Bird's Basic Engineering Mathematics

Now in its eighth edition, __Bird’s Basic 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 1,000 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 coverage makes this a great text for introductory level 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 revision. Its companion website provides extra materials for students and lecturers, including full solutions for all 1,700 further questions, lists of essential formulae, multiple choice tests, and illustrations, as well as full solutions to revision tests for course instructors. Cover Half Title Dedication Title Page Copyright Page Contents Preface Acknowledgements 1. Basic arithmetic 1.1. Introduction 1.2. Revision of addition and subtraction 1.3. Revision of multiplication and division 1.4. Highest common factors and lowest common multiples 1.5. Order of operation and brackets 2. Fractions 2.1. Introduction 2.2. Adding and subtracting fractions 2.3. Multiplication and division of fractions 2.4. Order of operation with fractions Revision Test 1 3. Decimals 3.1. Introduction 3.2. Converting decimals to fractions and vice versa 3.3. Significant figures and decimal places 3.4. Adding and subtracting decimal numbers 3.5. Multiplying and dividing decimal numbers 4. Using a calculator 4.1. Introduction 4.2. Adding, subtracting, multiplying and dividing 4.3. Further calculator functions 4.4. Evaluation of formulae 5. Percentages 5.1. Introduction 5.2. Percentage calculations 5.3. Further percentage calculations 5.4. More percentage calculations Revision Test 2 6. Ratio and proportion 6.1. Introduction 6.2. Ratios 6.3. Direct proportion 6.4. Inverse proportion 7. Powers, roots and laws of indices 7.1. Introduction 7.2. Powers and roots 7.3. Laws of indices 8. Units, prefixes and engineering notation 8.1. Introduction 8.2. SI units 8.3. Common prefixes 8.4. Standard form 8.5. Engineering notation 8.6. Metric conversions 8.7. Metric - US/Imperial conversions Revision Test 3 9. Basic algebra 9.1. Introduction 9.2. Basic operations 9.3. Laws of indices 10. Further algebra 10.1. Introduction 10.2. Brackets 10.3. Factorisation 10.4. Laws of precedence 11. Solving simple equations 11.1. Introduction 11.2. Solving equations 11.3. Practical problems involving simple equations Revision Test 4 12. Transposing formulae 12.1. Introduction 12.2. Transposing formulae 12.3. Further transposing of formulae 12.4. More difficult transposing of formulae 13. Solving simultaneous equations 13.1. Introduction 13.2. Solving simultaneous equations in two unknowns 13.3. Further solving of simultaneous equations 13.4. Solving more difficult simultaneous equations 13.5. Practical problems involving simultaneous equations 13.6. Solving simultaneous equations in three unknowns Revision Test 5 14. Solving quadratic equations 14.1. Introduction 14.2. Solution of quadratic equations by factorisation 14.3. Solution of quadratic equations by ‘completing the square’ 14.4. Solution of quadratic equations by formula 14.5. Practical problems involving quadratic equations 14.6. Solution of linear and quadratic equations simultaneously 15. Logarithms 15.1. Introduction to logarithms 15.2. Laws of logarithms 15.3. Indicial equations 15.4. Graphs of logarithmic functions 16. Exponential functions 16.1. Introduction to exponential functions 16.2. The power series for ex 16.3. Graphs of exponential functions 16.4. Napierian logarithms 16.5. Laws of growth and decay Revision Test 6 17. Straight line graphs 17.1. Introduction to graphs 17.2. Axes, scales and co-ordinates 17.3. Straight line graphs 17.4. Gradients, intercepts and equations of graphs 17.5. Practical problems involving straight line graphs 18. Graphs reducing non-linear laws to linear form 18.1. Introduction 18.2. Determination of law 18.3. Revision of laws of logarithms 18.4. Determination of laws involving logarithms 19. Graphical solution of equations 19.1. Graphical solution of simultaneous equations 19.2. Graphical solution of quadratic equations 19.3. Graphical solution of linear and quadratic equations simultaneously 19.4. Graphical solution of cubic equations 20. Graphs with logarithmic scales 20.1. Logarithmic scales and logarithmic graph paper 20.2. Graphs of the form y = axn 20.3. Graphs of the form y = abx 20.4. Graphs of the form y = aekx Revision Test 7 21. Angles and triangles 21.1. Introduction 21.2. Angular measurement 21.3. Triangles 21.4. Congruent triangles 