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Abstract
Were you looking for the book with access to MyLabMath Global? This product is the book alone, and does NOT come with access to MyLabMath Global. Buy Mathematics for Engineers, 5e by Croft with MyLabMaths Global access card 5e (ISBN 9781292267685) if you need access to the MyLab as well, and save money on this brilliant resource.
Understanding key mathematical concepts and applying them successfully to solve problems are vital skills that all engineering students must acquire. Mathematics for Engineers teaches, develops and nurtures those skills. Practical, informal and accessible, it begins with the foundations and gradually builds upon this knowledge as it introduces more complex concepts to cover all requirements for a first year engineering maths course, together with introductory material for even more advanced topics.
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Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Front Cover | Front Cover | ||
| Half Title Page | i | ||
| Title Page | iii | ||
| Copyright Page | iv | ||
| Dedication Page | v | ||
| Brief contents | vii | ||
| Contents | ix | ||
| Publisher’s acknowledgements | xv | ||
| Preface | xvi | ||
| Using mathematical software packages | xx | ||
| 1 Arithmetic | 1 | ||
| Block 1 Operations on numbers | 3 | ||
| Block 2 Prime numbers and prime factorisation | 10 | ||
| End of chapter exercises | 17 | ||
| 2 Fractions | 18 | ||
| Block 1 Introducing fractions | 20 | ||
| Block 2 Operations on fractions | 25 | ||
| End of chapter exercises | 33 | ||
| 3 Decimal numbers | 35 | ||
| Block 1 Introduction to decimal numbers | 37 | ||
| Block 2 Significant figures | 42 | ||
| End of chapter exercises | 43 | ||
| 4 Percentage and ratio | 45 | ||
| Block 1 Percentage | 47 | ||
| Block 2 Ratio | 51 | ||
| End of chapter exercises | 56 | ||
| 5 Basic algebra | 57 | ||
| Block 1 Mathematical notation and symbols | 59 | ||
| Block 2 Indices | 72 | ||
| Block 3 Simplification by collecting like terms | 88 | ||
| Block 4 Removing brackets | 91 | ||
| Block 5 Factorisation | 99 | ||
| Block 6 Arithmetic of algebraic fractions | 106 | ||
| Block 7 Formulae and transposition | 119 | ||
| End of chapter exercises | 133 | ||
| 6 Functions and mathematical models | 136 | ||
| Block 1 Basic concepts of functions | 138 | ||
| Block 2 The graph of a function | 147 | ||
| Block 3 Composition of functions | 155 | ||
| Block 4 One-to-one functions and inverse functions | 158 | ||
| Block 5 Parametric representation of a function | 165 | ||
| Block 6 Describing functions | 168 | ||
| Block 7 The straight line | 177 | ||
| Block 8 Common engineering functions | 192 | ||
| Block 9 The equation of a circle | 209 | ||
| End of chapter exercises | 212 | ||
| 7 Polynomial equations, inequalities, partial fractions and proportionality | 215 | ||
| Block 1 Solving linear equations | 218 | ||
| Block 2 Solving quadratic equations | 230 | ||
| Block 3 Factorising polynomial expressions and solving polynomial equations | 243 | ||
| Block 4 Solving simultaneous equations | 252 | ||
| Block 5 Solution of inequalities | 261 | ||
| Block 6 Partial fractions | 270 | ||
| Block 7 Proportionality | 282 | ||
| End of chapter exercises | 286 | ||
| 8 Logarithms and exponentials | 289 | ||
| Block 1 The exponential function | 291 | ||
| Block 2 Logarithms and their laws | 306 | ||
| Block 3 Solving equations involving logarithms and exponentials | 316 | ||
| Block 4 Applications of logarithms | 321 | ||
| End of chapter exercises | 332 | ||
| 9 Trigonometry | 335 | ||
| Block 1 Angles | 337 | ||
| Block 2 The trigonometrical ratios | 341 | ||
| Block 3 The trigonometrical ratios in all quadrants | 352 | ||
| Block 4 Trigonometrical functions and their graphs | 360 | ||
| Block 5 Trigonometrical identities | 372 | ||
| Block 6 Trigonometrical equations | 377 | ||
| Block 7 Engineering waves | 386 | ||
| End of chapter exercises | 399 | ||
| 10 Further trigonometry | 401 | ||
| Block 1 Pythagoras’s theorem and the solution of right-angled triangles | 403 | ||
| Block 2 Solving triangles using the sine rule | 413 | ||
| Block 3 Solving triangles using the cosine rule | 419 | ||
| Block 4 Surveying | 424 | ||
| Block 5 Resolution and resultant of forces | 435 | ||
| End of chapter exercises | 447 | ||
| 11 Complex numbers | 450 | ||
| Block 1 Arithmetic of complex numbers | 452 | ||
| Block 2 The Argand diagram and polar form of a complex number | 465 | ||
| Block 3 The exponential form of a complex number | 490 | ||
| Block 4 De Moivre’s theorem | 496 | ||
| Block 5 Solving equations and finding roots of complex numbers | 504 | ||
| Block 6 Phasors | 512 | ||
| End of chapter exercises | 518 | ||
| 12 Matrices and determinants | 521 | ||
| Block 1 Introduction to matrices | 523 | ||
