Basic Engineering Mathematics, Fourth Edition

Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically for the needs of engineers. The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult. All students taking vocational engineering courses who require fundamental knowledge of mathematics for engineering and do not have prior knowledge beyond basic school mathematics, will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering and Intermediate GNVQ, and is matched to BTEC First specifications. However Level 3 students will also find this text to be a useful resource for getting to grips with the essential mathematics concepts needed for their study, as the compulsory topics required in BTEC National and AVCE / A Level courses are also addressed. The fourth edition incorporates new material on adding waveforms, graphs with logarithmic scales, and inequalities - key topics needed for GCSE and Level 2 study. John Bird 's approach is based on numerous worked examples, supported by 600 worked problems, followed by 1050 further problems within exercises included throughout the text. In addition, 15 Assignments are included at regular intervals. Ideal for use as tests or homework, full solutions to the Assignments are supplied in the accompanying Instructor's Manual, available as a free download for lecturers from http://textbooks.elsevier.com. * Unique in introducing fundamental mathematics from an engineering perspective, with a starting point below GCSE level * Fully matched to BTEC First and BTEC National core unit specifications * Free instructor's manual available to download - contains worked solutions and suggested mark scheme Cover......Page 1 Basic Engineering Mathematics......Page 4 Contents......Page 6 Preface......Page 12 1.1 Arithmetic operations......Page 13 1.2 Highest common factors and lowest common multiples......Page 15 1.3 Order of precedence and brackets......Page 16 2.1 Fractions......Page 18 2.2 Ratio and proportion......Page 20 2.3 Decimals......Page 21 2.4 Percentages......Page 23 Assignment 1......Page 25 3.2 Worked problems on indices......Page 26 3.3 Further worked problems on indices......Page 28 3.4 Standard form......Page 29 3.5 Worked problems on standard form......Page 30 3.7 Engineering notation and common prefixes......Page 31 4.1 Errors and approximations......Page 33 4.2 Use of calculator......Page 34 4.3 Conversion tables and charts......Page 37 4.4 Evaluation of formulae......Page 39 Assignment 2......Page 41 5.2 Conversion of binary to denary......Page 42 5.3 Conversion of denary to binary......Page 43 5.4 Conversion of denary to binary via octal......Page 44 5.5 Hexadecimal numbers......Page 45 6.1 Basic operations......Page 49 6.2 Laws of indices......Page 51 6.3 Brackets and factorization......Page 53 6.4 Fundamental laws and precedence......Page 55 6.5 Direct and inverse proportionality......Page 57 Assignment 3......Page 58 7.2 Worked problems on simple equations......Page 59 7.3 Further worked problems on simple equations......Page 61 7.4 Practical problems involving simple equations......Page 62 7.5 Further practical problems involving simple equations......Page 64 8.2 Worked problems on transposition of formulae......Page 66 8.3 Further worked problems on transposition of formulae......Page 67 8.4 Harder worked problems on transposition of formulae......Page 69 Assignment 4......Page 71 9.2 Worked problems on simultaneous equations in two unknowns......Page 72 9.3 Further worked problems on simultaneous equations......Page 74 9.4 More difficult worked problems on simultaneous equations......Page 75 9.5 Practical problems involving simultaneous equations......Page 77 10.2 Solution of quadratic equations by factorization......Page 81 10.3 Solution of quadratic equations by ‘completing the square’......Page 83 10.4 Solution of quadratic equations by formula......Page 84 10.5 Practical problems involving quadratic equations......Page 85 10.6 The solution of linear and quadratic equations simultaneously......Page 87 11.2 Simple inequalities......Page 89 11.3 Inequalities involving a modulus......Page 90 11.5 Inequalities involving square functions......Page 91 11.6 Quadratic inequalities......Page 92 Assignment 5......Page 94 12.2 The straight line graph......Page 95 12.3 Practical problems involving straight line graphs......Page 100 13.1 Graphical solution of simultaneous equations......Page 106 13.2 Graphical solutions of quadratic equations......Page 107 13.3 Graphical solution of linear and quadratic equations simultaneously......Page 111 13.4 Graphical solution of cubic equations......Page 112 Assignment 6......Page 114 14.2 Laws of logarithms......Page 115 14.3 Indicial equations......Page 117 14.4 Graphs of logarithmic functions......Page 118 15.2 Evaluating exponential functions......Page 119 15.3 The power series for e[sup(x)]......Page 120 15.4 Graphs of exponential functions......Page 122 15.6 Evaluating Napierian logarithms......Page 123 15.7 Laws of growth and decay......Page 125 Assignment 7......Page 128 16.1 Determination of law......Page 129 16.2 Determination of law involving logarithms......Page 131 17.2 Graphs of the form y=ax[sup(n)]......Page 136 17.3 Graphs of the form y=ab[sup(x)]......Page 139 17.4 Graphs of the form y=ae[sup(kx)]......Page 140 18.1 Angular measurement......Page 143 18.2 Types and properties of angles......Page 144 18.3 Properties of triangles......Page 146 18.4 Congruent triangles......Page 148 18.5 Similar triangles......Page 149 