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Basic Engineering Mathematics PDF
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Basic Engineering Mathematics 5th Edition introduces and then consolidates basic mathematical principles and promotes awareness of mathematical concepts for students needing a broad base for further vocational studies. In this fifth edition, new material has been added to many of the chapters, particularly some of the earlier chapters, together with extra practice problems interspersed throughout the text. The extent of this fifth edition is such that four chapters from the previous edition have been removed and placed on the easily available website http://www.booksite.elsevier.com/newnes/bird. The chapters removed from the website are ‘Number sequences’, ‘Binary, octal and hexadecimal, ‘Inequalityties’, and ‘Graphs with logarithmic scales. The text is relevant to • ‘Mathematics for Engineering Technicians’ for BTEC First NQF Level 2 – Chapters 1–12, 16–18, 20, 21, 23, and 25–27 are needed for this module. • The mandatory ‘Mathematics for Technicians’ for BTEC National Certificate and National Diploma in Engineering, NQF Level 3 – Chapters 7–10, 14–17, 19, 20–23, 25–27, 31, 32, 34, and 35 are needed and, in addition, Chapters 1–6, 11 and 12 are helpful revision for this module. • Basic mathematics for a wide range of introductory/access/foundation mathematics courses. • GCSE revision and similar mathematics courses in English-speaking countries worldwide. Basic Engineering Mathematics 5th Edition provides a lead into Engineering Mathematics 6th Edition. Each topic considered in the text is presented in a way that assumes the reader has little previous knowledge of that topic. Each chapter begins with a brief outline of essential theory, definitions, formulae, laws, and procedures; however, these are kept to a minimum as problem-solving is extensively used to establish and exemplify the theory. It is intended that readers will gain real understanding by seeing problems solved and then solving similar problems themselves. This textbook contains some 750 worked problems, followed by over 1550 further problems (all with answers at the end of the book) contained within some 161 Practice Exercises; each Practice Exercise follows directly from the relevant section of work. In addition, 376 line diagrams enhance understanding of the theory. Where at all possible, the problems mirror potential practical situations found in engineering and science. Placed at regular intervals throughout the text are 14 Revision Tests (plus another for the website chapters) to check to understand. For example, Revision Test 1 covers material contained in Chapters 1 and 2, Revision Test 2 covers the material contained in Chapters 3–5, and so on. These Revision Tests do not have answers given since it is envisaged that lecturers/instructors could set the tests for students to attempt as part of their course structure. Lecturers/instructors may obtain a complimentary set of solutions of the Revision Tests in an Instructor’s Manual, available from the publishers via the internet – see http://www.booksite.elsevier.com/newnes/bird. At the end of the book, a list of relevant formulae contained within the text is included for the convenience of reference. The principle of learning by example is at the heart of Basic Engineering Mathematics 5th Edition.
Contents Of The Book :
Acknowledgements x
Instructor’s Manual xi
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 precedence and brackets
2 Fractions
2.1 Introduction
2.2 Adding and subtracting fractions
2.3 Multiplication and division of fractions
2.4 Order of precedence 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 Factorization
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 factorization
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 law 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
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
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 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
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
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 ln ax
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
36 Number sequences
36.1 Simple sequences
36.2 The n’th term of a series
36.3 Arithmetic progressions
36.4 Geometric progressions
37 Binary, octal and hexadecimal
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
Answers to practice exercises
Information Of The Book :
Title: Basic Engineering Mathematics Download PDF.
Language: English.
Size: 3,35 Mb.
Pages: 337.
Format: PDF.
Author: John Bird.