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Bird's Engineering Mathematics 9th edition [Hardback]

(Defence College of Technical Training, UK)
  • Formāts: Hardback, 742 pages, height x width: 280x210 mm, weight: 1560 g, 36 Tables, color; 8 Tables, black and white; 521 Line drawings, black and white; 23 Halftones, black and white; 544 Illustrations, black and white
  • Izdošanas datums: 16-Mar-2021
  • Izdevniecība: Routledge
  • ISBN-10: 0367643790
  • ISBN-13: 9780367643799
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Bird's Engineering Mathematics 9th editionPalielināt
  • Formāts: Hardback, 742 pages, height x width: 280x210 mm, weight: 1560 g, 36 Tables, color; 8 Tables, black and white; 521 Line drawings, black and white; 23 Halftones, black and white; 544 Illustrations, black and white
  • Izdošanas datums: 16-Mar-2021
  • Izdevniecība: Routledge
  • ISBN-10: 0367643790
  • ISBN-13: 9780367643799
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780367643799.html
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Now in its ninth edition, Bird’s Engineering Mathematics has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, supported by practical engineering examples and applications to ensure that readers can relate theory to practice. Some 1,300 engineering situations/problems have been ‘flagged-up’ to help demonstrate that engineering cannot be fully understood without a good knowledge of mathematics.

The extensive and thorough topic coverage makes this a great text for a range of level 2 and 3 engineering courses – such as for aeronautical, construction, electrical, electronic, mechanical, manufacturing engineering and vehicle technology – including for BTEC First, National and Diploma syllabuses, City & Guilds Technician Certificate and Diploma syllabuses, and even for GCSE and A-level revision.

Its companion website at www.routledge.com/cw/bird provides resources for both students and lecturers, including full solutions for all 2,000 further questions, lists of essential formulae, multiple-choice tests, and illustrations, as well as full solutions to revision tests for course instructors.

Preface xiv
Section 1 Number and algebra
1(166)
1 Revision of fractions, decimals and percentages
3(10)
1.1 Fractions
3(3)
1.2 Ratio and proportion
6(1)
1.3 Decimals
7(2)
1.4 Percentages
9(4)
2 Indices, engineering notation and metric conversions
13(17)
2.1 Indices
13(4)
2.2 Standard form
17(1)
2.3 Engineering notation and common prefixes
18(2)
2.4 Metric conversions
20(3)
2.5 Metric - US/imperial conversions
23(7)
3 Binary, octal and hexadecimal numbers
30(11)
3.1 Introduction
30(1)
3.2 Binary numbers
31(3)
3.3 Octal numbers
34(2)
3.4 Hexadecimal numbers
36(5)
4 Calculations and evaluation of formulae
41(13)
4.1 Errors and approximations
41(2)
4.2 Use of calculator
43(2)
4.3 Conversion tables and charts
45(1)
4.4 Evaluation of formulae
46(6)
Revision Test 1
52(2)
5 Algebra
54(12)
5.1 Basic operations
54(2)
5.2 Laws of indices
56(2)
5.3 Brackets and factorisation
58(2)
5.4 Fundamental laws and precedence
60(2)
5.5 Direct and inverse proportionality
62(4)
6 Further algebra
66(7)
6.1 Polynomial division
66(2)
6.2 The factor theorem
68(2)
6.3 The remainder theorem
70(3)
7 Partial fractions
73(7)
7.1 Introduction to partial fractions
73(1)
7.2 Partial fractions with linear factors
74(2)
7.3 Partial fractions with repeated linear factors
76(1)
7.4 Partial fractions with quadratic factors
77(3)
8 Solving simple equations
80(9)
8.1 Expressions, equations and identities
80(1)
8.2 Worked problems on simple equations
81(1)
8.3 Further worked problems on simple equations
