Basic Engineering Mathematics Fifth Edition by John Bird ISBN 978-1856176972 1856176975
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ISBN 10: 1856176975
ISBN 13: 978-1856176972
Author: John Bird
Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically to the needs of engineers. The result is a unique book written for engineering students that takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult.
Now in its fifth edition, Basic Engineering Mathematics is an established textbook that all students requiring a fundamental knowledge of mathematics of engineering with find essential reading. The content has been designed to meet the needs of students studying Level 2 courses, including GCSE Engineering, the Diploma, and BTEC First specifications. Level 3 students will also find this text to be a useful resource for getting to grips with essential mathematics concepts, because the compulsory topics in BTEC National and A Level Engineering courses are also fully addressed.
John Bird’s approach is based on numerous worked examples, supported by 750 worked problems and 1550 further problems contained within exercises throughout the text. In addition, 14 revision tests are included at regular intervals. Ideal for use as tests or homework, full solutions to the revision tests are supplied on the accompanying instructor’s website.
Table of contents:
Preface
Acknowledgements
Introduction
1 Basic Arithmetic
4.1. Introduction
4.2. Revision of Addition and Subtraction
4.3. Revision of Multiplication and Division
2 Fractions
5.1. Introduction
5.2. Adding and Subtracting Fractions
5.3. Multiplication and Division of Fractions
5.4. Order of Precedence with Fractions
3 Decimals
6.1. Introduction
6.2. Converting Decimals to Fractions and Vice-Versa
6.3. Significant Figures and Decimal Places
6.4. Adding and Subtracting Decimal Numbers
6.5. Multiplying and Dividing Decimal Numbers
4 Using a Calculator
7.1. Introduction
7.2. Adding, Subtracting, Multiplying and Dividing
7.3. Further Calculator Functions
7.4. Evaluation of Formulae
5 Percentages
8.1. Introduction
8.2. Percentage Calculations
8.3. Further Percentage Calculations
8.4. More Percentage Calculations
6 Ratio and Proportion
9.1. Introduction
9.2. Ratios
9.3. Direct Proportion
9.4. Inverse Proportion
7 Powers, Roots and Laws of Indices
10.1. Powers and Roots
10.2. Laws of Indices
8 Units, Prefixes and Engineering Notation
11.1. Introduction
11.2. SI Units
11.3. Common Prefixes
11.4. Standard Form
11.5. Engineering Notation
9 Further Algebra
12.1. Introduction
12.2. Basic Operations
12.3. Laws of Indices
10 Further Algebra
13.1. Introduction
13.2. Brackets
13.3. Factorization
13.4. Laws of Precedence
11 Solving Simple Equations
14.1. Introduction
14.2. Solving Equations
14.3. Practical Problems Involving Simple Equations
12 Transposing Formulae
15.1. Introduction
15.2. Transposing Formulae
15.3. Further Transposing of Formulae
15.4. More Difficult Transposing of Formulae
13 Solving Simultaneous Equations
16.1. Introduction
16.2. Solving Simultaneous Equations in Two Unknowns
16.3. Further Solving of Simultaneous Equations
Revision Test 1
Revision Test 2
Revision Test 3
Revision Test 4
Instructor’s Manual
Highest Common Factors and Lowest Common Multiples
13 Solving Simultaneous Equations
1.1. Solving Simultaneous Equations in Two Unknowns
1.2. Further Solving of Simultaneous Equations
1.3. Solving More Difficult Simultaneous Equations
1.4. Practical Problems Involving Simultaneous Equations
1.5. Solving Simultaneous Equations in Three Unknowns
14 Solving Quadratic Equations
2.1. Introduction
2.2. Solution of Quadratic Equations by Factorization
2.3. Solution of Quadratic Equations by Completing the Square
2.4. Solution of Quadratic Equations by Formula
2.5. Practical Problems Involving Quadratic Equations
2.6. Solution of Linear and Quadratic Equations Simultaneously
15 Logarithms
3.1. Introduction to Logarithms
3.2. Laws of Logarithms
3.3. Indicial Equations
3.4. Graphs of Logarithmic Functions
16 Exponential Functions
4.1. Introduction to Exponential Functions
4.2. The Power Series
4.3. Graphs of Exponential Functions
4.4. Napierian Logarithms
4.5. Laws of Growth and Decay
17 Straight Line Graphs
5.1. Introduction to Graphs
5.2. Axes, Scales and Coordinates
5.3. Straight Line Graphs
5.4. Gradients, Intercepts and Equations of Graphs
