"Technician Mathematics 3" is the third in a series which deal simply and carefully with the fundamental mathematics essential in the development of technicians and engineers. The material for this second edition of this textbook has been updated and expanded to cover (together with "Technician Mathematics 2") the main areas of the Business and Technology Educational Council's "Mathematics for Engineering module for National Certificate and Diploma courses likely to be studied in a "Mathematics" lesson. This book also fully covers the BTEC unit (4684B) which was prepared in collaboration with the Engineering Council, the Council for National Academic Awards and the Standing Conference on University Entrance. The unit corresponds with the mathematics module envisaged in the Engineering Council's Standards and Routes to Registration (SARTOR) document. First year undergraduates who need some remedial mathematics will also find that this book meets their needs. The definition and solution of engineering problems relies on the ability to represent systems and their behaviour in mathematical terms, which in turn, depends on the use of various mathematical tools.
This textbook deals with some of those mathematical skills and concepts relevant to effective performance in engineering employment at technician level. The aim of this book is to model simple engineering systems, to generate numerical values for system parameters, to manipulate data to determine system response in defined conditions, to evaluate the effects on systems of changes in variables and to communicate ideas mathematically. Each topic considered in the text is presented in a way that assumes in the reader only the knowledge attained in "Technician Mathematics 2". This practical mathematics book contains nearly 400 worked problems, followed by some 1400 further problems with answers. Although specifically written for the latter stages of BTEC National Certificate and Diploma Mathematics and for Engineering Access courses at Universities, the book will also be suitable for NVQ and GNVQ studies and for students studying A level Mathematics.
Table of Contents
1. The binomial expansion 2. Exponential functions and Naperian logarithms 3. Curves of exponential growth and decay 4. Determination of laws and use of log-linear graph paper 5. Curve sketching 6. Partial fractions 7. The notation of second order matrices and determinants 8. The solution of simultaneous equations using determinants and matrices 9. Complex numbers 10. Polar co-ordinates 11. Arithmetic and geometric progressions 12. The solution of triangles 13. The solution of three-dimensional triangulation problems 14. Graphs of trigonometric functions 15. Combining sinusoidal waveforms 16. Compound angles 17. Vectors 18. Introduction to differentiation 19. Methods of differentiation 20. Applications of differentiation 21. Introduction to integration 22. Integration by algebraic substitution 23. Integration using trigonometric identities and substitutions 24. Integration using partial fractions 25. The T = tan q/2 substitution 26. Integration by parts 27. Numerical integration 28. Areas under and between curves 29. Mean and root mean square values 30. Volumes of solids of revolution 31. Centroids of simple shapes 32. Second moments of area of regular sections 33. Introduction to differential equations 34. First order differential equations by separation of variables 35. Probability 36. The binominal and Poisson probability distributions 37. The normal probability distribution