Basic Engineering Mathematics

Now in its seventh edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, and full solutions for all 1,600 further questions. Contents......Page 3 Preface......Page 7 Introduction......Page 9 Revision of addition and subtraction......Page 10 Revision of multiplication and division......Page 11 Highest common factors and lowest common multiples......Page 13 Order of operation and brackets......Page 15 Introduction......Page 17 Adding and subtracting fractions......Page 18 Multiplication and division of fractions......Page 20 Order of operation with fractions......Page 22 Converting decimals to fractions and vice versa......Page 25 Significant figures and decimal places......Page 27 Adding and subtracting decimal numbers......Page 28 Multiplying and dividing decimal numbers......Page 29 Adding, subtracting, multiplying and dividing......Page 31 Further calculator functions......Page 33 Evaluation of formulae......Page 37 Introduction......Page 43 Percentage calculations......Page 44 Further percentage calculations......Page 45 More percentage calculations......Page 47 Introduction......Page 51 Ratios......Page 52 Direct proportion......Page 54 Inverse proportion......Page 58 Powers and roots......Page 60 Laws of indices......Page 62 SI units......Page 67 Common prefixes......Page 68 Standard form......Page 71 Engineering notation......Page 73 Metric conversions......Page 75 Metric – US/Imperial conversions......Page 78 Introduction......Page 84 Basic operations......Page 85 Laws of indices......Page 88 Brackets......Page 92 Factorisation......Page 94 Laws of precedence......Page 95 Solving equations......Page 98 Practical problems involving simple equations......Page 102 Transposing formulae......Page 110 Further transposing of formulae......Page 112 More difficult transposing of formulae......Page 115 Solving simultaneous equations in two unknowns......Page 119 Further solving of simultaneous equations......Page 121 Solving more difficult simultaneous equations......Page 123 Practical problems involving simultaneous equations......Page 125 Solving simultaneous equations in three unknowns......Page 129 Introduction......Page 132 Solution of quadratic equations by factorisation......Page 133 Solution of quadratic equations by ‘completing the square’......Page 135 Solution of quadratic equations by formula......Page 137 Practical problems involving quadratic equations......Page 138 Solution of linear and quadratic equations simultaneously......Page 141 Introduction to logarithms......Page 142 Laws of logarithms......Page 144 Indicial equations......Page 147 Graphs of logarithmic functions......Page 148 Introduction to exponential functions......Page 149 The power series for......Page 150 Graphs of exponential functions......Page 152 Napierian logarithms......Page 154 Laws of growth and decay......Page 157 Axes, scales and co-ordinates......Page 164 Straight line graphs......Page 166 Gradients, intercepts and equations of graphs......Page 169 Practical problems involving straight line graphs......Page 176 Determination of law......Page 183 Revision of laws of logarithms......Page 186 Determination of laws involving logarithms......Page 187 Graphical solution of simultaneous equations......Page 192 Graphical solution of quadratic equations......Page 194 Graphical solution of cubic equations......Page 198 Logarithmic scales and logarithmic graph paper......Page 201 Graphs of the form......Page 202 Angular measurement......Page 211 Triangles......Page 217 Congruent triangles......Page 221 Similar triangles......Page 223 Construction of triangles......Page 225 The theorem of Pythagoras......Page 228 Sines, cosines and tangents......Page 231 Evaluating trigonometric ratios of acute angles......Page 233 Solving right-angled triangles......Page 235 Angles of elevation and depression......Page 239 Graphs of trigonometric functions......Page 244 Angles of any magnitude......Page 245 Terminology involved with sine and cosine waves......Page 248 Sinusoidal form:......Page 251 The sine and cosine rules......Page 254 Workedproblemsonthesolution of triangles and their areas......Page 255 Further worked problems on the solution of triangles and their areas......Page 257 Practical situations involving trigonometry......Page 258 Further practical situations involving trigonometry......Page 260 Changing from Cartesian to polar co-ordinates......Page 263 Changing from polar to Cartesian co-ordinates......Page 265 Use of Pol/Rec functions on calculators......Page 266 Common shapes......Page 274 Areas of common shapes......Page 277 Areas of similar shapes......Page 284 Properties of circles......Page 286 Radians and degrees......Page 288 Arc length and area of circles and sectors......Page 289 The equation of a circle......Page 293 Volumes and surface areas of common shapes......Page 297 More complex volumes and surface areas......Page 304 Volumes and surface areas of frusta of pyramids and cones......Page 310 Volumes of similar shapes......Page 314 Areas of irregular figures......Page 315 Volumes of irregular solids......Page 318 Mean or average values of waveforms......Page 319 Scalars and vectors......Page 325 Drawing a vector......Page 326 Addition of vectors by drawing......Page 327 Resolving vectors into horizontal and vertical components......Page 329 Addition of vectors by calculation......Page 330 Vector subtraction......Page 334 Relative velocity......Page 335 notation......Page 336 Combining two periodic functions......Page 338 Plotting periodic functions......Page 339 Determining resultant phasors by drawing......Page 340 Determining resultant phasors by the sine and cosine rules......Page 342 Determining resultant phasors by horizontal and vertical components......Page 343 Presentation of statistical data......Page 351 Some statistical terminology......Page 352 Presentation of ungrouped data......Page 353 Presentation of grouped data......Page 356 Measures of central tendency......Page 363 Mean, median and mode for discrete data......Page 364 Mean, median and mode for grouped data......Page 365 Standard deviation......Page 366 Quartiles, deciles and percentiles......Page 368 Probability......Page 370 Introduction to probability......Page 371 Laws of probability......Page 372 Functional notation......Page 380 The gradient of a curve......Page 381 Differentiation from first principles......Page 382 by the general rule......Page 383 Differentiation of sine and cosine functions......Page 386 and......Page 388 Summary of standard derivatives......Page 389 Rates of change......Page 390 Differentiation of a product......Page 392 Differentiation of a quotient......Page 393 Function of a function......Page 394 The process of integration......Page 396 Standard integrals......Page 397 Definite integrals......Page 400 The area under a curve......Page 402 Simple sequences......Page 411 th term of a series......Page 412 Arithmetic progressions......Page 413 Geometric progressions......Page 416 Introduction......Page 420 Binary numbers......Page 421 Octal numbers......Page 424 Hexadecimal numbers......Page 427 Introduction to inequalities......Page 431 Inequalities involving a modulus......Page 432 Inequalities involving quotients......Page 433 Inequalities involving square functions......Page 434 Quadratic inequalities......Page 435 Chapter 2......Page 444 Chapter 4......Page 445 Chapter 7......Page 446 Chapter 8......Page 447 Chapter 10......Page 448 Chapter 12......Page 449 Chapter 14......Page 450 Chapter 16......Page 451 Chapter 19......Page 452 Chapter 21......Page 453 Chapter 23......Page 454 Chapter 26......Page 455 Chapter 29......Page 456 Chapter 32......Page 457 Chapter 34......Page 458 Chapter 35......Page 459 Chapter 37......Page 460 Chapter 39......Page 461 Index......Page 464