5.5. Practical Problems Involving Straight Line Graphs
18 Graphs Reducing Non-linear Laws to Linear Form
6.1. Introduction
6.2. Determination of Law
6.3. Revision of Laws of Logarithms
6.4. Determination of Law Involving Logarithms
19 Graphical Solution of Equations
7.1. Graphical Solution of Simultaneous Equations
7.2. Graphical Solution of Quadratic Equations
7.3. Graphical Solution of Linear and Quadratic Equations Simultaneously
7.4. Graphical Solution of Cubic Equations
20 Angles and Triangles
8.1. Introduction
8.2. Angular Measurement
8.3. Triangles
8.4. Congruent Triangles
8.5. Similar Triangles
8.6. Construction of Triangles
21 Introduction to Trigonometry
9.1. Introduction
9.2. The Theorem of Pythagoras
9.3. Sines, Cosines and Tangents
9.4. Evaluating Trigonometric Ratios of Acute Angles
9.5. Solving Right-angled Triangles
9.6. Angles of Elevation and Depression
22 Trigonometric Waveforms
10.1. Graphs of Trigonometric Functions
10.2. Angles of Any Magnitude
10.3. The Production of Sine and Cosine Waves
10.4. Terminology Involved with Sine and Cosine Waves
10.5. Sinusoidal Form: A sin(θ)
23 Non-right-angled Triangles and Some Practical Applications
11.1. The Sine and Cosine Rules
11.2. Area of Any Triangle
11.3. Worked Problems on the Solution of Triangles and Their Areas
11.4. Further Worked Problems on the Solution of Triangles and Their Areas
11.5. Practical Situations Involving Trigonometry
11.6. Further Practical Situations Involving Trigonometry
24 Cartesian and Polar Coordinates
12.1. Introduction
12.2. Changing from Cartesian to Polar Coordinates
12.3. Changing from Polar to Cartesian Coordinates
12.4. Use of Pol/Rec Functions on Calculators
Revision Tests
13.1. Revision Test 5
13.2. Revision Test 6
13.3. Revision Test 7
13.4. Revision Test 8
Revision Test 9
25 Areas of Common Shapes
2.1. Introduction
2.2. Common Shapes
2.3. Areas of Common Shapes
2.4. Areas of Similar Shapes
26 The Circle
3.1. Introduction
3.2. Properties of Circles
3.3. Radians and Degrees
3.4. Arc Length and Area of Circles and Sectors
3.5. The Equation of a Circle
27 Volumes of Common Solids
4.1. Introduction
4.2. Volumes and Surface Areas of Common Shapes
4.3. Summary of Volumes and Surface Areas of Common Solids
4.4. More Complex Volumes and Surface Areas
4.5. Volumes and Surface Areas of Frusta of Pyramids and Cones
4.6. Volumes of Similar Shapes
28 Irregular Areas and Volumes, and Mean Values
5.1. Areas of Irregular Figures
5.2. Volumes of Irregular Solids
5.3. Mean or Average Values of Waveforms
29 Vectors
6.1. Introduction
6.2. Scalars and Vectors
6.3. Drawing a Vector
6.4. Addition of Vectors by Drawing
6.5. Resolving Vectors into Horizontal and Vertical Components
6.6. Addition of Vectors by Calculation
6.7. Vector Subtraction
6.8. Relative Velocity
6.9. i, j and k Notation
30 Methods of Adding Alternating Waveforms
7.1. Combining Two Periodic Functions
7.2. Plotting Periodic Functions
7.3. Determining Resultant Phasors by Drawing
7.4. Determining Resultant Phasors by the Sine and Cosine Rules
7.5. Determining Resultant Phasors by Horizontal and Vertical Components
31 Presentation of Statistical Data
8.1. Some Statistical Terminology
8.2. Presentation of Ungrouped Data
8.3. Presentation of Grouped Data
32 Mean, Median, Mode and Standard Deviation
9.1. Measures of Central Tendency
9.2. Mean, Median and Mode for Discrete Data
9.3. Mean, Median and Mode for Grouped Data
9.4. Standard Deviation
9.5. Quartiles, Deciles and Percentiles
33 Probability
10.1. Introduction to Probability
10.2. Laws of Probability
34 Introduction to Differentiation
11.1. Introduction to Calculus
11.2. Functional Notation
11.3. The Gradient of a Curve
11.4. Differentiation from First Principles
11.5. Differentiation of y = axⁿ by the General Rule
11.6. Differentiation of Sine and Cosine Functions
11.7. Differentiation of e and ln ax
11.8. Summary of Standard Derivatives
11.9. Successive Differentiation
11.10. Rates of Change
35 Introduction to Integration
12.1. The Process of Integration
12.2. The General Solution of Integrals of the Form ax
12.3. Standard Integrals
12.4. Definite Integrals
12.5. The Area under a Curve
Revision Tests
13.1. Revision Test 10
13.2. Revision Test 11
13.3. Revision Test 12
13.4. Revision Test 13
13.5. Revision Test 14
List of Formulae
Answers to Practice Exercises
Index
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