377 Pages · 3.35 mb ·
Engineering Math
- Front Cover (Page 1) - Title Page (Page 4) - Copyright Page (Page 5) - Table of Contents (Page 6) - Preface (Page 10) - Acknowledgements (Page 11) - Instructor’s Manual (Page 12) - Chapter 1. Basic arithmetic (Page 14) - 1.1 Introduction (Page 14) - 1.2 Revision of addition and subtraction (Page 14) - 1.3 Revision of multiplication and division (Page 16) - 1.4 Highest common factors and lowest common multiples (Page 18) - 1.5 Order of precedence and brackets (Page 19) - Chapter 2. Fractions (Page 22) - 2.1 Introduction (Page 22) - 2.2 Adding and subtracting fractions (Page 23) - 2.3 Multiplication and division of fractions (Page 25) - 2.4 Order of precedence with fractions (Page 26) - Revision Test 1 (Page 28) - Chapter 3. Decimals (Page 29) - 3.1 Introduction (Page 29) - 3.2 Converting decimals to fractions and vice-versa (Page 29) - 3.3 Significant figures and decimal places (Page 30) - 3.4 Adding and subtracting decimal numbers (Page 31) - 3.5 Multiplying and dividing decimal numbers (Page 32) - Chapter 4. Using a calculator (Page 35) - 4.1 Introduction (Page 35) - 4.2 Adding, subtracting, multiplying and dividing (Page 35) - 4.3 Further calculator functions (Page 36) - 4.4 Evaluation of formulae (Page 41) - Chapter 5. Percentages (Page 46) - 5.1 Introduction (Page 46) - 5.2 Percentage calculations (Page 46) - 5.3 Further percentage calculations (Page 48) - 5.4 More percentage calculations (Page 49) - Revision Test 2 (Page 52) - Chapter 6. Ratio and proportion (Page 53) - 6.1 Introduction (Page 53) - 6.2 Ratios (Page 53) - 6.3 Direct proportion (Page 55) - 6.4 Inverse proportion (Page 58) - Chapter 7. Powers, roots and laws of indices (Page 60) - 7.1 Introduction (Page 60) - 7.2 Powers and roots (Page 60) - 7.3 Laws of indices (Page 61) - Chapter 8. Units, prefixes and engineering notation (Page 66) - 8.1 Introduction (Page 66) - 8.2 SI units (Page 66) - 8.3 Common prefixes (Page 66) - 8.4 Standard form (Page 69) - 8.5 Engineering notation (Page 70) - Revision Test 3 (Page 73) - Chapter 9. Basic algebra (Page 74) - 9.1 Introduction (Page 74) - 9.2 Basic operations (Page 74) - 9.3 Laws of indices (Page 77) - Chapter 10. Further algebra (Page 81) - 10.1 Introduction (Page 81) - 10.2 Brackets (Page 81) - 10.3 Factorization (Page 82) - 10.4 Laws of precedence (Page 84) - Chapter 11. Solving simple equations (Page 86) - 11.1 Introduction (Page 86) - 11.2 Solving equations (Page 86) - 11.3 Practical problems involving simple equations (Page 90) - Revision Test 4 (Page 95) - Chapter 12. Transposing formulae (Page 96) - 12.1 Introduction (Page 96) - 12.2 Transposing formulae (Page 96) - 12.3 Further transposing of formulae (Page 98) - 12.4 More difficult transposing of formulae (Page 100) - Chapter 13. Solving simultaneous equations (Page 103) - 13.1 Introduction (Page 103) - 13.2 Solving simultaneous equations in two unknowns (Page 103) - 13.3 Further solving of simultaneous equations (Page 105) - 13.4 Solving more difficult simultaneous equations (Page 107) - 13.5 Practical problems involving simultaneous equations (Page 109) - 13.6 Solving simultaneous equations in three unknowns (Page 112) - Revision Test 5 (Page 114) - Chapter 14. Solving quadratic equations (Page 115) - 14.1 Introduction (Page 115) - 14.2 Solution of quadratic equations by factorization (Page 115) - 14.3 Solution of quadratic equations by ‘completing the square’ (Page 118) - 14.4 