 The determinant of a 3 by 3 matrix

58.7 The inverse or reciprocal of a 3 by 3 matrix

Chapter 59 The solution of simultaneous equations by matrices and determinants

59.1 Solution of simultaneous equations by matrices

59.2 Solution of simultaneous equations by determinants

59.3 Solution of simultaneous equations using Cramer’s rule

59.4 Solution of simultaneous equations using the Gaussian elimination method

Revision Test 16 Boolean algebra, logic circuits, matrices and determinants

Section 11 Statistics

Chapter 60 Presentation of statistical data

60.1 Some statistical terminology

60.2 Presentation of ungrouped data

60.3 Presentation of grouped data

Chapter 61 Mean, median, mode and standard deviation

61.1. Measures of central tendency

61.2. Mean, median and mode for discrete data

Mean

Median

Mode

61.3. Mean, median and mode for grouped data

Histogram

61.4. Standard deviation

(a) Discrete data

(b) Grouped data

61.5. Quartiles, deciles and percentiles

Chapter 62 Probability

62.1. Introduction to probability

Expectation

Dependent event

Independent event

Conditional probability

62.2 Laws of probability

The addition law of probability

The multiplication law of probability

62.3. Worked problems on probability

62.4. Further worked problems on probability

(a) With replacement

(b) Without replacement

62.5. Permutations and combinations

Permutations

Combinations

62.6. Bayes’ theorem

Revision Test 17 Presentation of statistical data, mean, median, mode, standard deviation and probability

Chapter 63 The binomial and Poisson distribution

63.1. The binomial distribution

Industrial inspection

Histogram of probabilities

63.2. The Poisson distribution

Histogram of probabilities

Chapter 64 The normal distribution

64.1. Introduction to the normal distribution

64.2. Testing for a normal distribution

Revision Test 18 The binomial, Poisson and normal distributions

Chapter 65 Linear correlation

65.1. Introduction to linear correlation

65.2. The Pearson product-moment formula for determining the linear correlation coefficient

65.3. The significance of a coefficient of correlation

65.4. Worked problems on linear correlation

Chapter 66 Linear regression

66.1. Introduction to linear regression

66.2. The least-squares regression lines

66.3. Worked problems on linear regression

Chapter 67 Sampling and estimation theories

67.1 Introduction

67.2 Sampling distributions

67.3 The sampling distribution of the means

67.4 The estimation of population parameters based on a large sample size

Point and interval estimates

Confidence intervals

67.5 Estimating the mean of a population based on a small sample size

Revision Test 19 Presentation of statistical data, mean, median, mode, standard deviation and probability

List of essential formulae

Number and algebra

Length in metric units:

Areas in metric units:

Volumes in metric units:

Laws of indices:

Factor theorem

Remainder theorem

Partial fractions

Quadratic formula:

Definition of a logarithm:

Laws of logarithms:

Exponential series:

Arithmetic progression:

Geometric progression:

Binomial series:

Newton Raphson iterative method

Trigonometry

Theorem of Pythagoras:

Identities:

Triangle formulae:

Compound angle formulae

Double angles

Products of sines and cosines into sums or differences:

Sums or differences of sines and cosines into products:

Cartesian and polar co-ordinates

Areas and volumes

Areas of plane figures:

Volumes and surface areas of regular solids:

Irregular areas

Trapezoidal rule

Mid-ordinate rule

Volume of irregular solids

For a sine wave:

Graphs

Equations of functions

Odd and even functions

Complex numbers

Differential calculus

Standard derivatives

Function of a function:

Parametric differentiation

Implicit function:

Maximum and minimum values:

Points of inflexion

Tangents and normals

Maclaurin’s series

Integral calculus

Standard integrals

Numerical integration

Trapezoidal rule

Second moment of area and radius of gyration

Area under a curve:

Differential equations

First order differential equations

Further number and algebra

Boolean algebra

Matrices:

Statistics and probability

Mean, median, mode and standard deviation

Bayes’ theorem

Binomial probability distribution

Poisson distribution

Product-moment formula for the linear correlation coefficient:

Symbols:

Standard error of the means

The relationship between sample mean and population mean

Estimating the mean of a population (σ known)

Estimating the mean of a population (σ unknown)

Estimating the standard deviation of a population

Estimating the mean of a population based on a small sample size

Answers Answers to Practice Exercises

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