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Engineering Mathematics


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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

Revision Test 1

5. Algebra

6. Further algebra

7. Partial fractions

8. Solving simple equations

Revision Test 2

9. Transposition of formulae

10. Solving simultaneous equations

11. Solving quadratic equations

12. Inequalities

13. Logarithms

Revision Test 3

14. Exponential functions

15. Number sequences

16. The binomial series

17. Solving equations by iterative methods

Revision Test 4

Section 2: Areas and volumes

18. Areas of common shapes

19. The circle and its properties

20. Volumes and surface areas of common solids

21. Irregular areas and volumes and mean values of waveforms

Revision Test 5

Section 3: Trigonometry

22. Introduction to trigonometry

23. Trigonometric waveforms

24. Cartesian and polar co-ordinates

Revision Test 6

25. Triangles and some practical applications

26. Trigonometric identities and equations

27. Compound angles

Revision Test 7

Section 4: Graphs

28. Straight line graphs

29. Reduction of non-linear laws to linear form

30. Graphs with logarithmic scales

31. Graphical solution of equations

32. Functions and their curves

Revision Test 8

Section 5: Complex numbers

33. Complex numbers

34. De Moivre's theorem

Section 6: Vectors

35. Vectors

36. Methods of adding alternating waveforms

Revision Test 9

Section 7: Statistics

37. Presentation of statistical data

38. Mean, median, mode and standard deviation

39. Probability

Revision Test 10

40. The binomial and Poisson distribution

41. The normal distribution

Revision Test 11

42. Linear correlation

43. Linear regression

44. Sampling and estimation theories

Revision Test 12

Section 8: Differential Calculus

45. Introduction to differentiation

46. Methods of differentiation

47. Some applications of differentiation

48. Maclaurin's series

Revision Test 13

49. Differentiation of parametric equations

50. Differentiation of implicit functions

51. Logarithmic differentiation

Revision Test 14

Section 9: Integral calculus

52. Standard integration

53. Integration using algebraic substitutions

54. Integration using trigonometric substitutions

Revision Test 15

55. Integration using partial fractions

56. The t = tan /2 substitution

57. Integration by parts

58. Numerical integration

Revision Test 16

59. Areas under and between curves

60. Mean and root mean square values

61. Volumes and solids of revolution

62. Centroids of simple shapes

63. Second moments of area

Revision Test 17

Section 10: Differential equations

64. Introduction to differential equations

Revision Test 18

Section 11: Further Number and algebra

65. Boolean algebra and logic circuits

66. The theory of matrices and determinants

67. The solution of simultaneous equations by matrices and determinants

Revision Test 19

List of essential formulae

Answers to Practice Questions

Answers to multiple choice questions


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 is the author of some 130 textbooks on engineering 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, and is currently lecturing at the Defence School of Marine and Air Engineering in the Defence College of Technical Training at HMS Sultan, Gosport, Hampshire, UK.


'The book contains plenty of examples and problems with practical tutor resources online too, which include tests and sample answers.' Chris Collins, Lincoln College'Good all round text book with plenty of worked examples and exercises.' Eoin Fitzgerald, Limerick Institute of Technology'A very learner friendly text which is easy to follow, with many worked examples followed by graded exercises at the end of each chapter. Good coverage of the syllabus along with revision tests to consolidate the learning. The addition of free internet downloads make this an excellent text book.' Alun Furzer, Newport and District Group Training Association'Plenty of relevant worked examples. Coverage of the curriculum is excellent with a clear, readable font. Instructions for calculators are provided for a Casio which is a popular choice among my students.' Peter Dop, Deeside CollegeI love this book. It is well laid out and presented. It has good progression with good use of examples, questions and assessment John Langston, Qinetiq

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