18.6 Construction of triangles......Page 151 Assignment 8......Page 153 19.2 The theorem of Pythagoras......Page 154 19.3 Trigonometric ratios of acute angles......Page 155 19.4 Solution of right-angled triangles......Page 157 19.5 Angles of elevation and depression......Page 159 19.6 Evaluating trigonometric ratios of any angles......Page 160 20.1 Graphs of trigonometric functions......Page 163 20.2 Angles of any magnitude......Page 164 20.3 The production of a sine and cosine wave......Page 166 20.4 Sine and cosine curves......Page 167 20.5 Sinusoidal form A sin(ωt ± a)......Page 170 Assignment 9......Page 173 21.2 Changing from Cartesian into polar co-ordinates......Page 174 21.3 Changing from polar into Cartesian co-ordinates......Page 175 21.4 Use of R → P and P → R functions on calculators......Page 176 22.2 Properties of quadrilaterals......Page 178 22.3 Worked problems on areas of plane figures......Page 179 22.4 Further worked problems on areas of plane figures......Page 183 22.5 Areas of similar shapes......Page 184 Assignment 10......Page 185 23.2 Properties of circles......Page 186 23.3 Arc length and area of a sector......Page 187 23.4 The equation of a circle......Page 190 24.2 Worked problems on volumes and surface areas of regular solids......Page 192 24.3 Further worked problems on volumes and surface areas of regular solids......Page 194 24.4 Volumes and surface areas of frusta of pyramids and cones......Page 198 24.5 Volumes of similar shapes......Page 201 Assignment 11......Page 202 25.1 Areas of irregular figures......Page 203 25.2 Volumes of irregular solids......Page 205 25.3 The mean or average value of a waveform......Page 206 26.3 Worked problems on the solution of triangles and their areas......Page 210 26.4 Further worked problems on the solution of triangles and their areas......Page 212 26.5 Practical situations involving trigonometry......Page 213 26.6 Further practical situations involving trigonometry......Page 216 Assignment 12......Page 218 27.2 Vector addition......Page 219 27.3 Resolution of vectors......Page 221 27.4 Vector subtraction......Page 222 27.5 Relative velocity......Page 224 28.2 Plotting periodic functions......Page 226 28.3 Determining resultant phasors by calculation......Page 227 29.2 The n’th term of a series......Page 230 29.3 Arithmetic progressions......Page 231 29.4 Worked problems on arithmetic progression......Page 232 29.5 Further worked problems on arithmetic progressions......Page 233 29.6 Geometric progressions......Page 234 29.7 Worked problems on geometric progressions......Page 235 29.8 Further worked problems on geometric progressions......Page 236 Assignment 13......Page 237 30.1 Some statistical terminology......Page 238 30.2 Presentation of ungrouped data......Page 239 30.3 Presentation of grouped data......Page 242 31.2 Mean, median and mode for discrete data......Page 247 31.3 Mean, median and mode for grouped data......Page 248 31.4 Standard deviation......Page 249 31.5 Quartiles, deciles and percentiles......Page 251 32.2 Laws of probability......Page 253 32.3 Worked problems on probability......Page 254 32.4 Further worked problems on probability......Page 255 Assignment 14......Page 258 33.2 Functional notation......Page 259 33.3 The gradient of a curve......Page 260 33.4 Differentiation from first principles......Page 261 33.5 Differentiation of y=ax[sup(n)] by the general rule......Page 262 33.6 Differentiation of sine and cosine functions......Page 264 33.7 Differentiation of e[sup(ax)] and ln ax......Page 265 33.8 Summary of standard derivatives......Page 266 33.10 Rates of change......Page 267 34.3 Standard integrals......Page 269 34.4 Definite integrals......Page 272 34.5 Area under a curve......Page 273 Assignment 15......Page 277 List of formulae......Page 278 Answers to exercises......Page 282 D......Page 297 I......Page 298 Q......Page 299 Y......Page 300 Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically for the needs of engineers. The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult. All students taking vocational engineering courses who require fundamental knowledge of mathematics for engineering and do not have prior knowledge beyond basic school mathematics, will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering and Intermediate GNVQ, and is matched to BTEC First specifications. However Level 3 students will also find this text to be a useful resource for getting to grips with the essential mathematics concepts needed for their study, as the compulsory topics required in BTEC National and AVCE / A Level courses are also addressed. The fourth edition incorporates new material on adding waveforms, graphs with logarithmic scales, and inequalities - key topics needed for GCSE and Level 2 study. John Bird 's approach is based on numerous worked examples, supported by 600 worked problems, followed by 1050 further problems within exercises included throughout the text. In addition, 15 Assignments are included at regular intervals. Ideal for use as tests or homework, full solutions to the Assignments are supplied in the accompanying Instructor's Manual, available as a free download for lecturers from the Newnes website at * Unique in introducing fundamental mathematics from an engineering perspective, with a starting point below GCSE level * Fully matched to BTEC First and BTEC National core unit specifications * Free instructor's manual available to download - contains worked solutions and suggested mark scheme