82(2)
8.4 Practical problems involving simple equations
84(1)
8.5 Further practical problems involving simple equations
85(3)
Revision Test 2
88(1)
9 Transposition of formulae
89(9)
9.1 Introduction to transposition of formulae
89(1)
9.2 Worked problems on transposition of formulae
89(2)
9.3 Further worked problems on transposition of formulae
91(2)
9.4 Harder worked problems on transposition of formulae
93(5)
10 Solving simultaneous equations
98(11)
10.1 Introduction to simultaneous equations
98(1)
10.2 Worked problems on simultaneous equations in two unknowns
98(2)
10.3 Further worked problems on simultaneous equations
100(2)
10.4 More difficult worked problems on simultaneous equations
102(2)
10.5 Practical problems involving simultaneous equations
104(5)
11 Solving quadratic equations
109(11)
11.1 Introduction to quadratic equations
109(1)
11.2 Solution of quadratic equations by factorisation
110(1)
11.3 Solution of quadratic equations by `completing the square'
111(2)
11.4 Solution of quadratic equations by formula
113(1)
11.5 Practical problems involving quadratic equations
114(3)
11.6 The solution of linear and quadratic equations simultaneously
117(3)
12 Inequalities
120(6)
12.1 Introduction to inequalities
120(1)
12.2 Simple inequalities
121(1)
12.3 Inequalities involving a modulus
121(1)
12.4 Inequalities involving quotients
122(1)
12.5 Inequalities involving square functions
123(1)
12.6 Quadratic inequalities
124(2)
13 Logarithms
126(9)
13.1 Introduction to logarithms
126(2)
13.2 Laws of logarithms
128(2)
13.3 Indicial equations
130(2)
13.4 Graphs of logarithmic functions
132(2)
Revision Test 3
134(1)
14 Exponential functions
135(12)
14.1 Introduction to exponential functions
135(1)
14.2 The power series for ex
136(2)
14.3 Graphs of exponential functions
138(1)
14.4 Napierian logarithms
139(3)
14.5 Laws of growth and decay
142(5)
15 Number sequences
147(9)
15.1 Arithmetic progressions
147(1)
15.2 Worked problems on arithmetic progressions
148(1)
15.3 Further worked problems on arithmetic progressions
149(1)
15.4 Geometric progressions
150(1)
15.5 Worked problems on geometric progressions
151(1)
15.6 Further worked problems on geometric progressions
152(2)
15.7 Combinations and permutations
154(2)
16 The binomial series
156(11)
16.1 Pascal's triangle
156(2)
16.2 The binomial series
158(1)
16.3 Worked problems on the binomial series
158(1)
16.4 Further worked problems on the binomial series
159(3)
16.5 Practical problems involving the binomial theorem
162(3)
Revision Test 4
165(2)
Section 2 Trigonometry
167(68)
17 Introduction to trigonometry
169(15)
17.1 Trigonometry
169(1)
17.2 The theorem of Pythagoras
170(1)
17.3 Trigonometric ratios of acute angles
171(2)
17.4 Fractional and surd forms of trigonometric ratios
173(1)
17.5 Evaluating trigonometric ratios of any angles
174(4)
17.6 Solution of right-angled triangles
178(1)
17.7 Angle of elevation and depression
179(2)
17.8 Trigonometric approximations for small angles
181(3)
18 Trigonometric waveforms
184(12)
18.1 Graphs of trigonometric functions
184(1)
18.2 Angles of any magnitude
185(2)
18.3 The production of a sine and cosine wave
187(1)
18.4 Sine and cosine curves
188(4)
18.5 Sinusoidal form A sin(w; ± a)
192(2)
18.6 Waveform harmonics
194(2)
19 Cartesian and polar co-ordinates
196(7)
19.1 Introduction
197(1)
19.2 Changing from Cartesian into polar co-ordinates
197(1)
19.3 Changing from polar into Cartesian co-ordinates
198(2)
19.4 Use of Pol/Rec functions on calculators
200(2)
Revision Test 5
202(1)
20 Triangles and some practical applications
203(11)
20.1 Sine and cosine rules
203(1)
