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Bird's Higher Engineering Mathematics 9th edition [Mīkstie vāki]

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(Defence College of Technical Training, UK)
  • Formāts: Paperback / softback, 916 pages, height x width: 280x210 mm, weight: 2450 g, 251 Tables, color; 572 Line drawings, black and white; 31 Halftones, black and white; 603 Illustrations, black and white
  • Izdošanas datums: 26-Mar-2021
  • Izdevniecība: Routledge
  • ISBN-10: 0367643731
  • ISBN-13: 9780367643737
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Bird's Higher Engineering Mathematics 9th editionPalielināt
  • Formāts: Paperback / softback, 916 pages, height x width: 280x210 mm, weight: 2450 g, 251 Tables, color; 572 Line drawings, black and white; 31 Halftones, black and white; 603 Illustrations, black and white
  • Izdošanas datums: 26-Mar-2021
  • Izdevniecība: Routledge
  • ISBN-10: 0367643731
  • ISBN-13: 9780367643737
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Now in its ninth edition, Bird’s Higher 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 1,200 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 an ideal text for undergraduate degree courses, foundation degrees, and for higher-level vocational courses such as Higher National Certificate and Diploma courses in engineering disciplines.

Its companion website at www.routledge.com/cw/bird provides resources for both students and lecturers, including full solutions for all 2,100 further questions, lists of essential formulae, multiple-choice tests, and illustrations, as well as full solutions to revision tests for course instructors.

Preface xiv
Syllabus guidance xvi
Section A Number and algebra
1(86)
1 Algebra
3(1)
1.1 Introduction
3(1)
1.2 Revision of basic laws
3(2)
1.3 Revision of equations
5(4)
1.4 Polynomial division
9(2)
1.5 The factor theorem
11(2)
1.6 The remainder theorem
13(4)
2 Partial fractions
17(7)
2.1 Introduction to partial fractions
17(1)
2.2 Partial fractions with linear factors
17(3)
2.3 Partial fractions with repeated linear factors
20(2)
2.4 Partial fractions with quadratic factors
22(2)
3 Logarithms
24(8)
3.1 Introduction to logarithms
24(2)
3.2 Laws of logarithms
26(2)
3.3 Indicial equations
28(2)
3.4 Graphs of logarithmic functions
30(2)
4 Exponential functions
32(16)
4.1 Introduction to exponential functions
32(1)
4.2 The power series for ex
33(2)
4.3 Graphs of exponential functions
35(1)
4.4 Napierian logarithms
36(4)
4.5 Laws of growth and decay
40(3)
4.6 Reduction of exponential laws to linear form
43(4)
Revision Test 1
47(1)
5 The binomial series
48(9)
5.1 Pascal's triangle
48(2)
5.2 The binomial series
50(1)
5.3 Worked problems on the binomial series
50(1)
5.4 Further worked problems on the binomial series
51(3)
5.5 Practical problems involving the binomial theorem
54(3)
6 Solving equations by iterative methods
57(8)
6.1 Introduction to iterative methods
57(1)
6.2 The bisection method
58(3)
6.3 An algebraic method of successive approximations
61(4)
7 Boolean algebra and logic circuits
65(22)
7.1 Boolean algebra and switching circuits
66(4)
7.2 Simplifying Boolean expressions
70(1)
7.3 Laws and rules of Boolean algebra
70(2)
7.4 De Morgan's laws
72(1)
7.5 Karnaugh maps
73(4)
7.6 Logic circuits
77(4)
7.7 Universal logic gates
81(4)
Revision Test 2
85(2)
Section B Geometry and trigonometry
87(102)
8 Introduction to trigonometry
89(22)
8.1 Trigonometry
90(1)
8.2 The theorem of Pythagoras
90(1)
8.3 Trigonometric ratios of acute angles
91(2)
8.4 Evaluating trigonometric ratios
93(4)
8.5 Solution of right-angled triangles
97(2)
8.6 Angles of elevation and depression
99(1)
8.7 Sine and cosine rules
100(1)
8.8 Area of any triangle
101(1)
8.9 Worked problems on the solution of triangles and finding their areas
101(1)
8.10 Further worked problems on solving triangles and finding their areas
102(2)
8.11 Practical situations involving trigonometry
104(2)
8.12 Further practical situations involving trigonometry
106(5)
