### Additional Information

#### Book Details

### Abstract

*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 5^{th} 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.

### Table of Contents

Section Title | Page | Action | Price |
---|---|---|---|

Cover | Cover | ||

Title Page | iii | ||

Copyright Page | iv | ||

Dedication | v | ||

Contents | vii | ||

Preface | xvii | ||

Acknowledgements | xix | ||

Chapter 1 Review of algebraic techniques | 1 | ||

1.1 Introduction | 1 | ||

1.2 Laws of indices | 2 | ||

1.3 Number bases | 11 | ||

1.4 Polynomial equations | 20 | ||

1.5 Algebraic fractions | 26 | ||

1.6 Solution of inequalities | 33 | ||

1.7 Partial fractions | 39 | ||

1.8 Summation notation | 46 | ||

Review exercises 1 | 50 | ||

Chapter 2 Engineering functions | 54 | ||

2.1 Introduction | 54 | ||

2.2 Numbers and intervals | 55 | ||

2.3 Basic concepts of functions | 56 | ||

2.4 Review of some common engineering functions and techniques | 70 | ||

Review exercises 2 | 113 | ||

Chapter 3 The trigonometric functions | 115 | ||

3.1 Introduction | 115 | ||

3.2 Degrees and radians | 116 | ||

3.3 The trigonometric ratios | 116 | ||

3.4 The sine, cosine and tangent functions | 120 | ||

3.5 The sinc x function | 123 | ||

3.6 Trigonometric identities | 125 | ||

3.7 Modelling waves using sin t and cos t | 131 | ||

3.8 Trigonometric equations | 144 | ||

Review exercises 3 | 150 | ||

Chapter 4 Coordinate systems | 154 | ||

4.1 Introduction | 154 | ||

4.2 Cartesian coordinate system – two dimensions | 154 | ||

4.3 Cartesian coordinate system – three dimensions | 157 | ||

4.4 Polar coordinates | 159 | ||

4.5 Some simple polar curves | 163 | ||

4.6 Cylindrical polar coordinates | 166 | ||

4.7 Spherical polar coordinates | 170 | ||

Review exercises 4 | 173 | ||

Chapter 5 Discrete mathematics | 175 | ||

5.1 Introduction | 175 | ||

5.2 Set theory | 175 | ||

5.3 Logic | 183 | ||

5.4 Boolean algebra | 185 | ||

Review exercises 5 | 197 | ||

Chapter 6 Sequences and series | 200 | ||

6.1 Introduction | 200 | ||

6.2 Sequences | 201 | ||

6.3 Series | 209 | ||

6.4 The binomial theorem | 214 | ||

6.5 Power series | 218 | ||

6.6 Sequences arising from the iterative solution of non-linear equations | 219 | ||

Review exercises 6 | 222 | ||

Chapter 7 Vectors | 224 | ||

7.1 Introduction | 224 | ||

7.2 Vectors and scalars: basic concepts | 224 | ||

7.3 Cartesian components | 232 | ||

7.4 Scalar fields and vector fields | 240 | ||

7.5 The scalar product | 241 | ||

7.6 The vector product | 246 | ||

7.7 Vectors of n dimensions | 253 | ||

Review exercises 7 | 255 | ||

Chapter 8 Matrix algebra | 257 | ||

8.1 Introduction | 257 | ||

8.2 Basic definitions | 258 | ||

8.3 Addition, subtraction and multiplication | 259 | ||

8.4 Using matrices in the translation and rotation of vectors | 267 | ||

8.5 Some special matrices | 271 | ||

8.6 The inverse of a 2 x 2 matrix | 274 | ||

8.7 Determinants | 278 | ||

8.8 The inverse of a 3 x 3 matrix | 281 | ||

8.9 Application to the solution of simultaneous equations | 283 | ||

8.10 Gaussian elimination | 286 | ||

8.11 Eigenvalues and eigenvectors | 294 | ||

8.12 Analysis of electrical networks | 307 | ||

8.13 Iterative techniques for the solution of simultaneous equations | 312 | ||

8.14 Computer solutions of matrix problems | 319 | ||