20.2 Area of any triangle
204(1)
20.3 Worked problems on the solution of triangles and their areas
204(2)
20.4 Further worked problems on the solution of triangles and their areas
206(1)
20.5 Practical situations involving trigonometry
207(2)
20.6 Further practical situations involving trigonometry
209(5)
21 Trigonometric identities and equations
214(8)
21.1 Trigonometric identities
214(1)
21.2 Worked problems on trigonometric identities
215(1)
21.3 Trigonometric equations
216(1)
21.4 Worked problems (i) on trigonometric equations
217(1)
21.5 Worked problems (ii) on trigonometric equations
218(1)
21.6 Worked problems (iii) on trigonometric equations
219(1)
21.7 Worked problems (iv) on trigonometric equations
219(3)
22 Compound angles
222(13)
22.1 Compound angle formulae
222(2)
22.2 Conversion of a sin ωt + b cos ωt into R sin(ωt + α)
224(4)
22.3 Double angles
228(1)
22.4 Changing products of sines and cosines into sums or differences
229(1)
22.5 Changing sums or differences of sines and cosines into products
230(3)
Revision Test 6
233(2)
Section 3 Areas and volumes
235(52)
23 Areas of common shapes
237(10)
23.1 Introduction
237(1)
23.2 Properties of quadrilaterals
238(1)
23.3 Areas of common shapes
238(1)
23.4 Worked problems on areas of common shapes
239(3)
23.5 Further worked problems on areas of plane figures
242(1)
23.6 Worked problems on areas of composite figures
243(2)
23.7 Areas of similar shapes
245(2)
24 The circle and its properties
247(10)
24.1 Introduction
247(1)
24.2 Properties of circles
247(2)
24.3 Radians and degrees
249(1)
24.4 Arc length and area of circles and sectors
250(1)
24.5 Worked problems on arc length and area of circles and sectors
250(4)
24.6 The equation of a circle
254(3)
25 Volumes and surface areas of common solids
257(19)
25.1 Introduction
257(1)
25.2 Volumes and surface areas of regular solids
258(1)
25.3 Worked problems on volumes and surface areas of regular solids
258(2)
25.4 Further worked problems on volumes and surface areas of regular solids
260(6)
25.5 Volumes and surface areas of frusta of pyramids and cones
266(3)
25.6 The frustum and zone of a sphere
269(3)
25.7 Prismoidal rule
272(2)
25.8 Volumes of similar shapes
274(2)
26 Irregular areas and volumes and mean values of waveforms
276(11)
26.1 Area of irregular figures
277(2)
26.2 Volumes of irregular solids
279(1)
26.3 The mean or average value of a waveform
280(5)
Revision Test 7
285(2)
Section 4 Graphs
287(58)
27 Straight line graphs
289(15)
27.1 Introduction to graphs
289(1)
27.2 The straight line graph
290(5)
27.3 Practical problems involving straight line graphs
295(9)
28 Reduction of non-linear laws to linear form
304(9)
28.1 Determination of law
304(3)
28.2 Determination of law involving logarithms
307(6)
29 Graphs with logarithmic scales
313(8)
29.1 Logarithmic scales
313(1)
29.2 Graphs of the form y = axn
314(3)
29.3 Graphs of the form y = abx
317(1)
29.4 Graphs of the form y = aekx
318(3)
30 Graphical solution of equations
321(9)
30.1 Graphical solution of simultaneous equations
321(2)
30.2 Graphical solution of quadratic equations
323(3)
30.3 Graphical solution of linear and quadratic equations simultaneously
326(1)
30.4 Graphical solution of cubic equations
327(3)
31 Functions and their curves
330(15)
31.1 Standard curves
330(3)
31.2 Simple transformations
333(4)
31.3 Periodic functions
337(1)
31.4 Continuous and discontinuous functions
337(1)
31.5 Even and odd functions
338(1)
31.6 Inverse functions
339(4)
Revision Test 8
343(2)
Section 5 Complex numbers
345(20)
32 Complex numbers
347(13)
32.1 Cartesian complex numbers
347(2)
32.2 The Argand diagram
349(1)