9 Cartesian and polar co-ordinates
111(6)
9.1 Introduction
112(1)
9.2 Changing from Cartesian into polar co-ordinates
112(2)
9.3 Changing from polar into Cartesian co-ordinates
114(1)
9.4 Use of Pol/Rec functions on calculators
115(2)
10 The circle and its properties
117(15)
10.1 Introduction
117(1)
10.2 Properties of circles
117(2)
10.3 Radians and degrees
119(1)
10.4 Arc length and area of circles and sectors
120(3)
10.5 The equation of a circle
123(2)
10.6 Linear and angular velocity
125(1)
10.7 Centripetal force
126(4)
Revision Test 3
130(2)
11 Trigonometric waveforms
132(19)
11.1 Graphs of trigonometric functions
132(1)
11.2 Angles of any magnitude
133(3)
11.3 The production of a sine and cosine wave
136(1)
11.4 Sine and cosine curves
137(4)
11.5 Sinusoidal form A sin(ωt ±α)
141(3)
11.6 Harmonic synthesis with complex waveforms
144(7)
12 Hyperbolic functions
151(10)
12.1 Introduction to hyperbolic functions
151(2)
12.2 Graphs of hyperbolic functions
153(2)
12.3 Hyperbolic identities
155(2)
12.4 Solving equations involving hyperbolic functions
157(2)
12.5 Series expansions for cosh x and sinh x
159(2)
13 Trigonometric identities and equations
161(8)
13.1 Trigonometric identities
161(1)
13.2 Worked problems on trigonometric identities
162(1)
13.3 Trigonometric equations
163(1)
13.4 Worked problems (i) on trigonometric equations
164(1)
13.5 Worked problems (ii) on trigonometric equations
165(1)
13.6 Worked problems (iii) on trigonometric equations
166(1)
13.7 Worked problems (iv) on trigonometric equations
166(3)
14 The relationship between trigonometric and hyperbolic functions
169(4)
14.1 The relationship between trigonometric and hyperbolic functions
169(1)
14.2 Hyperbolic identities
170(3)
15 Compound angles
173(16)
15.1 Compound angle formulae
173(2)
15.2 Conversion of a sin ωt + b cos cot ωt into R sin(ωt + α)
175(4)
15.3 Double angles
179(2)
15.4 Changing products of sines and cosines into sums or differences
181(1)
15.5 Changing sums or differences of sines and cosines into products
182(1)
15.6 Power waveforms in a.c. circuits
183(4)
Revision Test 4
187(2)
Section C Graphs
189(36)
16 Functions and their curves
191(22)
16.1 Standard curves
191(3)
16.2 Simple transformations
194(5)
16.3 Periodic functions
199(1)
16.4 Continuous and discontinuous functions
199(1)
16.5 Even and odd functions
200(1)
16.6 Inverse functions
201(2)
16.7 Asymptotes
203(5)
16.8 Brief guide to curve sketching
208(1)
16.9 Worked problems on curve sketching
208(5)
17 Irregular areas, volumes and mean values of waveforms
213(12)
17.1 Areas of irregular figures
213(3)
17.2 Volumes of irregular solids
216(1)
17.3 The mean or average value of a waveform
217(6)
Revision Test 5
223(2)
Section D Complex numbers
225(26)
18 Complex numbers
227(14)
18.1 Cartesian complex numbers
228(1)
18.2 The Argand diagram
229(1)
18.3 Addition and subtraction of complex numbers
229(1)
18.4 Multiplication and division of complex numbers
230(2)
18.5 Complex equations
232(1)
18.6 The polar form of a complex number
233(2)
18.7 Multiplication and division in polar form
235(1)
18.8 Applications of complex numbers
236(5)
19 De Moivre's theorem
241(10)
19.1 Introduction
242(1)
19.2 Powers of complex numbers
242(1)
19.3 Roots of complex numbers
243(2)
19.4 The exponential form of a complex number
245(1)
19.5 Introduction to locus problems
246(5)
Section E Matrices and determinants
251(32)
20 The theory of matrices and determinants
253(12)
20.1 Matrix notation
253(1)
20.2 Addition, subtraction and multiplication of matrices
254(3)
20.3 The unit matrix
257(1)
20.4 The determinant of a 2 by 2 matrix
257(1)
20.5 The inverse or reciprocal of a 2 by 2 matrix
258(1)
20.6 The determinant of a 3 by 3 matrix
259(2)
20.7 The inverse or reciprocal of a 3 by 3 matrix
261(4)
21 Applications of matrices and determinants
265(18)
21.1 Solution of simultaneous equations by matrices
266(2)
21.2 Solution of simultaneous equations by determinants
268(3)
21.3 Solution of simultaneous equations using Cramer's rule
271(1)