Review exercises 8 | 321 | ||

Chapter 9 Complex numbers | 324 | ||

9.1 Introduction | 324 | ||

9.2 Complex numbers | 325 | ||

9.3 Operations with complex numbers | 328 | ||

9.4 Graphical representation of complex numbers | 332 | ||

9.5 Polar form of a complex number | 333 | ||

9.6 Vectors and complex numbers | 336 | ||

9.7 The exponential form of a complex number | 337 | ||

9.8 Phasors | 340 | ||

9.9 De Moivre’s theorem | 344 | ||

9.10 Loci and regions of the complex plane | 351 | ||

Review exercises 9 | 354 | ||

Chapter 10 Differentiation | 356 | ||

10.1 Introduction | 356 | ||

10.2 Graphical approach to differentiation | 357 | ||

10.3 Limits and continuity | 358 | ||

10.4 Rate of change at a specific point | 362 | ||

10.5 Rate of change at a general point | 364 | ||

10.6 Existence of derivatives | 370 | ||

10.7 Common derivatives | 372 | ||

10.8 Differentiation as a linear operator | 375 | ||

Review exercises 10 | 385 | ||

Chapter 11 Techniques of differentiation | 386 | ||

11.1 Introduction | 386 | ||

11.2 Rules of differentiation | 386 | ||

11.3 Parametric, implicit and logarithmic differentiation | 393 | ||

11.4 Higher derivatives | 400 | ||

Review exercises 11 | 404 | ||

Chapter 12 Applications of differentiation | 406 | ||

12.1 Introduction | 406 | ||

12.2 Maximum points and minimum points | 406 | ||

12.3 Points of inflexion | 415 | ||

12.4 The Newton–Raphson method for solving equations | 418 | ||

12.5 Differentiation of vectors | 423 | ||

Review exercises 12 | 427 | ||

Chapter 13 Integration | 428 | ||

13.1 Introduction | 428 | ||

13.2 Elementary integration | 429 | ||

13.3 Definite and indefinite integrals | 442 | ||

Review exercises 13 | 453 | ||

Chapter 14 Techniques of integration | 457 | ||

14.1 Introduction | 457 | ||

14.2 Integration by parts | 457 | ||

14.3 Integration by substitution | 463 | ||

14.4 Integration using partial fractions | 466 | ||

Review exercises 14 | 468 | ||

Chapter 15 Applications of integration | 471 | ||

15.1 Introduction | 471 | ||

15.2 Average value of a function | 471 | ||

15.3 Root mean square value of a function | 475 | ||

Review exercises 15 | 479 | ||

Chapter 16 Further topics in integration | 480 | ||

16.1 Introduction | 480 | ||

16.2 Orthogonal functions | 480 | ||

16.3 Improper integrals | 483 | ||

16.4 Integral properties of the delta function | 489 | ||

16.5 Integration of piecewise continuous functions | 491 | ||

16.6 Integration of vectors | 493 | ||

Review exercises 16 | 494 | ||

Chapter 17 Numerical integration | 496 | ||

17.1 Introduction | 496 | ||

17.2 Trapezium rule | 496 | ||

17.3 Simpson’s rule | 500 | ||

Review exercises 17 | 505 | ||

Chapter 18 Taylor polynomials, Taylor series and Maclaurin series | 507 | ||

18.1 Introduction | 507 | ||

18.2 Linearization using first-order Taylor polynomials | 508 | ||

18.3 Second-order Taylor polynomials | 513 | ||

18.4 Taylor polynomials of the nth order | 517 | ||

18.5 Taylor’s formula and the remainder term | 521 | ||

18.6 Taylor and Maclaurin series | 524 | ||

Review exercises 18 | 532 | ||

Chapter 19 Ordinary differential equations I | 534 | ||

19.1 Introduction | 534 | ||

19.2 Basic definitions | 535 | ||

19.3 First-order equations: simple equations and separation of variables | 540 | ||