32.3 Addition and subtraction of complex numbers
349(1)
32.4 Multiplication and division of complex numbers
350(2)
32.5 Complex equations
352(1)
32.6 The polar form of a complex number
353(1)
32.7 Multiplication and division in polar form
354(1)
32.8 Applications of complex numbers
355(5)
33 De Moivre's theorem
360(5)
33.1 Introduction
360(1)
33.2 Powers of complex numbers
360(1)
33.3 Roots of complex numbers
361(4)
Section 6 Vectors
365(30)
34 Vectors
367(16)
34.1 Introduction
367(1)
34.2 Scalars and vectors
367(1)
34.3 Drawing a vector
368(1)
34.4 Addition of vectors by drawing
368(3)
34.5 Resolving vectors into horizontal and vertical components
371(1)
34.6 Addition of vectors by calculation
372(5)
34.7 Vector subtraction
377(2)
34.8 Relative velocity
379(1)
34.9 I, j, and k notation
380(3)
35 Methods of adding alternating wav eforms
383(12)
35.1 Combination of two periodic functions
383(1)
35.2 Plotting periodic functions
384(1)
35.3 Determining resultant phasors by drawing
385(2)
35.4 Determining resultant phasors by the sine and cosine rules
387(1)
35.5 Determining resultant phasors by horizontal and vertical components
388(2)
35.6 Determining resultant phasors by complex numbers
390(4)
Revision Test 9
394(1)
Section 7 Differential calculus
395(72)
36 Introduction to differentiation
397(11)
36.1 Introduction to calculus
397(1)
36.2 Functional notation
397(1)
36.3 The gradient of a curve
398(1)
36.4 Differentiation from first principles
399(3)
36.5 Differentiation of y = axn by the general rule
402(1)
36.6 Differentiation of sine and cosine functions
403(2)
36.7 Differentiation of eax and In ax
405(3)
37 Methods of differentiation
408(9)
37.1 Differentiation of common functions
408(2)
37.2 Differentiation of a product
410(1)
37.3 Differentiation of a quotient
411(2)
37.4 Function of a function
413(1)
37.5 Successive differentiation
414(3)
38 Some applications of differentiation
417(18)
38.1 Rates of change
417(2)
38.2 Velocity and acceleration
419(3)
38.3 Turning points
422(3)
38.4 Practical problems involving maximum and minimum values
425(4)
38.5 Points of inflexion
429(1)
38.6 Tangents and normals
430(2)
38.7 Small changes
432(3)
39 Solving equations by Newton's method
435(4)
39.1 Introduction to iterative methods
435(1)
39.2 The Newton-Raphson method
436(1)
39.3 Worked problems on the Newton-Raphson method
436(3)
40 Maclaurin's series
439(8)
40.1 Introduction
440(1)
40.2 Derivation of Maclaurin's theorem
440(1)
40.3 Conditions of Maclaurin's series
441(1)
40.4 Worked problems on Maclaurin's series
441(5)
Revision Test 10
446(1)
41 Differentiation of parametric equations
447(6)
41.1 Introduction to parametric equations
447(1)
41.2 Some common parametric equations
448(1)
41.3 Differentiation in parameters
448(2)
41.4 Further worked problems on differentiation of parametric equations
450(3)
42 Differentiation of implicit functions
453(6)
42.1 Implicit functions
453(1)
42.2 Differentiating implicit functions
453(1)
42.3 Differentiating implicit functions containing products and quotients
454(1)
42.4 Further implicit differentiation
455(4)
43 Logarithmic differentiation
459(8)
43.1 Introduction to logarithmic differentiation
459(1)
43.2 Laws of logarithms
459(1)
43.3 Differentiation of logarithmic functions
460(1)
43.4 Differentiation of further logarithmic functions
460(2)
43.5 Differentiation of [ f(x)]x
462(3)
Revision Test 11
465(2)
Section 8 Integral calculus
467(92)
44 Standard integration
469(7)
44.1 The process of integration
469(1)
44.2 The general solution of integrals of the form axn
470(1)
44.3 Standard integrals
470(3)
44.4 Definite integrals
473(3)
45 Integration using algebraic substitutions
