Basic Engineering Mathematics

Cover
Half Title
Dedication
Title Page
Copyright Page
Table of 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
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
Multiple choice questions Test 1
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
Multiple choice questions Test 2
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
Revision Test 7
20 Angles and triangles
20.1 Introduction
20.2 Angular measurement
20.3 Triangles
20.4 Congruent triangles
20.5 Similar triangles
20.6 Construction of triangles
21 Introduction to trigonometry
21.1 Introduction
21.2 The theorem of Pythagoras
21.3 Sines, cosines and tangents
21.4 Evaluating trigonometric ratios of acute angles
21.5 Solving right-angled triangles
21.6 Angles of elevation and depression
Revision Test 8
22 Trigonometric waveforms
22.1 Graphs of trigonometric functions
22.2 Angles of any magnitude
22.3 The production of sine and cosine waves
22.4 Terminology involved with sine and cosine waves
22.5 Sinusoidal form: Asin(ωt ±α)
23 Non-right-angled triangles and some practical applications
23.1 The sine and cosine rules
23.2 Area of any triangle
23.3 Worked problems on the solution of triangles and their areas
23.4 Further worked problems on the solution of triangles and their areas
23.5 Practical situations involving trigonometry
23.6 Further practical situations involving trigonometry
24 Cartesian and polar co-ordinates
24.1 Introduction
24.2 Changing from Cartesian to polar co-ordinates
24.3 Changing from polar to Cartesian co-ordinates
24.4 Use of Pol/Rec functions on calculators
Revision Test 9
Multiple choice questions Test 3
25 Areas of common shapes
25.1 Introduction
25.2 Common shapes
25.3 Areas of common shapes
25.4 Areas of similar shapes
26 The circle and its properties
26.1 Introduction
26.2 Properties of circles
26.3 Radians and degrees
26.4 Arc length and area of circles and sectors
26.5 The equation of a circle
Revision Test 10
27 Volumes and surface areas of common solids
27.1 Introduction
27.2 Volumes and surface areas of common shapes
27.3 Summary of volumes and surface areas of common solids
27.4 More complex volumes and surface areas
27.5 Volumes and surface areas of frusta of pyramids and cones
27.6 Volumes of similar shapes
28 Irregular areas and volumes and mean values
28.1 Areas of irregular figures
28.2 Volumes of irregular solids
28.3 Mean or average values of waveforms
Revision Test 11
29 Vectors
29.1 Introduction
29.2 Scalars and vectors
29.3 Drawing a vector
29.4 Addition of vectors by drawing
29.5 Resolving vectors into horizontal and vertical components
29.6 Addition of vectors by calculation
29.7 Vector subtraction
29.8 Relative velocity
29.9 i, j and k notation
30 Methods of adding alternating waveforms
30.1 Combining two periodic functions
30.2 Plotting periodic functions
30.3 Determining resultant phasors by drawing
30.4 Determining resultant phasors by the sine and cosine rules
30.5 Determining resultant phasors by horizontal and vertical components
Revision Test 12
Multiple choice questions Test 4
31 Presentation of statistical data
31.1 Some statistical terminology
31.2 Presentation of ungrouped data
31.3 Presentation of grouped data
32 Mean, median, mode and standard deviation
32.1 Measures of central tendency
32.2 Mean, median and mode for discrete data
32.3 Mean, median and mode for grouped data
32.4 Standard deviation
32.5 Quartiles, deciles and percentiles
33 Probability
33.1 Introduction to probability
33.2 Laws of probability
Revision Test 13
Multiple choice questions Test 5
34 Introduction to differentiation
34.1 Introduction to calculus
34.2 Functional notation
34.3 The gradient of a curve
34.4 Differentiation from first principles
34.5 Differentiation of y=axn by the general rule
34.6 Differentiation of sine and cosine functions
34.7 Differentiation of eax and lnax
34.8 Summary of standard derivatives
34.9 Successive differentiation
34.10 Rates of change
35 Introduction to integration
35.1 The process of integration
35.2 The general solution of integrals of the form axn
35.3 Standard integrals
35.4 Definite integrals
35.5 The area under a curve
Revision Test 14
Multiple choice questions Test 6
36 Number sequences
36.1 Simple sequences
36.2 The nth term of a series
36.3 Arithmetic progressions
36.4 Geometric progressions
37 Binary, octal and hexadecimal numbers
37.1 Introduction
37.2 Binary numbers
37.3 Octal numbers
37.4 Hexadecimal numbers
38 Inequalities
38.1 Introduction to inequalities
38.2 Simple inequalities
38.3 Inequalities involving a modulus
38.4 Inequalities involving quotients
38.5 Inequalities involving square functions
38.6 Quadratic inequalities
39 Graphs with logarithmic scales
39.1 Logarithmic scales and logarithmic graph paper
39.2 Graphs of the form y=axn
39.3 Graphs of the form y=abx
39.4 Graphs of the form y=aekx
Revision Test 15
Multiple choice questions Test 7
List of formulae
Answers to Practice Exercises
Answers to multiple choice questions
Index