Mathematics for engineers : a modern interactive approach / Anthony Croft, Robert Davison.

Includes index.

1Arithmetic1 Block 1Operations on numbers3 Block 2Prime numbers and prime factorisation9 End of chapter exercises14 2Fractions15 Block 1Introducing fractions17 Block 2Operations on fractions22 End of chapter exercises30 3Decimal numbers32 Block 1Introduction to decimal numbers34 Block 2Significant figures38 End of chapter exercises39 4Percentage and ratio41 Block 1Percentage43 Block 2Ratio47 End of chapter exercises51 5Basic algebra52 Block 1Mathematical notation and symbols54 Block 2Indices67 Block 3Simplification by collecting like terms83 Block 4Removing brackets86 Block 5Factorisation94 Block 6Arithmetic of algebraic fractions101 Block 7Formulae and transposition114 End of chapter exercises127 6Functions130 Block 1Basic concepts of functions132 Block 2The graph of a function139 Block 3Composition of functions147 Block 4One-to-one functions and inverse functions151 Block 5Parametric representation of a function158 Block 6Describing functions161 Block 7The straight line170 Block 8Common engineering functions181 End of chapter exercises192 7Polynomial equations, inequalities, partial fractions and proportionality195 Block 1Solving linear equations198 Block 2Solving quadratic equations209 Block 3Factorising polynomial expressions and solving polynomial equations221 Block 4Solving simultaneous equations229 Block 5Solution of inequalities238 Block 6Partial fractions248 Block 7Proportionality259 End of chapter exercises263 8Logarithms and exponentials265 Block 1The exponential function267 Block 2Logarithms and their laws282 Block 3Solving equations involving logarithms and exponentials292 Block 4Applications of logarithms297 End of chapter exercises308 9Trigonometry311 Block 1Angles313 Block 2The trigonometrical ratios317 Block 3The trigonometrical ratios in all quadrants326 Block 4Trigonometrical functions and their graphs334 Block 5Trigonometrical identities345 Block 6Trigonometrical equations350 Block 7Engineering waves359 End of chapter exercises372 10Further trigonometry375 Block 1Pythagoras's theorem and the solution of right-angled triangles377 Block 2Solving triangles using the sine rule385 Block 3Solving triangles using the cosine rule391 Block 4Surveying396 Block 5Resolution and resultant of forces407 End of chapter exercises419 11Complex numbers422 Block 1Arithmetic of complex numbers424 Block 2The Argand diagram and polar form of a complex number435 Block 3The exponential form of a complex number450 Block 4De Moivre's theorem456 Block 5Solving equations and finding roots of complex numbers 464 Block 6Phasors472 End of chapter exercises478 12Matrices and determinants481 Block 1Introduction to matrices483 Block 2Multiplication of matrices493 Block 3Determinants502 Block 4The inverse of a matrix521 Block 5Computer graphics530 End of chapter exercises553

13Using matrices and determinants to solve equations558 Block 1Cramer's rule561 Block 2Using the inverse matrix to solve simultaneous equations565 Block 3Gaussian elimination573 Block 4Eigenvalues and eigenvectors586 Block 5Iterative techniques602 Block 6Electrical networks611 End of chapter exercises621 14Vectors625 Block 1Basic concepts of vectors627 Block 2Cartesian components of vectors641 Block 3The scalar product, or dot product659 Block 4The vector product, or cross product671 Block 5The vector equation of a line and a plane682 End of chapter exercises690 15Differentiation692 Block 1Interpretation of a derivative694 Block 2Using a table of derivatives703 Block 3Higher derivatives712 End of chapter exercises715 16Techniques and applications of differentiation717 Block 1The product rule and the quotient rule719 Block 2The chain rule725 Block 3Implicit differentiation731 Block 4Parametric differentiation737 Block 5Logarithmic differentiation741 Block 6Tangents and normals745 Block 7Maximum and minimum values of a function755 End of chapter exercises769 17Integration772 Block 1Integration as differentiation in reverse774 Block 2Definite integrals786 Block 3The area bounded by a curve793 Block 4Computational approaches to integration803 Block 5Integration by parts815 Block 6Integration by substitution822 Block 7Integration using partial fractions833 Block 8Integration of trigonometrical functions836 End of chapter exercises840 18Applications of integration843 Block 1Integration as the limit of a sum845 Block 2Volumes of revolution851 Block 3Calculating centres of mass858 Block 4Moment of inertia871 Block 5The length of a curve and the area of a surface of revolution877 Block 6The mean value and root-mean-square value of a function883 End of chapter exercises890 19Sequences and series891 Block 1Sequences and series893 Block 2Sums of whole numbers, their squares and cubes904 Block 3Pascal's triangle and the binomial theorem907 Block 4Taylor series and Maclaurin series913 End of chapter exercises919 20Differential equations921 Block 1Basic concepts of differential equations924 Block 2Separation of variables937 Block 3Solving first-order linear equations using an integrating factor945 Block 4Computational approaches to differential equations953 Block 5Second-order linear constant-coefficient equations I963 Block 6Second-order linear constant-coefficient equations II976 End of chapter exercises988 21Functions of more than one variable and partial differentiation990 Block 1Functions of two independent variables, and their graphs992 Block 2Partial differentiation1002 Block 3Higher-order derivatives1011 Block 4Stationary values of a function of two variables1015 End of chapter exercises1020 22The Laplace transform1022 Block 1The Laplace transform1024 Block 2The inverse Laplace transform1033 Block 3Solving differential equations using the Laplace transform1042 End of chapter exercises1050 23Statistics and probability1053 Block 1Data1055 Block 2Data averages1057 Block 3Variation of data1065 Block 4Elementary probability1070 Block 5Laws of probability1079 Block 6Probability distributions1093 Block 7The binomial distribution1101 Block 8The Poisson distribution1109 Block 9The normal distribution1118 End of chapter exercises1134 24An introduction to Fourier series and the Fourier transform1137 Block 1Periodic waveforms and their Fourier representation1139 Block 2Introducing the Fourier transform1149 End of chapter exercises1156 Typical examination papers1158 Appendix 1: SI units and prefixes1164 Index1165

Mathematics is crucial to all aspects of engineering and technology. Understanding key mathematical concepts and applying them successfully to solve problems are vital skills every engineering student must acquire. This text teaches, applies and nurtures those skills.

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