Bird's basic engineering mathematics

Cover
Half Title
Dedication
Title Page
Copyright Page
Contents
Preface
Acknowledgements
1.
Basic arithmetic
1.1.
Introduction
1.2.
Revision of addition and subtraction
1.3.
Revision of multiplication and division
1.4.
Highest common factors and lowest common multiples
1.5.
Order of operation and brackets
2.
Fractions
2.1. Introduction
2.2.
Adding and subtracting fractions
2.3.
Multiplication and division of fractions
2.4.
Order of operation with fractions
Revision Test 1
3.
Decimals
3.1.
Introduction
3.2.
Converting decimals to fractions and vice versa
3.3.
Significant figures and decimal places
3.4.
Adding and subtracting decimal numbers
3.5.
Multiplying and dividing decimal numbers
4.
Using a calculator
4.1. Introduction
4.2. Adding, subtracting, multiplying and dividing
4.3.
Further calculator functions
4.4.
Evaluation of formulae
5.
Percentages
5.1.
Introduction
5.2.
Percentage calculations
5.3.
Further percentage calculations
5.4.
More percentage calculations
Revision Test 2
6.
Ratio and proportion
6.1.
Introduction
6.2.
Ratios
6.3.
Direct proportion
6.4.
Inverse proportion
7.
Powers, roots and laws of indices
7.1.
Introduction
7.2.
Powers and roots
7.3.
Laws of indices
8.
Units, prefixes and engineering notation
8.1.
Introduction
8.2.
SI units
8.3.
Common prefixes
8.4.
Standard form
8.5.
Engineering notation
8.6.
Metric conversions
8.7.
Metric - US/Imperial conversions
Revision Test 3
9.
Basic algebra
9.1.
Introduction
9.2.
Basic operations
9.3.
Laws of indices
10.
Further algebra
10.1.
Introduction
10.2.
Brackets
10.3.
Factorisation
10.4.
Laws of precedence
11.
Solving simple equations
11.1.
Introduction
11.2.
Solving equations
11.3.
Practical problems involving simple equations
Revision Test 4
12.
Transposing formulae
12.1.
Introduction
12.2.
Transposing formulae
12.3.
Further transposing of formulae
12.4.
More difficult transposing of formulae
13.
Solving simultaneous equations
13.1.
Introduction
13.2.
Solving simultaneous equations in two unknowns
13.3.
Further solving of simultaneous equations
13.4.
Solving more difficult simultaneous equations
13.5.
Practical problems involving simultaneous equations
13.6.
Solving simultaneous equations in three unknowns
Revision Test 5
14. Solving quadratic equations
14.1.
Introduction
14.2.
Solution of quadratic equations by factorisation
14.3.
Solution of quadratic equations by ‘completing the square’
14.4.
Solution of quadratic equations by formula
14.5.
Practical problems involving quadratic equations
14.6.
Solution of linear and quadratic equations simultaneously
15.
Logarithms
15.1.
Introduction to logarithms
15.2.
Laws of logarithms
15.3.
Indicial equations
15.4.
Graphs of logarithmic functions
16.
Exponential functions
16.1.
Introduction to exponential functions
16.2. The power series for ex
16.3.
Graphs of exponential functions
16.4.
Napierian logarithms
16.5.
Laws of growth and decay
Revision Test 6
17.
Straight line graphs
17.1.
Introduction to graphs
17.2.
Axes, scales and co-ordinates
17.3.
Straight line graphs
17.4.
Gradients, intercepts and equations of graphs
17.5.
Practical problems involving straight line graphs
18.
Graphs reducing non-linear laws to linear form
18.1.
Introduction
18.2.
Determination of law
18.3.
Revision of laws of logarithms
18.4.
Determination of laws involving logarithms
19.
Graphical solution of equations
19.1.
Graphical solution of simultaneous equations
19.2.
Graphical solution of quadratic equations
19.3.
Graphical solution of linear and quadratic equations simultaneously
19.4.
Graphical solution of cubic equations
20.
Graphs with logarithmic scales
20.1.
Logarithmic scales and logarithmic graph paper
20.2.
Graphs of the form y = axn
20.3.
Graphs of the form y = abx
20.4.
Graphs of the form y = aekx
Revision Test 7
21.
Angles and triangles
21.1.
Introduction
21.2.
Angular measurement
21.3.
Triangles
21.4.
Congruent triangles
21.5.
Similar triangles
21.6.