unlike Most Engineering Maths Texts, This Book Does Not Assume A Firm Grasp Of Gcse Maths, And Unlike Low-level General Maths Texts, The Content Is Tailored Specifically To The Needs Of Engineers. The Result Is A Unique Book Written For Engineering Students That Takes A Starting Point Below Gcse Level. Basic Engineering Mathematics Is Therefore Ideal For Students Of A Wide Range Of Abilities, Especially For Those Who Find The Theoretical Side Of Mathematics Difficult.

now In Its Fifth Edition, Basic Engineering Mathematics Is An Established Textbook, With The Previous Edition Selling Nearly 7500 Copies. All Students That Require A Fundamental Knowledge Of Mathematics For Engineering Will Find This Book Essential Reading. The Content Has Been Designed Primarily To Meet The Needs Of Students Studying Level 2 Courses, Including Gcse Engineering, The Diploma, And The Btec First Specifications. Level 3 Students Will Also Find This Text To Be A Useful Resource For Getting To Grips With Essential Mathematics Concepts, Because The Compulsory Topics In Btec National And A Level Engineering Courses Are Also Addressed.

• Numerous Worked Examples Supported By 600 Worked Problems And 1050 Further Problems Within Exercises Included Throughout The Text. Additionally, There Are 15 Assignments Included At Regular Intervals.
• Free Instructor’s Manual Available For Download, Which Includes Solutions To Assignments.

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this Textbook For A Level 2 Math Course Takes A Starting Point Below The Gcse Level, Covering Fractions, Algebra, Graphical Solution Of Equations, Trigonometry, Areas, Volumes, And Number Sequences. The Second Edition Matches Year 2000 Intermediate Gnvq Specifications. Annotation C. Book News, Inc., Portland, Or (booknews.com)

Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically for the needs of engineers. The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult.All students taking vocational engineering courses who require fundamental knowledge of mathematics for engineering and do not have prior knowledge beyond basic school mathematics, will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering and Intermediate GNVQ, and is matched to BTEC First specifications. However, Level 3 students will also find this text to be a useful resource for getting to grips with the essential mathematics concepts needed for their study, as the compulsory topics required in BTEC National and AVCE / A Level courses are also addressed.The fourth edition incorporates new material on adding waveforms, graphs with logarithmic scales, and inequalities - key topics needed for GCSE and Level 2 study.John Bird's approach is based on numerous worked examples, supported by 600 worked problems, followed by 1050 further problems within exercises included throughout the text. In addition, 15 Assignments are included at regular intervals. Ideal for use as tests or homework, full solutions to the Assignments are supplied in the accompanying Instructor's Manual, available as a free download for lecturers (please refer to the preface for URL and download instructions).