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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 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.
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 |