Solution of quadratic equations by formula (Page 119) - 14.5 Practical problems involving quadratic equations (Page 121) - 14.6 Solution of linear and quadratic equations simultaneously (Page 123) - Chapter 15. Logarithms (Page 124) - 15.1 Introduction to logarithms (Page 124) - 15.2 Laws of logarithms (Page 126) - 15.3 Indicial equations (Page 128) - 15.4 Graphs of logarithmic functions (Page 129) - Chapter 16. Exponential functions (Page 131) - 16.1 Introduction to exponential functions (Page 131) - 16.2 The power series for ex (Page 132) - 16.3 Graphs of exponential functions (Page 133) - 16.4 Napierian logarithms (Page 135) - 16.5 Laws of growth and decay (Page 138) - Revision Test 6 (Page 142) - Chapter 17. Straight line graphs (Page 143) - 17.1 Introduction to graphs (Page 143) - 17.2 Axes, scales and co-ordinates (Page 143) - 17.3 Straight line graphs (Page 145) - 17.4 Gradients, intercepts and equations of graphs (Page 147) - 17.5 Practical problems involving straight line graphs (Page 154) - Chapter 18. Graphs reducing non-linear laws to linear form (Page 160) - 18.1 Introduction (Page 160) - 18.2 Determination of law (Page 160) - 18.3 Revision of laws of logarithms (Page 163) - 18.4 Determination of laws involving logarithms (Page 163) - Chapter 19. Graphical solution of equations (Page 168) - 19.1 Graphical solution of simultaneous equations (Page 168) - 19.2 Graphical solution of quadratic equations (Page 169) - 19.3 Graphical solution of linear and quadratic equations simultaneously (Page 173) - 19.4 Graphical solution of cubic equations (Page 174) - Revision Test 7 (Page 176) - Chapter 20. Angles and triangles (Page 178) - 20.1 Introduction (Page 178) - 20.2 Angular measurement (Page 178) - 20.3 Triangles (Page 184) - 20.4 Congruent triangles (Page 188) - 20.5 Similar triangles (Page 189) - 20.6 Construction of triangles (Page 192) - Chapter 21. Introduction to trigonometry (Page 194) - 21.1 Introduction (Page 194) - 21.2 The theorem of Pythagoras (Page 194) - 21.3 Sines, cosines and tangents (Page 196) - 21.4 Evaluating trigonometric ratios of acute angles (Page 198) - 21.5 Solving right-angled triangles (Page 201) - 21.6 Angles of elevation and depression (Page 204) - Revision Test 8 (Page 206) - Chapter 22. Trigonometric waveforms (Page 208) - 22.1 Graphs of trigonometric functions (Page 208) - 22.2 Angles of any magnitude (Page 209) - 22.3 The production of sine and cosine waves (Page 211) - 22.4 Terminology involved with sine and cosine waves (Page 212) - 22.5 Sinusoidal form: A sin(ωt ± α) (Page 215) - Chapter 23. Non-right-angled triangles and some practical applications (Page 218) - 23.1 The sine and cosine rules (Page 218) - 23.2 Area of any triangle (Page 218) - 23.3 Worked problems on the solution of triangles and their areas (Page 219) - 23.4 Further worked problems on the solution of triangles and their areas (Page 220) - 23.5 Practical situations involving trigonometry (Page 222) - 23.6 Further practical situations involving trigonometry (Page 224) - Chapter 24. Cartesian and polar co-ordinates (Page 227) - 24.1 Introduction (Page 227) - 24.2 Changing from Cartesian to polar co-ordinates (Page 227) - 24.3 Changing from polar to Cartesian co-ordinates (Page 229) - 24.4 Use of Pol/Rec functions on calculators (Page 230) - Revision Test 9 (Page 231) - Chapter 25. Areas of common shapes (Page 232) - 25.1 Introduction (Page 232) - 25.2 Common shapes (Page 232) - 25.3 