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E-raamat: Engineering Mathematics

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  • Formaat: 1 pages
  • Ilmumisaeg: 26-Jul-2017
  • Kirjastus: Pearson Education Limited
  • Keel: eng
  • ISBN-13: 9781292146669
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Engineering MathematicsSuurem pilt
  • Formaat: 1 pages
  • Ilmumisaeg: 26-Jul-2017
  • Kirjastus: Pearson Education Limited
  • Keel: eng
  • ISBN-13: 9781292146669
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Engineering Mathematics is the unparalleled undergraduate textbook for students of electrical, electronic, communications and systems engineering.  Tried and tested over many years, this widely used textbook is now in its 5th edition, having been fully updated and revised.  This new edition includes an even greater emphasis on the application of mathematics within a range of engineering contexts.  It features detailed explanation of why a technique is important to engineers.  In addition, it provides essential guidance in how to use mathematics to solve engineering problems. This approach ensures a deep and practical understanding of the role of mathematics in modern engineering.
Preface xvii
Acknowledgements xix
Chapter 1 Review of algebraic techniques
1(53)
1.1 Introduction
1(1)
1.2 Laws of indices
2(9)
1.3 Number bases
11(9)
1.4 Polynomial equations
20(6)
1.5 Algebraic fractions
26(7)
1.6 Solution of inequalities
33(6)
1.7 Partial fractions
39(7)
1.8 Summation notation
46(8)
Review exercises 1
50(4)
Chapter 2 Engineering functions
54(61)
2.1 Introduction
54(1)
2.2 Numbers and intervals
55(1)
2.3 Basic concepts of functions
56(14)
2.4 Review of some common engineering functions and techniques
70(45)
Review exercises 2
113(2)
Chapter 3 The trigonometric functions
115(39)
3.1 Introduction
115(1)
3.2 Degrees and radians
116(1)
3.3 The trigonometric ratios
116(4)
3.4 The sine, cosine and tangent functions
120(3)
3.5 The sine x function
123(2)
3.6 Trigonometric identities
125(6)
3.7 Modelling waves using sin t and cos t
131(13)
3.8 Trigonometric equations
144(10)
Review exercises 3
150(4)
Chapter 4 Coordinate systems
154(21)
4.1 Introduction
154(1)
4.2 Cartesian coordinate system - two dimensions
154(3)
4.3 Cartesian coordinate system - three dimensions
157(2)
4.4 Polar coordinates
159(4)
4.5 Some simple polar curves
163(3)
4.6 Cylindrical polar coordinates
166(4)
4.7 Spherical polar coordinates
170(5)
Review exercises 4
173(2)
Chapter 5 Discrete mathematics
175(25)
5.1 Introduction
175(1)
5.2 Set theory
175(8)
5.3 Logic
183(2)
5.4 Boolean algebra
185(15)
Review exercises 5
197(3)
Chapter 6 Sequences and series
200(24)
6.1 Introduction
200(1)
6.2 Sequences
201(8)
6.3 Series
209(5)
6.4 The binomial theorem
214(4)
6.5 Power series
218(1)
6.6 Sequences arising from the iterative solution of non-linear equations
219(5)
Review exercises 6
222(2)
Chapter 7 Vectors
224(33)
7.1 Introduction
224(1)
7.2 Vectors and scalars: basic concepts
224(8)
7.3 Cartesian components
232(8)
7.4 Scalar fields and vector fields
240(1)
7.5 The scalar product
241(5)
7.6 The vector product
246(7)
7.7 Vectors of n dimensions
253(4)
Review exercises 7
255(2)
Chapter 8 Matrix algebra
257(67)
8.1 Introduction
257(1)
8.2 Basic definitions
258(1)
8.3 Addition, subtraction and multiplication
259(8)
8.4 Using matrices in the translation and rotation of vectors
267(4)
8.5 Some special matrices
271(3)
8.6 The inverse of a 2 × 2 matrix
274(4)
8.7 Determinants
278(3)
8.8 The inverse of a 3 × 3 matrix
281(2)
8.9 Application to the solution of simultaneous equations
283(3)
8.10 Gaussian elimination
286(8)
8.11 Eigenvalues and eigenvectors
294(13)
8.12 Analysis of electrical networks
307(5)
8.13 Iterative techniques for the solution of simultaneous equations
312(7)
8.14 Computer solutions of matrix problems
319(5)
Review exercises 8
321(3)
Chapter 9 Complex numbers
324(32)
9.1 Introduction
324(1)
9.2 Complex numbers
325(3)
9.3 Operations with complex numbers
328(4)
9.4 Graphical representation of complex numbers
332(1)
9.5 Polar form of a complex number
333(3)
9.6 Vectors and complex numbers
336(1)
9.7 The exponential form of a complex number
337(3)
9.8 Phasors
340(4)
9.9 De Moivre's theorem
344(7)
9.10 Loci and regions of the complex plane
351(5)
Review exercises 9
354(2)
Chapter 10 Differentiation
356(30)
10.1 Introduction
356(1)
10.2 Graphical approach to differentiation
357(1)
10.3 Limits and continuity
358(4)
10.4 Rate of change at a specific point
362(2)
10.5 Rate of change at a general point
364(6)
10.6 Existence of derivatives
370(2)
10.7 Common derivatives
372(3)
10.8 Differentiation as a linear operator
375(11)
Review exercises 10
385(1)
Chapter 11 Techniques of differentiation
386(20)
11.1 Introduction
386(1)
11.2 Rules of differentiation
386(7)