19.4 First-order linear equations: use of an integrating factor | 547 | ||

19.5 Second-order linear equations | 558 | ||

19.6 Constant coefficient equations | 560 | ||

19.7 Series solution of differential equations | 584 | ||

19.8 Bessel’s equation and Bessel functions | 587 | ||

Review exercises 19 | 601 | ||

Chapter 20 Ordinary differential equations II | 603 | ||

20.1 Introduction | 603 | ||

20.2 Analogue simulation | 603 | ||

20.3 Higher order equations | 606 | ||

20.4 State-space models | 609 | ||

20.5 Numerical methods | 615 | ||

20.6 Euler’s method | 616 | ||

20.7 Improved Euler method | 620 | ||

20.8 Runge–Kutta method of order 4 | 623 | ||

Review exercises 20 | 626 | ||

Chapter 21 The Laplace transform | 627 | ||

21.1 Introduction | 627 | ||

21.2 Definition of the Laplace transform | 628 | ||

21.3 Laplace transforms of some common functions | 629 | ||

21.4 Properties of the Laplace transform | 631 | ||

21.5 Laplace transform of derivatives and integrals | 635 | ||

21.6 Inverse Laplace transforms | 638 | ||

21.7 Using partial fractions to find the inverse Laplace transform | 641 | ||

21.8 Finding the inverse Laplace transform using complex numbers | 643 | ||

21.9 The convolution theorem | 647 | ||

21.10 Solving linear constant coefficient differential equations using the Laplace transform | 649 | ||

21.11 Transfer functions | 659 | ||

21.12 Poles, zeros and the s plane | 668 | ||

21.13 Laplace transforms of some special functions | 675 | ||

Review exercises 21 | 678 | ||

Chapter 22 Difference equations and the z transform | 681 | ||

22.1 Introduction | 681 | ||

22.2 Basic definitions | 682 | ||

22.3 Rewriting difference equations | 686 | ||

22.4 Block diagram representation of difference equations | 688 | ||

22.5 Design of a discrete-time controller | 693 | ||

22.6 Numerical solution of difference equations | 695 | ||

22.7 Definition of the z transform | 698 | ||

22.8 Sampling a continuous signal | 702 | ||

22.9 The relationship between the z transform and the Laplace transform | 704 | ||

22.10 Properties of the z transform | 709 | ||

22.11 Inversion of z transforms | 715 | ||

22.12 The z transform and difference equations | 718 | ||

Review exercises 22 | 720 | ||

Chapter 23 Fourier series | 722 | ||

23.1 Introduction | 722 | ||

23.2 Periodic waveforms | 723 | ||

23.3 Odd and even functions | 726 | ||

23.4 Orthogonality relations and other useful identities | 732 | ||

23.5 Fourier series | 733 | ||

23.6 Half-range series | 745 | ||

23.7 Parseval’s theorem | 748 | ||

23.8 Complex notation | 749 | ||

23.9 Frequency response of a linear system | 751 | ||

Review exercises 23 | 755 | ||

Chapter 24 The Fourier transform | 757 | ||

24.1 Introduction | 757 | ||

24.2 The Fourier transform – definitions | 758 | ||

24.3 Some properties of the Fourier transform | 761 | ||

24.4 Spectra | 766 | ||

24.5 The t-ω duality principle | 768 | ||

24.6 Fourier transforms of some special functions | 770 | ||

24.7 The relationship between the Fourier transform and the Laplace transform | 772 | ||

24.8 Convolution and correlation | 774 | ||

24.9 The discrete Fourier transform | 783 | ||

24.10 Derivation of the d.f.t. | 787 | ||

24.11 Using the d.f.t. to estimate a Fourier transform | 790 | ||

24.12 Matrix representation of the d.f.t. | 792 | ||

24.13 Some properties of the d.f.t. | 793 | ||