21.4 Solution of simultaneous equations using the Gaussian elimination method
272(2)
21.5 Stiffness matrix
274(1)
21.6 Eigenvalues and eigenvectors
275(6)
Revision Test 6
281(2)
Section F Vector geometry
283(42)
22 Vectors
285(16)
22.1 Introduction
285(1)
22.2 Scalars and vectors
285(1)
22.3 Drawing a vector
286(1)
22.4 Addition of vectors by drawing
287(2)
22.5 Resolving vectors into horizontal and vertical components
289(1)
22.6 Addition of vectors by calculation
290(5)
22.7 Vector subtraction
295(2)
22.8 Relative velocity
297(1)
22.9 I, J and K notation
298(3)
23 Methods of adding alternating waveforms
301(11)
23.1 Combination of two periodic functions
301(1)
23.2 Plotting periodic functions
302(1)
23.3 Determining resultant phasors by drawing
303(2)
23.4 Determining resultant phasors by the sine and cosine rules
305(1)
23.5 Determining resultant phasors by horizontal and vertical components
306(2)
23.6 Determining resultant phasors by using complex numbers
308(4)
24 Scalar and vector products
312(13)
24.1 The unit triad
312(1)
24.2 The scalar product of two vectors
313(4)
24.3 Vector products
317(4)
24.4 Vector equation of a line
321(2)
Revision Test 7
323(2)
Section G Differential calculus
325(96)
25 Methods of differentiation
327(13)
25.1 Introduction to calculus
327(1)
25.2 The gradient of a curve
327(1)
25.3 Differentiation from first principles
328(1)
25.4 Differentiation of common functions
329(3)
25.5 Differentiation of a product
332(2)
25.6 Differentiation of a quotient
334(1)
25.7 Function of a function
335(2)
25.8 Successive differentiation
337(3)
26 Some applications of differential inn
340(23)
26.1 Rates of change
340(2)
26.2 Velocity and acceleration
342(3)
26.3 The Newton-Raphson method
345(3)
26.4 Turning points
348(3)
26.5 Practical problems involving maximum and minimum values
351(4)
26.6 Points of inflexion
355(2)
26.7 Tangents and normals
357(1)
26.8 Small changes
358(4)
Revision Test 8
362(1)
27 Differentiation of parametric equations
363(6)
27.1 Introduction to parametric equations
363(1)
27.2 Some common parametric equations
364(1)
27.3 Differentiation in parameters
364(2)
27.4 Further worked problems on differentiation of parametric equations
366(3)
28 Differentiation of implicit functions
369(6)
28.1 Implicit functions
369(1)
28.2 Differentiating implicit functions
369(1)
28.3 Differentiating implicit functions containing products and quotients
370(1)
28.4 Further implicit differentiation
371(4)
29 Logarithmic differentiation
375(7)
29.1 Introduction to logarithmic differentiation
375(1)
29.2 Laws of logarithms
375(1)
29.3 Differentiation of logarithmic functions
376(1)
29.4 Differentiation of further logarithmic functions
376(2)
29.5 Differentiation of [ f(x)]x
378(3)
Revision Test 9
381(1)
30 Differentiation of hyperbolic functions
382(4)
30.1 Standard differential coefficients of hyperbolic functions
382(1)
30.2 Further worked problems on differentiation of hyperbolic functions
383(3)
31 Differentiation of inverse trigonometric and hyperbolic functions
386(11)
31.1 Inverse functions
386(2)
31.2 Differentiation of inverse trigonometric functions
388(3)
31.3 Logarithmic forms of the inverse hyperbolic functions
391(2)
31.4 Differentiation of inverse hyperbolic functions
393(4)
32 Partial differentiation
397(7)
32.1 Introduction to partial derivatives
397(1)
32.2 First-order partial derivatives
397(3)
32.3 Second-order partial derivatives
400(4)
33 Total differential, rates of change and small changes
404(7)
33.1 Total differential
404(1)
33.2 Rates of change
405(3)
33.3 Small changes
408(3)
34 Maxima, minima and saddle points for functions of two variables
411(10)
34.1 Functions of two independent variables
411(1)
34.2 Maxima, minima and saddle points
412(1)
34.3 Procedure to determine maxima, minima and saddle points for functions of two variables
413(1)
34.4 Worked problems on maxima, minima and saddle points for functions of two variables
413(2)
34.5 Further worked problems on maxima, minima and saddle points for functions of two variables