Areas of common shapes (Page 234) - 25.4 Areas of similar shapes (Page 242) - Chapter 26. The circle (Page 243) - 26.1 Introduction (Page 243) - 26.2 Properties of circles (Page 243) - 26.3 Radians and degrees (Page 245) - 26.4 Arc length and area of circles and sectors (Page 246) - 26.5 The equation of a circle (Page 249) - Revision Test 10 (Page 251) - Chapter 27. Volumes of common solids (Page 253) - 27.1 Introduction (Page 253) - 27.2 Volumes and surface areas of common shapes (Page 253) - 27.3 Summary of volumes and surface areas of common solids (Page 260) - 27.4 More complex volumes and surface areas (Page 260) - 27.5 Volumes and surface areas of frusta of pyramids and cones (Page 265) - 27.6 Volumes of similar shapes (Page 269) - Chapter 28. Irregular areas and volumes, and mean values (Page 270) - 28.1 Areas of irregular figures (Page 270) - 28.2 Volumes of irregular solids (Page 272) - 28.3 Mean or average values of waveforms (Page 273) - Revision Test 11 (Page 277) - Chapter 29. Vectors (Page 279) - 29.1 Introduction (Page 279) - 29.2 Scalars and vectors (Page 279) - 29.3 Drawing a vector (Page 279) - 29.4 Addition of vectors by drawing (Page 280) - 29.5 Resolving vectors into horizontal and vertical components (Page 282) - 29.6 Addition of vectors by calculation (Page 283) - 29.7 Vector subtraction (Page 287) - 29.8 Relative velocity (Page 289) - 29.9 i, j and k notation (Page 290) - Chapter 30. Methods of adding alternating waveforms (Page 291) - 30.1 Combining two periodic functions (Page 291) - 30.2 Plotting periodic functions (Page 291) - 30.3 Determining resultant phasors by drawing (Page 293) - 30.4 Determining resultant phasors by the sine and cosine rules (Page 294) - 30.5 Determining resultant phasors by horizontal and vertical components (Page 296) - Revision Test 12 (Page 299) - Chapter 31. Presentation of statistical data (Page 301) - 31.1 Some statistical terminology (Page 301) - 31.2 Presentation of ungrouped data (Page 302) - 31.3 Presentation of grouped data (Page 305) - Chapter 32. Mean, median, mode and standard deviation (Page 312) - 32.1 Measures of central tendency (Page 312) - 32.2 Mean, median and mode for discrete data (Page 312) - 32.3 Mean, median and mode for grouped data (Page 313) - 32.4 Standard deviation (Page 315) - 32.5 Quartiles, deciles and percentiles (Page 316) - Chapter 33. Probability (Page 319) - 33.1 Introduction to probability (Page 319) - 33.2 Laws of probability (Page 320) - Revision Test 13 (Page 325) - Chapter 34. Introduction to differentiation (Page 326) - 34.1 Introduction to calculus (Page 326) - 34.2 Functional notation (Page 326) - 34.3 The gradient of a curve (Page 327) - 34.4 Differentiation from first principles (Page 328) - 34.5 Differentiation of y = axn by the general rule (Page 328) - 34.6 Differentiation of sine and cosine functions (Page 331) - 34.7 Differentiation of eax and ln ax (Page 333) - 34.8 Summary of standard derivatives (Page 334) - 34.9 Successive differentiation (Page 335) - 34.10 Rates of change (Page 336) - Chapter 35. Introduction to integration (Page 338) - 35.1 The process of integration (Page 338) - 35.2 The general solution of integrals of the form axn (Page 338) - 35.3 Standard integrals (Page 339) - 35.4 Definite integrals (Page 341) - 35.5 The area under a curve (Page 343) - Revision Test 14 (Page 348) - List of formulae (Page 349) - Answers to practice exercises (Page 353) - Index (Page 369)