Table of Contents

Section 1: Number and Algebra 1. Revision of fractions, decimals, and percentages 2. Indices, standard form, and engineering notation 3. Binary, octal, and hexadecimal numbers 4. Calculations and evaluation of formulae 5. Algebra 6. Further algebra 7. Partial fractions 8. Solving simple equations 9. Transposition of formulae 10. Solving simultaneous equations 11. Solving quadratic equations 12. Inequalities 13. Logarithms 14. Exponential functions 15. Number sequences 16. The binomial series Section 2: Trigonometry 17. Introduction to trigonometry 18. Trigonometric waveforms 19. Cartesian and polar co-ordinates 20. Triangles and some practical applications 21. Trigonometric identities and equations 22. Compound angles Section 3: Areas and volumes 23. Areas of common shapes 24. The circle and its properties 25. Volumes and surface areas of common solids 26. Irregular areas and volumes and mean values of waveforms Section 4: Graphs 27. Straight line graphs 28. Reduction of non-linear laws to linear form 29. Graphs with logarithmic scales 30. Graphical solution of equations 31. Functions and their curves Section 5: Complex numbers 32. Complex numbers 33. De Moivre’s theorem Section 6: Vectors 34. Vectors 35. Methods of adding alternating waveforms Section 7: Differential Calculus 36. Introduction to differentiation 37. Methods of differentiation 38. Some applications of differentiation 39. Solving equations by iterative methods 40. Maclaurin’s series 41. Differentiation of parametric equations 42. Differentiation of implicit functions 43. Logarithmic differentiation Section 8: Integral calculus 44. Standard integration 45. Integration using algebraic substitutions 46. Integration using trigonometric substitutions 47. Integration using partial fractions 48. The t = tan θ/2 substitution 49. Integration by parts 50. Numerical integration 51. Areas under and between curves 52. Mean and root mean square values 53. Volumes and solids of revolution 54. Centroids of simple shapes 55. Second moments of area Section 9: Differential equations 56. Introduction to differential equations Section 10: Further Number and algebra 57. Boolean algebra and logic circuits 58. The theory of matrices and determinants 59. The solution of simultaneous equations by matrices and determinants Section 11: Statistics 60. Presentation of statistical data 61. Mean, median, mode and standard deviation 62. Probability 63. The binomial and Poisson distribution 64. The normal distribution 65. Linear correlation 66. Linear regression 67. Sampling and estimation theories

About the Author

John Bird, BSc (Hons), CEng, CMath, CSci, FIMA, FIET, FCollT, is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with Examiner responsibilities for Advanced Mathematics with City and Guilds and examining for the International Baccalaureate Organisation. He has over 45 years’ experience of successfully teaching, lecturing, instructing, training, educating and planning trainee engineers study programmes. He is the author of 146 textbooks on engineering, science and mathematical subjects, with worldwide sales of over one million copies. He is a chartered engineer, a chartered mathematician, a chartered scientist and a Fellow of three professional institutions. He has recently retired from lecturing at the Royal Navy's Defence College of Marine Engineering in the Defence College of Technical Training at H.M.S. Sultan, Gosport, Hampshire, UK, one of the largest engineering training establishments in Europe.