415(5)
Revision Test 10
420(1)
Section H Integral calculus
421(102)
35 Standard integration
423(8)
35.1 The process of integration
423(1)
35.2 The general solution of integrals of the form axn
424(1)
35.3 Standard integrals
424(3)
35.4 Definite integrals
427(4)
36 Some applications of integration
431(19)
36.1 Introduction
432(1)
36.2 Areas under and between curves
432(1)
36.3 Mean and rms values
433(2)
36.4 Volumes of solids of revolution
435(1)
36.5 Centroids
436(2)
36.6 Theorem of Pappus
438(2)
36.7 Second moments of area of regular sections
440(9)
Revision Test 11
449(1)
37 Maclaurin's series and limiting values
450(11)
37.1 Introduction
451(1)
37.2 Derivation of Maclaurin's theorem
451(1)
37.3 Conditions of Maclaurin's series
452(1)
37.4 Worked problems on Maclaurin's series
452(3)
37.5 Numerical integration using Maclaurin's series
455(2)
37.6 Limiting values
457(4)
38 Integration using algebraic substitutions
461(6)
38.1 Introduction
461(1)
38.2 Algebraic substitutions
461(1)
38.3 Worked problems on integration using algebraic substitutions
462(1)
38.4 Further worked problems on integration using algebraic substitutions
463(1)
38.5 Change of limits
464(3)
39 Integration using trigonometric and hyperbolic substitutions
467(12)
39.1 Introduction
467(1)
39.2 Worked problems on integration of sin2 x, cos2 x, tan2 x and cot2 x
467(3)
39.3 Worked problems on integration of powers of sines and cosines
470(1)
39.4 Worked problems on integration of products of sines and cosines
471(1)
39.5 Worked problems on integration using the sin θ substitution
472(2)
39.6 Worked problems on integration using the tan θ substitution
474(1)
39.7 Worked problems on integration using the sinh θ substitution
474(2)
39.8 Worked problems on integration using the cosh θ substitution
476(3)
40 Integration using partial fractions
479(6)
40.1 Introduction
479(1)
40.2 Integration using partial fractions with linear factors
479(2)
40.3 Integration using partial fractions with repeated linear factors
481(1)
40.4 Integration using partial fractions with quadratic factors
482(3)
41 The t = tan θ/2 substitution
485(6)
41.1 Introduction
485(1)
41.2 Worked problems on the t = tan θ/2 substitution
486(1)
41.3 Further worked problems on the t = tan θ/2 substitution
487(3)
Revision Test 12
490(1)
42 Integration by parts
491(6)
42.1 Introduction
491(1)
42.2 Worked problems on integration by parts
491(2)
42.3 Further worked problems on integration by parts
493(4)
43 Reduction formulae
497(9)
43.1 Introduction
497(1)
43.2 Using reduction formulae for integrals of the form ∞xnexdx
497(1)
43.3 Using reduction formulae for integrals of the form ∞xncosxdx and ∞xnsinxdx
498(3)
43.4 Using reduction formulae for integrals of the form ∞sinnxdx and ∞cosnxdx
501(2)
43.5 Further reduction formulae
503(3)
44 Double and triple integrals
506(6)
44.1 Double integrals
506(2)
44.2 Triple integrals
508(4)
45 Numerical integration
512(11)
45.1 Introduction
512(1)
45.2 The trapezoidal rule
512(3)
45.3 The mid-ordinate rule
515(1)
45.4 Simpson's rule
516(4)
45.5 Accuracy of numerical integration
520(1)
Revision Test 13
521(2)
Section I Differential equations
523(94)
46 Introduction to differential equations
525(9)
46.1 Family of curves
525(1)
46.2 Differential equations
526(1)
46.3 The solution of equations of the form dy/dx = ∞(x)
527(1)
46.4 The solution of equations of the form dy/dx = ∞(y)
528(2)
46.5 The solution of equations of the form dy/dx = ∞(x)∞(y)
530(4)
47 Homogeneous first-order differential equations
534(4)
47.1 Introduction
534(1)
47.2 Procedure to solve differential equations of the form Pdy/dx=Q
534(1)
47.3 Worked problems on homogeneous first-order differential equations
535(1)
47.4 Further worked problems on homogeneous first-order differential equations
536(2)
48 Linear first-order differential equations
538(5)
48.1 Introduction
538(1)
48.2 Procedure to solve differential equations of the form dy/dx + Py = Q
539(1)
48.3 Worked problems on linear first-order differential equations