| Block 2 Multiplication of matrices | 534 | ||
| Block 3 Determinants | 544 | ||
| Block 4 The inverse of a matrix | 563 | ||
| Block 5 Computer graphics | 572 | ||
| End of chapter exercises | 595 | ||
| 13 Using matrices and determinants to solve equations | 600 | ||
| Block 1 Cramer’s rule | 603 | ||
| Block 2 Using the inverse matrix to solve simultaneous equations | 607 | ||
| Block 3 Gaussian elimination | 615 | ||
| Block 4 Eigenvalues and eigenvectors | 628 | ||
| Block 5 Iterative techniques | 646 | ||
| Block 6 Electrical networks | 655 | ||
| End of chapter exercises | 665 | ||
| 14 Vectors | 669 | ||
| Block 1 Basic concepts of vectors | 671 | ||
| Block 2 Cartesian components of vectors | 685 | ||
| Block 3 The scalar product, or dot product | 703 | ||
| Block 4 The vector product, or cross product | 715 | ||
| Block 5 The vector equation of a line and a plane | 726 | ||
| End of chapter exercises | 738 | ||
| 15 Differentiation | 740 | ||
| Block 1 Interpretation of a derivative | 742 | ||
| Block 2 Using a table of derivatives | 755 | ||
| Block 3 Higher derivatives | 764 | ||
| End of chapter exercises | 769 | ||
| 16 Techniques and applications of differentiation | 771 | ||
| Block 1 The product rule and the quotient rule | 773 | ||
| Block 2 The chain rule | 779 | ||
| Block 3 Implicit differentiation | 785 | ||
| Block 4 Parametric differentiation | 791 | ||
| Block 5 Logarithmic differentiation | 795 | ||
| Block 6 Tangents and normals | 799 | ||
| Block 7 Maximum and minimum values of a function | 809 | ||
| End of chapter exercises | 823 | ||
| 17 Integration | 826 | ||
| Block 1 Integration as differentiation in reverse | 828 | ||
| Block 2 Definite integrals | 840 | ||
| Block 3 The area bounded by a curve | 847 | ||
| Block 4 Computational approaches to integration | 857 | ||
| Block 5 Integration by parts | 867 | ||
| Block 6 Integration by substitution | 874 | ||
| Block 7 Integration using partial fractions | 885 | ||
| Block 8 Integration of trigonometrical functions | 888 | ||
| End of chapter exercises | 892 | ||
| 18 Applications of integration | 895 | ||
| Block 1 Integration as the limit of a sum | 897 | ||
| Block 2 Volumes of revolution | 903 | ||
| Block 3 Calculating centres of mass | 910 | ||
| Block 4 Moment of inertia | 923 | ||
| Block 5 The length of a curve and the area of a surface of revolution | 929 | ||
| Block 6 The mean value and root-mean-square value of a function | 935 | ||
| End of chapter exercises | 942 | ||
| 19 Sequences and series | 943 | ||
| Block 1 Sequences and series | 945 | ||
| Block 2 Sums of whole numbers, their squares and cubes | 958 | ||
| Block 3 Pascal’s triangle and the binomial theorem | 921 | ||
| Block 4 Taylor, Maclaurin and other series | 967 | ||
| End of chapter exercises | 975 | ||
| 20 Differential equations | 977 | ||
| Block 1 Basic concepts of differential equations | 980 | ||
| Block 2 Separation of variables | 995 | ||
| Block 3 Solving first-order linear equations using an integrating factor | 1003 | ||
| Block 4 Computational approaches to differential equations | 1011 | ||
| Block 5 Second-order linear constant-coefficient equations I | 1021 | ||
| Block 6 Second-order linear constant-coefficient equations II | 1034 | ||
| End of chapter exercises | 1046 | ||
| 21 Functions of more than one variable and partial differentiation | 1048 | ||
| Block 1 Functions of two independent variables, and their graphs | 1050 | ||
| Block 2 Partial differentiation | 1060 | ||
| Block 3 Higher-order derivatives | 1070 | ||
| Block 4 Partial differential equations | 1075 | ||
| Block 5 Stationary values of a function of two variables | 1087 | ||
| End of chapter exercises | 1092 | ||
| 22 The Laplace transform | 1094 | ||
| Block 1 The Laplace transform | 1096 | ||
| Block 2 The inverse Laplace transform | 1107 | ||
| Block 3 Solving differential equations using the Laplace transform | 1116 | ||
| End of chapter exercises | 1126 | ||
| 23 Statistics and probability | 1129 | ||
| Block 1 Data | 1131 | ||
| Block 2 Data averages | 1133 | ||
| Block 3 Variation of data | 1141 | ||
| Block 4 Elementary probability | 1146 | ||
| Block 5 Laws of probability | 1155 | ||
| Block 6 Probability distributions | 1169 | ||
| Block 7 The binomial distribution | 1177 | ||
| Block 8 The Poisson distribution | 1185 | ||
| Block 9 The normal distribution | 1194 | ||
| End of chapter exercises | 1210 | ||
| 24 An introduction to Fourier series and the Fourier transform | 1213 | ||
| Block 1 Periodic waveforms and their Fourier representation | 1215 | ||
| Block 2 Introducing the Fourier transform | 1232 | ||
| End of chapter exercises | 1240 | ||
| Typical examination papers | 1242 | ||
| Appendix 1: SI units and prefixes | 1248 | ||
| Index | 1249 | ||
| Back Cover | Back Cover |