Bird's Engineering Mathematics

Now in its ninth edition, Bird’s Engineering Mathematics has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, supported by practical engineering examples and applications to ensure that readers can relate theory to practice. Some 1,300 engineering situations/problems have been ‘flagged-up’ to help demonstrate that engineering cannot be fully understood without a good knowledge of mathematics.

The extensive and thorough topic coverage makes this a great text for a range of level 2 and 3 engineering courses – such as for aeronautical, construction, electrical, electronic, mechanical, manufacturing engineering and vehicle technology – including for BTEC First, National and Diploma syllabuses, City & Guilds Technician Certificate and Diploma syllabuses, and even for GCSE and A-level revision.

Its companion website at www.routledge.com/cw/bird provides resources for both students and lecturers, including full solutions for all 2,000 further questions, lists of essential formulae, multiple-choice tests, and illustrations, as well as full solutions to revision tests for course instructors.

Table of Contents

Section 1: Number and algebra

1. Revision of fractions, decimals and percentages

2. Indices, engineering notation and metric conversions

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 Newton's method

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 of 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

List of essential formulae

Answers to Practice Exercises