476(6)
45.1 Introduction
476(1)
45.2 Algebraic substitutions
476(1)
45.3 Worked problems on integration using algebraic substitutions
477(1)
45.4 Further worked problems on integration using algebraic substitutions
478(1)
45.5 Change of limits
479(3)
46 Integration using trigonometric substitutions
482(9)
46.1 Introduction
482(1)
46.2 Worked problems on integration of sin2 x, cos2 x, tan2 x and cot2 x
482(3)
46.3 Worked problems on integration of powers of sines and cosines
485(1)
46.4 Worked problems on integration of products of sines and cosines
486(1)
46.5 Worked problems on integration using the sin θ substitution
487(1)
46.6 Worked problems on integration using the tan θ substitution
488(2)
Revision Test 12
490(1)
47 Integration using partial fractions
491(5)
47.1 Introduction
491(1)
47.2 Integration using partial fractions with linear factors
491(2)
47.3 Integration using partial fractions with repeated linear factors
493(1)
47.4 Integration using partial fractions with quadratic factors
494(2)
48 The t = tan &heta;2 substitution
496(5)
48.1 Introduction
496(1)
48.2 Worked problems on the t = tan &heta;/2 substitution
497(1)
48.3 Further worked problems on the t = tan &heta;/2 substitution
498(3)
49 Integration by parts
501(6)
49.1 Introduction
501(1)
49.2 Worked problems on integration by parts
501(2)
49.3 Further worked problems on integration by parts
503(4)
50 Numerical integration
507(10)
50.1 Introduction
507(1)
50.2 The trapezoidal rule
507(3)
50.3 The mid-ordinate rule
510(1)
50.4 Simpson's rule
511(3)
50.5 Accuracy of numerical integration
514(2)
Revision Test 13
516(1)
51 Areas under and between curves
517(10)
51.1 Area under a curve
517(1)
51.2 Worked problems on the area under a curve
518(3)
51.3 Further worked problems on the area under a curve
521(3)
51.4 The area between curves
524(3)
52 Mean and root mean square values
527(5)
52.1 Mean or average values
527(2)
52.2 Root mean square values
529(3)
53 Volumes of solids of revolution
532(6)
53.1 Introduction
532(1)
53.2 Worked problems on volumes of solids of revolution
533(1)
53.3 Further worked problems on volumes of solids of revolution
534(4)
54 Centroids of simple shapes
538(10)
54.1 Centroids
538(1)
54.2 The first moment of area
538(1)
54.3 Centroid of area between a curve and the x-axis
539(1)
54.4 Centroid of area between a curve and the y-axis
539(1)
54.5 Worked problems on centroids of simple shapes
539(2)
54.6 Further worked problems on centroids of simple shapes
541(2)
54.7 Theorem of Pappus
543(5)
55 Second moments of area
548(11)
55.1 Second moments of area and radius of gyration
548(1)
55.2 Second moment of area of regular sections
549(1)
55.3 Parallel axis theorem
549(1)
55.4 Perpendicular axis theorem
549(1)
55.5 Summary of derived results
550(1)
55.6 Worked problems on second moments of area of regular sections
550(4)
55.7 Worked problems on second moments of area of composite areas
554(3)
Revision Test 14
557(2)
Section 9 Differential equations
559(12)
56 Introduction to differential equations
561(10)
56.1 Family of curves
561(1)
56.2 Differential equations
562(1)
56.3 The solution of equations of the form dy/dx =∞(x)
563(1)
56.4 The solution of equations of the form dy/dx =∞(y)
564(2)
56.5 The solution of equations of the form dy/dx =∞(x)·e;∞(y)
566(4)
Revision Test 15
570(1)
Section 10 Further number and algebra
571(44)
57 Boolean algebra and logic circuits
573(19)
57.1 Boolean algebra and switching circuits
574(4)
57.2 Simplifying Boolean expressions
578(1)
57.3 Laws and rules of Boolean algebra
578(2)
57.4 De Morgan's laws
580(1)
57.5 Karnaugh maps
581(4)