539(1)
48.4 Further worked problems on linear first-order differential equations
540(3)
49 Numerical methods for first-order differential equations
543(18)
49.1 Introduction
543(1)
49.2 Euler's method
544(1)
49.3 Worked problems on Euler's method
545(4)
49.4 The Euler-Cauchy method
549(5)
49.5 The Runge-Kutta method
554(6)
Revision Test 14
560(1)
50 Second-order differential equations of the formal ad2y/dx2 + bdy/dy + cy = 0
561(7)
50.1 Introduction
561(1)
50.2 Procedure to solve differential equations of the forma ad2y/dx2 + bdy/dx + cy = 0
562(1)
50.3 Worked problems on differential equations of the form ad2y/dx2 + bdy/dx + cy = 0
562(2)
50.4 Further worked problems on practical differential equations of the form ad2y/dx2 + bdy/dx + cy = 0
564(4)
51 Second-order differential equations of the for ad2y/dx2 + bdy/dx + cy = ∞(x)
568(10)
51.1 Complementary function and particular integral
569(1)
51.2 Procedure to solve differential equations of the form ad2y/dx2 + bdy/dx + cy =∞(x)
570(1)
51.3 Differential equations of the form ad2y/dx2 + bdy/dx + cy =∞(x) where ∞(x) is a constant or polynomial
570(1)
51.4 Differential equations of the form ad2y/dx2 + bdy/dx + cy = ∞(x) where ∞(x) is an exponential function
571(2)
51.5 Differential equations of the form ad2y/dx2 + bdy/dx + cy = ∞(x) where ∞(x) is a sine or cosine function
573(2)
51.6 Differential equations of the form ad2y/dx2 + bdy/dx + cy = ∞(x) where ∞(x) is a sum or a product
575(3)
52 Power series methods of solving ordinary differential equations
578(23)
52.1 Introduction
578(1)
52.2 Higher order differential coefficients as series
579(1)
52.3 Leibniz's theorem
580(3)
52.4 Power series solution by the Leibniz-Maclaurin method
583(2)
52.5 Power series solution by the Frobenius method
585(7)
52.6 Bessel's equation and Bessel's functions
592(5)
52.7 Legendre's equation and Legendre polynomials
597(4)
53 An introduction to partial differential equations
601(16)
53.1 Introduction
602(1)
53.2 Partial integration
602(1)
53.3 Solution of partial differential equations by direct partial integration
602(2)
53.4 Some important engineering partial differential equations
604(1)
53.5 Separating the variables
605(1)
53.6 The wave equation
606(4)
53.7 The heat conduction equation
610(2)
53.8 Laplace's equation
612(3)
Revision Test 15
615(2)
Section J Laplace transforms
617(44)
54 Introduction to Laplace transforms
619(6)
54.1 Introduction
619(1)
54.2 Definition of a Laplace transform
619(1)
54.3 Linearity property of the Laplace transform
620(1)
54.4 Laplace transforms of elementary functions
620(1)
54.5 Worked problems on standard Laplace transforms
621(4)
55 Properties of Laplace transforms
625(7)
55.1 The Laplace transform of eat∞(t)
625(1)
55.2 Laplace transforms of the form eat∞(t)
625(2)
55.3 The Laplace transforms of derivatives
627(2)
55.4 The initial and final value theorems
629(3)
56 Inverse Laplace transforms
632(8)
56.1 Definition of the inverse Laplace transform
632(1)
56.2 Inverse Laplace transforms of simple functions
632(3)
56.3 Inverse Laplace transforms using partial fractions
635(2)
56.4 Poles and zeros
637(3)
57 The Laplace transform of the Heaviside function
640(8)
57.1 Heaviside unit step function
640(4)
57.2 Laplace transforms of H(t - c)
644(1)
57.3 Laplace transforms of H(t - c).∞(t - c)
644(1)
57.4 Inverse Laplace transforms of Heaviside functions
645(3)
58 The solution of differential equations using Laplace transforms
648(5)
58.1 Introduction
648(1)
58.2 Procedure to solve differential equations using Laplace transforms
648(1)
58.3 Worked problems on solving differential equations using Laplace transforms
649(4)
59 The solution of simultaneous differential equations using Laplace transforms
653(8)
59.1 Introduction
653(1)
59.2 Procedure to solve simultaneous differential equations using Laplace transforms
653(1)
59.3 Worked problems on solving simultaneous differential equations using Laplace transforms
654(5)
Revision Test 16
659(2)
Section K Fourier series
661(50)
