Croft And Davison Mathematics For Engineers Pdf
PDF 2012 – Pearson – ISBN: 0273719777 – Engineering Mathematics – A Foundation for Electronic, Electrical, Communications and Systems Engineers By Anthony Croft, Robert Davison, Martin Hargreaves, James Flint # 6864
(4th edition)
Published: 2012-07-12 | | PDF | 984 pages | 120.92 MB
Popular electrical engineering maths textbook, packed full of relevant modern applications and a huge number of examples and exercises.
Engineering Mathematics is the leading undergraduate textbook for courses in electrical and electronic engineering, systems and communications engineering. It is aimed primarily at Years 1 and 2.
Key features of the book:
· Integrates engineering and mathematics through an applications-focused treatment
· Carefully develops, in a single comprehensive volume, the foundation and advanced mathematical techniques most appropriate to students of electrical, electronic, systems and communications engineering, including: algebra, trigonometry and calculus, as well as set theory, sequences and series, Boolean algebra, logic and difference equations
· The relevance of mathematics is illustrated through a diverse range of examples, providing motivation for students of all abilities
· Clear, comprehensive explanations written in an accessible and user-friendly style
Chapter 1 Review of algebraic techniques i
1.1 Introduction 1
1.2 Laws of indices 1
1.3 Number bases 11
1.A Polynomial equations 20
1.5 Algebraic fractions 26
1.6 Solution of inequalities 33
1.7 Partial fractions 38
1.8 Summation notation 65
Review exercises 1 69
Chapter 2 Engineering functions 52
2.1 Introduction 52
2.2 Numbers and intervals 53
2.3 Basic concepts of functions 56
2.6 Review of some common engineering functions and techniques 66
Review exercises 2 106
Chapter3 The trigonometric functions 109
3.1 Introduction 109
3.2 Degrees and radians 110
3.3 The trigonometric ratios 110
3.6 The sine, cosine and tangent functions 116
3.5 The sine x function 117
3.6 Trigonometric identities 119
3.7 Modelling waves using sin r and cos / 125
3.8 Trigonometric equations 137
Review exercises 3 166
4 Coordinate systems
4.1 Introduction
4.2 Cartesian coordinate system – two dimensions
4.3 Cartesian coordinate system – three dimensions
4.4 Polar coordinates
4.5 Some simple polar curves
4.6 Cylindrical polar coordinates
4.7 Spherical polar coordinates
Review exercises 4
5 Discrete mathematics
5.1 Introduction
5.2 Set theory
5.3 Logic
5.4 Boolean algebra
Review exercises 5
6 Sequences and series
6.1 Introduction
6.2 Sequences
6.3 Series
6.4 The binomial theorem
6.5 Power series
6.6 Sequences arising from the iterative solution
of non-linear equations
Review exercises 6
7 Vectors
7.1 Introduction
7.2 Vectors and scalars: basic concepts
7.3 Cartesian components
7.4 Scalar fields and vector fields
7.5 The scalar product
7.6 The vector product
7.7 Vectors of n dimensions
Review exercises 7
8 Matrix algebra
8.1 Introduction
8.2 Basic definitions
Contents ix
8.3 Addition, subtraction and multiplication 247
8.A Robot coordinate frames 254
8.5 Some special matrices 257
8.6 The inverse of a 2 x 2 matrix 260
8.7 Determinants 264
8.8 The inverse of a 3 x 3 matrix 268
8.9 Application to the solution of simultaneous equations 269
8.10 Gaussian elimination 272
8.11 Eigenvalues and eigenvectors 280
8.12 Analysis of electrical networks 292
8.13 Iterative techniques for the solution of simultaneous equations 298
8.1A Computer solutions of matrix problems 304
Review exercises 8 306
Chapter? Complex numbers 309
9.1 Introduction 309
9.2 Complex numbers 310
9.3 Operations with complex numbers 313
9.6 Graphical representation of complex numbers 317
9.5 Polar form of a complex number 318
9.6 Vectors and complex numbers 321
9.7 The exponential form of a complex number 322
9.8 Phasors 325
9.9 De Moivre's theorem 329
9.10 Loci and regions of the complex plane 335
