Understanding engineering mathematics / J.O. Bird

Includes index.

Section A. Number and Algebra -- Section B. Further number and algebra -- Section C. Areas and volumes -- Section D. Graphs -- Section E. Geometry and trigonometry -- Section F. Complex numbers -- Section G. Matrices and determinants -- Section H. Vector geometry -- Section I. Differential calculus -- Section J. Integral calculus -- Section K. Differential equations -- Section L. Statistics and probability -- Section M. Laplace transforms -- Section N. Fourier series Section A. Number and Algebra -- 1. Basic arithmetic -- 2. Fractions -- 3. Decimals -- 4. Using a calculator -- 5. Percentages -- 6. Ratio and proportion -- 7. Powers, roots and laws of indices -- 8. Units, prefixes and engineering notation -- 9. Basic algebra -- 10. Further algebra -- 11. Solving simple equations -- 12. Transposing formulae -- 13. Solving simultaneous equations -- 14. Solving quadratic equations -- 15. Logarithms -- 16. Exponential functions -- 17. Inequalities -- -- Section B. Further number and algebra -- 18. Polynomial division and the factor and remainder theorems -- 19. Number sequences -- 20. Binary, octal and hexadecimal numbers -- 21. Partial fractions -- 22. The binomial series -- 23. Maclaurin's series -- 24. Hyperbolic functions -- 25. Solving equations by iterative methods -- 26. Boolean algebra and logic circuits -- -- Section C. Areas and volumes -- 27. Areas of common shapes -- 28. The circle and its properties -- 29. Volumes and surface areas of common solids -- 30. Irregular areas and volumes, and mean values -- -- Section D. Graphs -- 31. Straight line graphs -- 32. Graphs reducing non-linear laws to linear form -- 33. Graphs with logarithmic scales -- 34. Polar curves -- 35. Graphical solution of equations -- 36. Functions and their curves -- -- Section E. Geometry and trigonometry -- 37. Angles and triangles -- 38. Introduction to trigonometry -- 39. Trigonometric waveforms -- 40. Cartesian and polar co-ordinates -- 41. Non-right-angled triangles and some practical applications -- 42. Trigonometric identities and equations -- 43. The relationship between trigonometric and hyperbolic functions -- 44. Compound angles -- -- Section F. Complex numbers -- 45. Complex numbers -- 46. De Moivre's theorem -- -- Section G. Matrices and determinants -- 47. The theory of matrices and determinants -- 48. Applications of matrices and determinants -- -- Section H. Vector geometry -- 49. Vectors -- 50. Methods of adding alternating waveforms -- 51. Scalar and vector products -- -- Section I. Differential calculus -- 52. Introduction to differentiation -- 53. Methods of differentiation -- 54. Some applications of differentiation -- 55. Differentiation of parametric equations -- 56. Differentiation of implicit functions -- 57. Logarithmic differentiation -- 58. Differentiation of hyperbolic functions -- 59. Differentiation of inverse trigonometric and hyperbolic functions -- 60. Partial differentiation -- 61. Total differential, rates of change and small changes -- 62. Maxima, minima and saddle points for functions of two variables

Studying engineering, whether it is mechanical, electrical or civil relies heavily on an understanding of mathematics. This new textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them to solve real-life engineering problems. It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher. Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures are introduced before real world situations, practicals and problem solving demonstrate how the theory is applied. Focusing on learning through practice, it contains examples, supported by 1,600 worked problems and 3,000 further problems contained within exercises throughout the text. In addition, 34 revision tests are included at regular intervals. An interactive companion website is also provided containing 2,750 further problems with worked solutions and instructor materials--EBL