Construction of triangles
22.
Introduction to trigonometry
22.1.
Introduction
22.2.
The theorem of Pythagoras
22.3.
Sines, cosines and tangents
22.4.
Evaluating trigonometric ratios of acute angles
22.5.
Solving right-angled triangles
22.6.
Angles of elevation and depression
Revision Test 8
23.
Trigonometric waveforms
23.1.
Graphs of trigonometric functions
23.2.
Angles of any magnitude
23.3.
The production of sine and cosine waves
23.4.
Terminology involved with sine and cosine waves
23.5. Sinusoidal form: A sin(ωt ± α)
24.
Non-right-angled triangles and some practical applications
24.1.
The sine and cosine rules
24.2.
Area of any triangle
24.3.
Worked problems on the solution of triangles and their areas
24.4.
Further worked problems on the solution of triangles and their areas
24.5.
Practical situations involving trigonometry
24.6.
Further practical situations involving trigonometry
25.
Cartesian and polar co-ordinates
25.1.
Introduction
25.2.
Changing from Cartesian to polar co-ordinates
25.3.
Changing from polar to Cartesian co-ordinates
25.4.
Use of Pol/Rec functions on calculators
Revision Test 9
26.
Areas of common shapes
26.1.
Introduction
26.2.
Common shapes
26.3.
Areas of common shapes
26.4.
Areas of similar shapes
27.
The circle and its properties
27.1.
Introduction
27.2.
Properties of circles
27.3.
Radians and degrees
27.4.
Arc length and area of circles and sectors
27.5.
The equation of a circle
Revision Test 10
28.
Volumes and surface areas of common solids
28.1.
Introduction
28.2.
Volumes and surface areas of common shapes
28.3.
Summary of volumes and surface areas of common solids
28.4.
More complex volumes and surface areas
28.5.
Volumes and surface areas of frusta of pyramids and cones
28.6.
Volumes of similar shapes
29.
Irregular areas and volumes and mean values
29.1.
Areas of irregular figures
29.2.
Volumes of irregular solids
29.3.
Mean or average values of waveforms
Revision Test 11
30.
Vectors
30.1.
Introduction
30.2.
Scalars and vectors
30.3.
Drawing a vector
30.4.
Addition of vectors by drawing
30.5.
Resolving vectors into horizontal and vertical components
30.6.
Addition of vectors by calculation
30.7.
Vector subtraction
30.8.
Relative velocity
30.9. i, j and k notation
31.
Methods of adding alternating waveforms
31.1.
Combining two periodic functions
31.2.
Plotting periodic functions
31.3.
Determining resultant phasors by drawing
31.4.
Determining resultant phasors by the sine and cosine rules
31.5.
Determining resultant phasors by horizontal and vertical components
Revision Test 12
32.
Presentation of statistical data
32.1.
Some statistical terminology
32.2.
Presentation of ungrouped data
32.3.
Presentation of grouped data
33.
Mean, median, mode and standard deviation
33.1.
Measures of central tendency
33.2.
Mean, median and mode for discrete data
33.3.
Mean, median and mode for grouped data
33.4.
Standard deviation
33.5.
Quartiles, deciles and percentiles
34.
Probability
34.1.
Introduction to probability
34.2.
Laws of probability
Revision Test 13
35.
Introduction to differentiation
35.1.
Introduction to calculus
35.2.
Functional notation
35.3.
The gradient of a curve
35.4.
Differentiation from first principles
35.5 Differentiation of y = axn by the general rule
35.6.
Differentiation of sine and cosine functions
35.7.
Differentiation of eax and ln ax
35.8.
Summary of standard derivatives
35.9.
Successive differentiation
35.10.
Rates of change
35.11.
Differentiation of a product
35.12.
Differentiation of a quotient
35.13.
Function of a function
36.
Standard integration
36.1.
The process of integration
36.2.
The general solution of integrals of the form axn
36.3.
Standard integrals
36.4.
Definite integrals
36.5.
The area under a curve
Revision Test 14
37.
Number sequences
37.1.
Simple sequences
37.2.
The nth term of a series
37.3.
Arithmetic progressions
37.4.
Geometric progressions
38.
Binary, octal and hexadecimal numbers
38.1.
Introduction
38.2.
Binary numbers
38.3.
Octal numbers
38.4.
Hexadecimal numbers
Revision Test 15
List of formulae
Answers to Practice Exercises
Index