11.3 Parametric, implicit and logarithmic differentiation
393(7)
11.4 Higher derivatives
400(6)
Review exercises 11
404(2)
Chapter 12 Applications of differentiation
406(22)
12.1 Introduction
406(1)
12.2 Maximum points and minimum points
406(9)
12.3 Points of inflexion
415(3)
12.4 The Newton--Raphson method for solving equations
418(5)
12.5 Differentiation of vectors
423(5)
Review exercises 12
427(1)
Chapter 13 Integration
428(29)
13.1 Introduction
428(1)
13.2 Elementary integration
429(13)
13.3 Definite and indefinite integrals
442(15)
Review exercises 13
453(4)
Chapter 14 Techniques of integration
457(14)
14.1 Introduction
457(1)
14.2 Integration by parts
457(6)
14.3 Integration by substitution
463(3)
14.4 Integration using partial fractions
466(5)
Review exercises 14
468(3)
Chapter 15 Applications of integration
471(9)
15.1 Introduction
471(1)
15.2 Average value of a function
471(4)
15.3 Root mean square value of a function
475(5)
Review exercises 15
479(1)
Chapter 16 Further topics in integration
480(16)
16.1 Introduction
480(1)
16.2 Orthogonal functions
480(3)
16.3 Improper integrals
483(6)
16.4 Integral properties of the delta function
489(2)
16.5 Integration of piecewise continuous functions
491(2)
16.6 Integration of vectors
493(3)
Review exercises 16
494(2)
Chapter 17 Numerical integration
496(11)
17.1 Introduction
496(1)
17.2 Trapezium rule
496(4)
17.3 Simpson's rule
500(7)
Review exercises 17
505(2)
Chapter 18 Taylor polynomials, Taylor series and Maclaurin series
507(27)
18.1 Introduction
507(1)
18.2 Linearization using first-order Taylor polynomials
508(5)
18.3 Second-order Taylor polynomials
513(4)
18.4 Taylor polynomials of the nth order
517(4)
18.5 Taylor's formula and the remainder term
521(3)
18.6 Taylor and Maclaurin series
524(10)
Review exercises 18
532(2)
Chapter 19 Ordinary differential equations I
534(69)
19.1 Introduction
534(1)
19.2 Basic definitions
535(5)
19.3 First-order equations: simple equations and separation of variables
540(7)
19.4 First-order linear equations: use of an integrating factor
547(11)
19.5 Second-order linear equations
558(2)
19.6 Constant coefficient equations
560(24)
19.7 Series solution of differential equations
584(3)
19.8 Bessel's equation and Bessel functions
587(16)
Review exercises 19
601(2)
Chapter 20 Ordinary differential equations II
603(24)
20.1 Introduction
603(1)
20.2 Analogue simulation
603(3)
20.3 Higher order equations
606(3)
20.4 State-space models
609(6)
20.5 Numerical methods
615(1)
20.6 Euler's method
616(4)
20.7 Improved Euler method
620(3)
20.8 Runge--Kutta method of order 4
623(4)
Review exercises 20
626(1)
Chapter 21 The Laplace transform
627(54)
21.1 Introduction
627(1)
21.2 Definition of the Laplace transform
628(1)
21.3 Laplace transforms of some common functions
629(2)
21.4 Properties of the Laplace transform
631(4)
21.5 Laplace transform of derivatives and integrals
635(3)
21.6 Inverse Laplace transforms
638(3)
21.7 Using partial fractions to find the inverse Laplace transform
641(2)
21.8 Finding the inverse Laplace transform using complex numbers
643(4)
21.9 The convolution theorem
647(2)
21.10 Solving linear constant coefficient differential equations using the Laplace transform
649(10)
21.11 Transfer functions
659(9)
21.12 Poles, zeros and the s plane
668(7)
21.13 Laplace transforms of some special functions
675(6)
Review exercises 21
678(3)
Chapter 22 Difference equations and the z transform
681(41)
22.1 Introduction
681(1)
22.2 Basic definitions
682(4)
22.3 Rewriting difference equations
686(2)
22.4 Block diagram representation of difference equations
688(5)
22.5 Design of a discrete-time controller
693(2)
22.6 Numerical solution of difference equations
695(3)
22.7 Definition of the z transform
698(4)
22.8 Sampling a continuous signal
702(2)
22.9 The relationship between the z transform and the Laplace transform
704(5)
22.10 Properties of the z transform
709(6)
22.11 Inversion of z transforms
715(3)
22.12 The z transform and difference equations
718(4)
Review exercises 22
720(2)
Chapter 23 Fourier series
722(35)
23.1 Introduction
722(1)
23.2 Periodic waveforms
723(3)
23.3 Odd and even functions
726(6)
23.4 Orthogonality relations and other usefulidentities
732(1)
23.5 Fourier series
733(12)
23.6 Half-range series
745(3)
23.7 Parseval's theorem
748(1)
23.8 Complex notation
749(2)
23.9 Frequency response of a linear system
751(6)
Review exercises 23
755(2)
Chapter 24 The Fourier transform
757(66)
24.1 Introduction
757(1)
24.2 The Fourier transform - definitions
758(3)
24.3 Some properties of the Fourier transform
761(5)
24.4 Spectra
766(2)
24.5 The t--ω duality principle
768(2)
24.6 Fourier transforms of some special functions
770(2)
24.7 The relationship between the Fourier transform and the Laplace transform
772(2)
24.8 Convolution and correlation
774(9)
24.9 The discrete Fourier transform
783(4)