21.5. Similar triangles 21.6. Construction of triangles 22. Introduction to trigonometry 22.1. Introduction 22.2. The theorem of Pythagoras 22.3. Sines, cosines and tangents 22.4. Evaluating trigonometric ratios of acute angles 22.5. Solving right-angled triangles 22.6. Angles of elevation and depression Revision Test 8 23. Trigonometric waveforms 23.1. Graphs of trigonometric functions 23.2. Angles of any magnitude 23.3. The production of sine and cosine waves 23.4. Terminology involved with sine and cosine waves 23.5. Sinusoidal form: A sin(ωt ± α) 24. Non-right-angled triangles and some practical applications 24.1. The sine and cosine rules 24.2. Area of any triangle 24.3. Worked problems on the solution of triangles and their areas 24.4. Further worked problems on the solution of triangles and their areas 24.5. Practical situations involving trigonometry 24.6. Further practical situations involving trigonometry 25. Cartesian and polar co-ordinates 25.1. Introduction 25.2. Changing from Cartesian to polar co-ordinates 25.3. Changing from polar to Cartesian co-ordinates 25.4. Use of Pol/Rec functions on calculators Revision Test 9 26. Areas of common shapes 26.1. Introduction 26.2. Common shapes 26.3. Areas of common shapes 26.4. Areas of similar shapes 27. The circle and its properties 27.1. Introduction 27.2. Properties of circles 27.3. Radians and degrees 27.4. Arc length and area of circles and sectors 27.5. The equation of a circle Revision Test 10 28. Volumes and surface areas of common solids 28.1. Introduction 28.2. Volumes and surface areas of common shapes 28.3. Summary of volumes and surface areas of common solids 28.4. More complex volumes and surface areas 28.5. Volumes and surface areas of frusta of pyramids and cones 28.6. Volumes of similar shapes 29. Irregular areas and volumes and mean values 29.1. Areas of irregular figures 29.2. Volumes of irregular solids 29.3. Mean or average values of waveforms Revision Test 11 30. Vectors 30.1. Introduction 30.2. Scalars and vectors 30.3. Drawing a vector 30.4. Addition of vectors by drawing 30.5. Resolving vectors into horizontal and vertical components 30.6. Addition of vectors by calculation 30.7. Vector subtraction 30.8. Relative velocity 30.9. i, j and k notation 31. Methods of adding alternating waveforms 31.1. Combining two periodic functions 31.2. Plotting periodic functions 31.3. Determining resultant phasors by drawing 31.4. Determining resultant phasors by the sine and cosine rules 31.5. Determining resultant phasors by horizontal and vertical components Revision Test 12 32. Presentation of statistical data 32.1. Some statistical terminology 32.2. Presentation of ungrouped data 32.3. Presentation of grouped data 33. Mean, median, mode and standard deviation 33.1. Measures of central tendency 33.2. Mean, median and mode for discrete data 33.3. Mean, median and mode for grouped data 33.4. Standard deviation 33.5. Quartiles, deciles and percentiles 34. Probability 34.1. Introduction to probability 34.2. Laws of probability Revision Test 13 35. Introduction to differentiation 35.1. Introduction to calculus 35.2. Functional notation 35.3. The gradient of a curve 35.4. Differentiation from first principles 35.5 Differentiation of y = axn by the general rule 35.6. Differentiation of sine and cosine functions 35.7. Differentiation of eax and ln ax 35.8. Summary of standard derivatives 35.9. Successive differentiation 35.10. Rates of change 35.11. Differentiation of a product 35.12. Differentiation of a quotient 35.13. Function of a function 36. Standard integration 36.1. The process of integration 36.2. The general solution of integrals of the form axn 36.3. Standard integrals 36.4. Definite integrals 36.5. The area under a curve Revision Test 14 37. Number sequences 37.1. Simple sequences 37.2. The nth term of a series 37.3. Arithmetic progressions 37.4. Geometric progressions 38. Binary, octal and hexadecimal numbers 38.1. Introduction 38.2. Binary numbers 38.3. Octal numbers 38.4. Hexadecimal numbers Revision Test 15 List of formulae Answers to Practice Exercises Index "Mathematical theories are explained in a straightforward manner, with over 500 practical engineering examples and applications. The companion website provides essential formulae, multiple choice tests, and full solutions for all 1,700 further questions; and illustrations and answers to revision tests for adopting course instructors"-- Provided by publisher