57.6 Logic circuits
585(4)
57.7 Universal logic gates
589(3)
58 The theory of matrices and determinants
592(11)
58.1 Matrix notation
592(1)
58.2 Addition, subtraction and multiplication of matrices
593(3)
58.3 The unit matrix
596(1)
58.4 The determinant of a 2 by 2 matrix
596(1)
58.5 The inverse or reciprocal of a 2 by 2 matrix
597(1)
58.6 The determinant of a 3 by 3 matrix
598(2)
58.7 The inverse or reciprocal of a 3 by 3 matrix
600(3)
59 The solution of simultaneous equations by matrices and determinants
603(12)
59.1 Solution of simultaneous equations by matrices
603(3)
59.2 Solution of simultaneous equations by determinants
606(3)
59.3 Solution of simultaneous equations using Cramers rule
609(1)
59.4 Solution of simultaneous equations using the Gaussian elimination method
610(3)
Revision Test 16
613(2)
Section 11 Statistics
615(75)
60 Presentation of statistical data
617(12)
60.1 Some statistical terminology
618(1)
60.2 Presentation of ungrouped data
619(3)
60.3 Presentation of grouped data
622(7)
61 Mean, median, mode and standard deviation
629(8)
61.1 Measures of central tendency
629(1)
61.2 Mean, median and mode for discrete data
630(1)
61.3 Mean, median and mode for grouped data
631(1)
61.4 Standard deviation
632(2)
61.5 Quartiles, deciles and percentiles
634(3)
62 Probability
637(12)
62.1 Introduction to probability
638(1)
62.2 Laws of probability
638(1)
62.3 Worked problems on probability
639(2)
62.4 Further worked problems on probability
641(3)
62.5 Permutations and combinations
644(1)
62.6 Bayes' theorem
645(3)
Revision Test 17
648(1)
63 The binomial and Poisson distribution
649(7)
63.1 The binomial distribution
649(3)
63.2 The Poisson distribution
652(4)
64 The normal distribution
656(10)
64.1 Introduction to the normal distribution
656(5)
64.2 Testing for a normal distribution
661(4)
Revision Test 18
665(1)
65 Linear correlation
666(5)
65.1 Introduction to linear correlation
666(1)
65.2 The Pearson product-moment formula for determining the linear correlation coefficient
666(1)
65.3 The significance of a coefficient of correlation
667(1)
65.4 Worked problems on linear correlation
667(4)
66 Linear regression
671(6)
66.1 Introduction to linear regression
671(1)
66.2 The least-squares regression lines
671(1)
66.3 Worked problems on linear regression
672(5)
67 Sampling and estimation theories
677(13)
67.1 Introduction
677(1)
67.2 Sampling distributions
677(1)
67.3 The sampling distribution of the means
678(3)
67.4 The estimation of population parameters based on a large sample size
681(4)
67.5 Estimating the mean of a population based on a small sample size
685(4)
Revision Test 19
689(1)
List of essential formulae 690(11)
Answers to Practice Exercises 701(37)
Index 738
John Bird, BSc (Hons), CEng, CMath, CSci, FIMA, FIET, FCollT, is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with Examiner responsibilities for Advanced Mathematics with City and Guilds and examining for the International Baccalaureate Organisation. He has over 45 years experience of successfully teaching, lecturing, instructing, training, educating and planning trainee engineers study programmes. He is the author of 146 textbooks on engineering, science and mathematical subjects, with worldwide sales of over one million copies. He is a chartered engineer, a chartered mathematician, a chartered scientist and a Fellow of three professional institutions. He has recently retired from lecturing at the Royal Navy's Defence College of Marine Engineering in the Defence College of Technical Training at H.M.S. Sultan, Gosport, Hampshire, UK, one of the largest engineering training establishments in Europe.