24.10 Derivation of the d.f.t.
787(3)
24.11 Using the d.f.t. to estimate a Fourier transform
790(2)
24.12 Matrix representation of the d.f.t.
792(1)
24.13 Some properties of the d.f.t.
793(2)
24.14 The discrete cosine transform
795(6)
24.15 Discrete convolution and correlation
801(22)
Review exercises 24
821(2)
Chapter 25 Functions of several variables
823(26)
25.1 Introduction
823(1)
25.2 Functions of more than one variable
823(2)
25.3 Partial derivatives
825(4)
25.4 Higher order derivatives
829(3)
25.5 Partial differential equations
832(3)
25.6 Taylor polynomials and Taylor series in two variables
835(6)
25.7 Maximum and minimum points of a function of two variables
841(8)
Review exercises 25
846(3)
Chapter 26 Vector calculus
849(18)
26.1 Introduction
849(1)
26.2 Partial differentiation of vectors
849(2)
26.3 The gradient of a scalar field
851(5)
26.4 The divergence of a vector field
856(3)
26.5 The curl of a vector field
859(2)
26.6 Combining the operators grad, div and curl
861(3)
26.7 Vector calculus and electromagnetism
864(3)
Review exercises 26
865(2)
Chapter 27 Line integrals and multiple integrals
867(36)
27.1 Introduction
867(1)
27.2 Line integrals
867(4)
27.3 Evaluation of line integrals in two dimensions
871(2)
27.4 Evaluation of line integrals in three dimensions
873(2)
27.5 Conservative fields and potential functions
875(5)
27.6 Double and triple integrals
880(9)
27.7 Some simple volume and surface integrals
889(6)
27.8 The divergence theorem and Stokes' theorem
895(4)
27.9 Maxwell's equations in integral form
899(4)
Review exercises 27
901(2)
Chapter 28 Probability
903(30)
28.1 Introduction
903(1)
28.2 Introducing probability
904(5)
28.3 Mutually exclusive events: the addition law of probability
909(4)
28.4 Complementary events
913(2)
28.5 Concepts from communication theory
915(4)
28.6 Conditional probability: the multiplication law
919(6)
28.7 Independent events
925(8)
Review exercises 28
930(3)
Chapter 29 Statistics and probability distributions
933(46)
29.1 Introduction
933(1)
29.2 Random variables
934(1)
29.3 Probability distributions-discrete variable
935(1)
29.4 Probability density functions - continuous variable
936(2)
29.5 Mean value
938(3)
29.6 Standard deviation
941(2)
29.7 Expected value of a random variable
943(3)
29.8 Standard deviation of a random variable
946(2)
29.9 Permutations and combinations
948(5)
29.10 The binomial distribution
953(4)
29.11 The Poisson distribution
957(4)
29.12 The uniform distribution
961(1)
29.13 The exponential distribution
962(1)
29.14 The normal distribution
963(7)
29.15 Reliability engineering
970(9)
Review exercises 29
977(2)
Appendix I Representing a continuous function and a sequence as a sum of weighted impulses 979(2)
Appendix II Greek alphabet 981(1)
Appendix III SI units and prefixes 982(1)
Appendix IV The binomial expansion of (n-N/n)n 982(1)
Index 983
Anthony Croft is Professor of Mathematics Education at Loughborough University.

Robert Davison was formerly Head of Quality at the Faculty of Technology, De Montfort University.

Martin Hargreaves is a Chartered Physicist

James Flint is Senior Lecturer in Wireless Systems Engineering at Loughborough University.
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