Review exercises 9 339
Chapter 10 Differentiation 340
10.1 Introduction 340
10.2 Graphical approach to differentiation 341
10.3 Limits and continuity 342
10.6 Rate of change at a specific point 346
10.5 Rate of change at a general point 348
10.6 Existence of derivatives 354
10.7 Common derivatives 356
10.8 Differentiation as a linear operator 359
Review exercises 10 366
Chapter 11 Techniques of differentiation
11.1 Introduction
11.2 Rules of differentiation
11.3 Parametric, implicit and logarithmic differentiation
11.4 Higher derivatives
Review exercises 11
Applications of differentiation
12.1 Introduction
12.2 Maximum points and minimum points
12.3 Points of inflexion
12.4 The Newton-Raphson method for solving equations
12.5 Differentiation of vectors
Review exercises 12
Integration
13.1 Introduction
13.2 Elementary integration
13.3 Definite and indefinite integrals
Review exercises 13
Techniques of integration
14.1 Introduction
14.2 Integration by parts
14.3 Integration by substitution
14.4 Integration using partial fractions
Review exercises 14
Applications of integration
15.1 Introduction
15.2 Average value of a function
15.3 Root mean square value of a function
Review exercises 15
Further topics in integration
16.1 Introduction
16.2 Orthogonal functions
16.3 Improper integrals
16.4 Integral properties of the delta function
16.5 Integration of piecewise continuous functions
16.6 Integration of vectors
Review exercises 16
Contents xi
Chapter 17 Numerical integration un
17.1 Introduction 477
17.2 Trapezium rule 477
17.3 Simpson's rule 481
Review exercises 17 486
Chapter 18 Taylor polynomialsp Taylor series and Maclaurin series 488
18.1 Introduction 488
18.2 Linearization using first-order Taylor polynomials 489
18.3 Second-order Taylor polynomials 493
18.4 Taylor polynomials of the/?th order 497
18.5 Taylor's formula and the remainder term 501
18.6 Taylor and Maclaurin series 504
Review exercises 18 512
Chapter 19 Ordinary differential equations I bu
19.1 Introduction 514
19.2 Basic definitions 515
19.3 First-order equations: simple equations and separation
of variables 520
19.4 First-order linear equations: use of an integrating factor 527
19.5 Second-order linear equations 537
Review exercises 19 564
Chapter 20 Ordinary differential equations II 566
20.1 Introduction 566
20.2 Analogue simulation 566
20.3 Fligher order equations 569
20.4 State-space models 572
20.5 N umerical methods 578
20.6 Euler's method 578
20.7 I mproved Euler method 582
20.8 Runge-Kutta method of order 4 585
Review exercises 20 589
Chapter 21 The Laplace transform 590
21.1 Introduction 590
21.2 Definition of the Laplace transform 591
21.3 Laplace transforms of some common functions 592
21.4 Properties of the Laplace transform 594
xii Contents
21.5 LapLace transform of derivatives and integrals 598
21.6 I nverse Laplace transforms 601
21.7 Using partial fractions to find the inverse Laplace transform 604
21.8 Finding the inverse Laplace transform using complex numbers 606
21.9 The convolution theorem 610
21.10 Solving linear constant coefficient differential
equations using the Laplace transform 612
21.11 Transfer functions 622
21.12 Poles, zeros and the s plane 630
21.13 Laplace transforms of some special functions 638
Review exercises 21 641
Chapter 22 Difference equations and the z transform 644
22.1 Introduction 644
22.2 Basic definitions 645
22.3 Rewriting difference equations 649
22.4 Block diagram representation of difference equations 651
22.5 Design of a discrete-time controller 655
22.6 Numerical solution of difference equations 657
22.7 Definition of the ztransform 660
22.8 Sampling a continuous signal 664
22.9 The relationship between the ztransform and the
Laplace transform 666
22.10 Properties of the ztransform 671
22.11 Inversion of z transforms 677
22.12 The z transform and difference equations 681
Review exercises 22 683
Chapter 23 Fourier series 684
23.1 Introduction 684