60 Fourier series for periodic functions of period 2π
663(7)
60.1 Introduction
664(1)
60.2 Periodic functions
664(1)
60.3 Fourier series
664(1)
60.4 Worked problems on Fourier series of periodic functions of period 2π
665(5)
61 Fourier series for a non-periodic function over period 2π
670(6)
61.1 Expansion of non-periodic functions
670(1)
61.2 Worked problems on Fourier series of non-periodic functions over a range of 2π
671(5)
62 Even and odd functions and half-range Fourier series
676(8)
62.1 Even and odd functions
676(1)
62.2 Fourier cosine and Fourier sine series
676(4)
62.3 Half-range Fourier series
680(4)
63 Fourier series over any range
684(6)
63.1 Expansion of a periodic function of period L
684(4)
63.2 Half-range Fourier series for functions defined over range L
688(2)
64 A numerical method of harmonic analysis
690(8)
64.1 Introduction
690(1)
64.2 Harmonic analysis on data given in tabular or graphical form
690(4)
64.3 Complex waveform considerations
694(4)
65 The complex or exponential form of a Fourier series
698(13)
65.1 Introduction
698(1)
65.2 Exponential or complex notation
698(1)
65.3 Complex coefficients
699(4)
65.4 Symmetry relationships
703(3)
65.5 The frequency spectrum
706(1)
65.6 Phasors
707(4)
Section L Z-transforms
711(18)
66 An introduction to z-transforms
713(16)
66.1 Sequences
714(3)
66.2 Some properties of z-transforms
717(3)
66.3 Inverse z-transforms
720(2)
66.4 Using z-transforms to solve difference equations
722(5)
Revision Test 17
727(2)
Section M Statistics and probability
729(117)
67 Presentation of statistical data
731(12)
67.1 Some statistical terminology
732(1)
67.2 Presentation of ungrouped data
733(3)
67.3 Presentation of grouped data
736(7)
68 Mean, median, mode and standard deviation
743(8)
68.1 Measures of central tendency
743(1)
68.2 Mean, median and mode for discrete data
744(1)
68.3 Mean, median and mode for grouped data
745(1)
68.4 Standard deviation
746(2)
68.5 Quartiles, deciles and percentiles
748(3)
69 Probability
751(13)
69.1 Introduction to probability
752(1)
69.2 Laws of probability
752(1)
69.3 Worked problems on probability
753(2)
69.4 Further worked problems on probability
755(3)
69.5 Permutations and combinations
758(1)
69.6 Bayes' theorem
759(3)
Revision Test 18
762(2)
70 The binomial and Poisson distributions
764(7)
70.1 The binomial distribution
764(3)
70.2 The Poisson distribution
767(4)
71 The normal distribution
771(9)
71.1 Introduction to the normal distribution
771(5)
71.2 Testing for a normal distribution
776(4)
72 Linear correlation
780(5)
72.1 Introduction to linear correlation
780(1)
72.2 The Pearson product-moment formula for determining the linear correlation coefficient
780(1)
72.3 The significance of a coefficient of correlation
781(1)
72.4 Worked problems on linear correlation
781(4)
73 Linear regression
785(7)
73.1 Introduction to linear regression
785(1)
73.2 The least-squares regression lines
785(1)
73.3 Worked problems on linear regression
786(5)
Revision Test 19
791(1)
74 Sampling and estimation theories
792(13)
74.1 Introduction
792(1)
74.2 Sampling distributions
792(1)
74.3 The sampling distribution of the means
793(3)
74.4 The estimation of population parameters based on a large sample size
796(5)
74.5 Estimating the mean of a population based on a small sample size
801(4)
75 Significance testing
805(1)
75.1 Hypotheses
805(1)
75.2 Type I and type II errors
806(6)
75.3 Significance tests for population means
812(5)
75.4 Comparing two sample means
817(5)
76 Chi-square and distribution-free tests
822(1)
76.1 Chi-square values
822(2)
76.2 Fitting data to theoretical distributions
824(6)
76.3 Introduction to distribution-free tests
830(1)
76.4 The sign test
830(3)
76.5 Wilcoxon signed-rank test
833(4)
76.6 The Mann-Whitney test
837(7)
Revision Test 20
844(2)
Essential formulae 846(17)
Answers to Practice Exercises 863(47)
Index 910
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 of 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 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.