24.14 The discrete cosine transform | 795 | ||

24.15 Discrete convolution and correlation | 801 | ||

Review exercises 24 | 821 | ||

Chapter 25 Functions of several variables | 823 | ||

25.1 Introduction | 823 | ||

25.2 Functions of more than one variable | 823 | ||

25.3 Partial derivatives | 825 | ||

25.4 Higher order derivatives | 829 | ||

25.5 Partial differential equations | 832 | ||

25.6 Taylor polynomials and Taylor series in two variables | 835 | ||

25.7 Maximum and minimum points of a function of two variables | 841 | ||

Review exercises 25 | 846 | ||

Chapter 26 Vector calculus | 849 | ||

26.1 Introduction | 849 | ||

26.2 Partial differentiation of vectors | 849 | ||

26.3 The gradient of a scalar field | 851 | ||

26.4 The divergence of a vector field | 856 | ||

26.5 The curl of a vector field | 859 | ||

26.6 Combining the operators grad, div and curl | 861 | ||

26.7 Vector calculus and electromagnetism | 864 | ||

Review exercises 26 | 865 | ||

Chapter 27 Line integrals and multiple integrals | 867 | ||

27.1 Introduction | 867 | ||

27.2 Line integrals | 867 | ||

27.3 Evaluation of line integrals in two dimensions | 871 | ||

27.4 Evaluation of line integrals in three dimensions | 873 | ||

27.5 Conservative fields and potential functions | 875 | ||

27.6 Double and triple integrals | 880 | ||

27.7 Some simple volume and surface integrals | 889 | ||

27.8 The divergence theorem and Stokes’ theorem | 895 | ||

27.9 Maxwell’s equations in integral form | 899 | ||

Review exercises 27 | 901 | ||

Chapter 28 Probability | 903 | ||

28.1 Introduction | 903 | ||

28.2 Introducing probability | 904 | ||

28.3 Mutually exclusive events: the addition law of probability | 909 | ||

28.4 Complementary events | 913 | ||

28.5 Concepts from communication theory | 915 | ||

28.6 Conditional probability: the multiplication law | 919 | ||

28.7 Independent events | 925 | ||

Review exercises 28 | 930 | ||

Chapter 29 Statistics and probability distributions | 933 | ||

29.1 Introduction | 933 | ||

29.2 Random variables | 934 | ||

29.3 Probability distributions – discrete variable | 935 | ||

29.4 Probability density functions – continuous variable | 936 | ||

29.5 Mean value | 938 | ||

29.6 Standard deviation | 941 | ||

29.7 Expected value of a random variable | 943 | ||

29.8 Standard deviation of a random variable | 946 | ||

29.9 Permutations and combinations | 948 | ||

29.10 The binomial distribution | 953 | ||

29.11 The Poisson distribution | 957 | ||

29.12 The uniform distribution | 961 | ||

29.13 The exponential distribution | 962 | ||

29.14 The normal distribution | 963 | ||

29.15 Reliability engineering | 970 | ||

Review exercises 29 | 977 | ||

Appendix I Representing a continuous function and a sequence as a sum of weighted impulses | 979 | ||

Appendix II The Greek alphabet | 981 | ||

Appendix III SI units and prefixes | 982 | ||

Appendix IV The binomial expansion of (n-N/n)n | 982 | ||

Index | 983 | ||

A | 983 | ||

B | 984 | ||

C | 984 | ||

D | 987 | ||

E | 988 | ||

F | 990 | ||

G | 991 | ||

H | 991 | ||

I | 992 | ||

J | 993 | ||

K | 993 | ||

L | 993 | ||

M | 995 | ||

N | 996 | ||

O | 996 | ||

P | 996 | ||

Q | 998 | ||

R | 998 | ||

S | 999 | ||

T | 1001 | ||

U | 1002 | ||

V | 1002 | ||

W | 1003 | ||

X | 1003 | ||

Y | 1004 | ||

Z | 1004 |