23.2 Periodic waveforms 685
23.3 Odd and even functions 688
23.4 Orthogonality relations and other useful identities 694
23.5 Fourier series 695
23.6 Half-range series 707
23.7 Parseval's theorem 710
23.8 Complex notation 711
23.9 Frequency response of a linear system 713
Review exercises 23 717
Contents xiii
Chapter 24 The Fourier transform 719
24.1 Introduction 719
24.2 The Fourier transform – definitions 720
24.3 Some properties of the Fourier transform 723
24.4 Spectra 728
24.5 The f—a> duality principle 730
24.6 Fourier transforms of some special functions 732
24.7 The relationship between the Fourier transform
and the Laplace transform 734
24.8 Convolution and correlation 736
24.9 The discrete Fourier transform 745
24.10 Derivation of the d.f.t. 749
24.11 Using the d.f.t. to estimate a Fourier transform 752
24.12 Matrix representation of the d.f.t. 754
24.13 Some properties of the d.f.t. 755
24.14 The discrete cosine transform 757
24.15 Discrete convolution and correlation 763
Review exercises 24 783
Chapter 25 Functions of several variables 785
25.1 Introduction 785
25.2 Functions of more than one variable 785
25.3 Partial derivatives 787
25.4 Fligher order derivatives 791
25.5 Partial differential equations 794
25.6 Taylor polynomials and Taylor series in two variables 797
25.7 Maximum and minimum points of a function of two variables 803
Review exercises 25 808
Chapter 26 Vector calculus sn
26.1 Introduction 811
26.2 Partial differentiation of vectors 811
26.3 The gradient of a scalar field 813
26.4 The divergence of a vector field 817
26.5 The curl of a vector field 821
26.6 Combining the operators grad, div and curl 823
26.7 Vector calculus and electromagnetism 825
Review exercises 26 826
xiv Contents
Chapter 27 Line integrals and multiple integrals 829
27.1 Introduction 829
27.2 Line integrals 830
27.3 Evaluation of line integrals in two dimensions 833
11.U Evaluation of line integrals in three dimensions 835
27.5 Conservative fields and potential functions 837
27.6 Double and triple integrals 842
27.7 Some simple volume and surface integrals 851
27.8 The divergence theorem and Stokes' theorem 856
27.9 Maxwell's equations in integral form 861
Review exercises 27 862
Chapter 28 Probability 864
28.1 Introduction 864
28.2 Introducing probability 865
28.3 Mutually exclusive events: the addition law of probability 870
28.4 Complementary events 874
28.5 Concepts from communication theory 875
28.6 Conditional probability: the multiplication law 879
28.7 Independent events 884
Review exercises 28 889
Chapter 29 Statistics and probability distributions 89i
29.1 Introduction 891
29.2 Random variables 892
29.3 Probability distributions – discrete variable 893
29.4 Probability density functions – continuous variable 894
29.5 Mean value 896
29.6 Standard deviation 899
29.7 Expected value of a random variable 901
29.8 Standard deviation of a random variable 904
29.9 Permutations and combinations 906
29.10 The binomial distribution 911
29.11 The Poisson distribution 915
29.12 The uniform distribution 918
29.13 The exponential distribution 919
29.14 The normal distribution 921
29.15 Reliability engineering 927
Review exercises 29 934
Contents xv
Appendix I Representing a continuous function and a sequence as
a sum of weighted impulses 937
Appendix II The Greek alphabet 939
Appendix III SI units and prefixes 940
Appendix IV The binomial expansion of (^p-)" 940
Index 941
Lecturer Resources
For password-protected online resources tailored to
support the use of this textbook in teaching, please visit
www.pearsoned.co.uk/croft
Croft And Davison Mathematics For Engineers Pdf
Source: http://digitallibrarynepal.com/engineering-tech/pdf-pearson-engineering-mathematics-foundation-electronic-electrical-communications-systems-engineers-6864/
Posted by: smithmisho1978.blogspot.com
0 Response to "Croft And Davison Mathematics For Engineers Pdf"
Post a Comment