Basic engineering mathematics / J. O. Bird

Enhanced descriptions from Syndetics:

A wide range of courses have an intake that requires a basic, easy introduction to the key maths topics for engineering - Basic Engineering Mathematics is designed to fulfil that need. Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, yet unlike low-level general maths texts the content is tailored for the needs of engineers. The result is a unique text written for engineering students, but which takes a starting point below GCSE level. The textbook is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult. John Bird's approach is based on numerous worked examples, supported by 525 worked problems and followed by 925 further problems. The content has been designed to match current level 2 courses, including Intermediate GNVQ and the new specifications for BTEC First. Level 3 students who struggle with their maths will also find this book particularly useful. With this in mind, all topics within the compulsory units of the AVCE (Applied Mathematics for Engineering) and the new specifications for BTEC National (Mathematics for Technicians) are covered. Lecturers' support materials: Throughout the book Assignments are provided that are ideal for use as tests or homework. These are the only problems where answers are not provided in the book. Full worked solutions are available to lecturers only as a free download from the Newnes website: www.newnespress.com * Unique in being written for engineering students but taking a starting point below GCSE level * Coverage fully matched to the requirements of the core units of the new BTEC First and BTEC National specifications * Ideal for a wide range of Level 2 courses including City & Guilds certificates and EMTA/EAL NVQs

Table of contents provided by Syndetics

• Preface (p. xi)
• 1. Basic arithmetic (p. 1)
• 1.1 Arithmetic operations (p. 1)
• 1.2 Highest common factors and lowest common multiples (p. 3)
• 1.3 Order of precedence and brackets (p. 4)
• 2. Fractions, decimals and percentages (p. 6)
• 2.1 Fractions (p. 6)
• 2.2 Ratio and proportion (p. 8)
• 2.3 Decimals (p. 9)
• 2.4 Percentages (p. 11)
• Assignment 1 (p. 12)
• 3. Indices and standard form (p. 14)
• 3.1 Indices (p. 14)
• 3.2 Worked problems on indices (p. 14)
• 3.3 Further worked problems on indices (p. 16)
• 3.4 Standard form (p. 17)
• 3.5 Worked problems on standard form (p. 18)
• 3.6 Further worked problems on standard form (p. 19)
• 4. Calculations and evaluation of formulae (p. 20)
• 4.1 Errors and approximations (p. 20)
• 4.2 Use of calculator (p. 21)
• 4.3 Conversion tables and charts (p. 24)
• 4.4 Evaluation of formulae (p. 26)
• Assignment 2 (p. 28)
• 5. Computer numbering systems (p. 29)
• 5.1 Binary numbers (p. 29)
• 5.2 Conversion of binary to denary (p. 29)
• 5.3 Conversion of denary to binary (p. 30)
• 5.4 Conversion of denary to binary via octal (p. 31)
• 5.5 Hexadecimal numbers (p. 32)
• 6. Algebra (p. 36)
• 6.1 Basic operations (p. 36)
• 6.2 Laws of Indices (p. 38)
• 6.3 Brackets and factorization (p. 40)
• 6.4 Fundamental laws and precedence (p. 42)
• 6.5 Direct and inverse proportionality (p. 44)
• Assignment 3 (p. 45)
• 7. Simple equations (p. 46)
• 7.1 Expressions, equations and identities (p. 46)
• 7.2 Worked problems on simple equations (p. 46)
• 7.3 Further worked problems on simple equations (p. 48)
• 7.4 Practical problems involving simple equations (p. 49)
• 7.5 Further practical problems involving simple equations (p. 51)
• 8. Transposition of formulae (p. 53)
• 8.1 Introduction to transposition of formulae (p. 53)
• 8.2 Worked problems on transposition of formulae (p. 53)
• 8.3 Further worked problems on transposition of formulae (p. 54)
• 8.4 Harder worked problems on transposition of formulae (p. 56)
• Assignment 4 (p. 58)
• 9. Simultaneous equations (p. 59)
• 9.1 Introduction to simultaneous equations (p. 59)
• 9.2 Worked problems on simultaneous equations in two unknowns (p. 59)
• 9.3 Further worked problems on simultaneous equations (p. 61)
• 9.4 More difficult worked problems on simultaneous equations (p. 62)
• 9.5 Practical problems involving simultaneous equations (p. 64)
• 10. Quadratic equations (p. 68)
• 10.1 Introduction to quadratic equations (p. 68)
• 10.2 Solution of quadratic equations by factorization (p. 68)
• 10.3 Solution of quadratic equations by 'completing the square' (p. 70)
• 10.4 Solution of quadratic equations by formula (p. 71)
• 10.5 Practical problems involving quadratic equations (p. 72)
• 10.6 The solution of linear and quadratic equations simultaneously (p. 74)
• Assignment 5 (p. 75)
• 11. Straight line graphs (p. 76)
• 11.1 Introduction to graphs (p. 76)
• 11.2 The straight line graph (p. 76)
• 11.3 Practical problems involving straight line graphs (p. 81)
• 12. Graphical solution of equations (p. 87)
• 12.1 Graphical solution of simultaneous equations (p. 87)
• 12.2 Graphical solutions of quadratic equations (p. 88)
• 12.3 Graphical solution of linear and quadratic equations simultaneously (p. 92)
• 12.4 Graphical solution of cubic equations (p. 93)
• Assignment 6 (p. 94)
• 13. Logarithms (p. 96)
• 13.1 Introduction to logarithms (p. 96)
• 13.2 Laws of logarithms (p. 96)
• 13.3 Indicial equations (p. 98)
• 13.4 Graphs of logarithmic functions (p. 99)
• 14. Exponential functions (p. 100)
• 14.1 The exponential function (p. 100)
• 14.2 Evaluating exponential functions (p. 100)
• 14.3 The power series for e[superscript x] (p. 101)
• 14.4 Graphs of exponential functions (p. 103)
• 14.5 Napierian logarithms (p. 104)
• 14.6 Evaluating Napierian logarithms (p. 104)
• 14.7 Laws of growth and decay (p. 106)
• Assignment 7 (p. 109)
• 15. Reduction of non-linear laws to linear form (p. 110)
• 15.1 Determination of law (p. 110)
• 15.2 Determination of law involving logarithms (p. 112)
• 16. Geometry and triangles (p. 117)
• 16.1 Angular measurement (p. 117)
• 16.2 Types and properties of angles (p. 118)
• 16.3 Properties of triangles (p. 120)
• 16.4 Congruent triangles (p. 122)
• 16.5 Similar triangles (p. 123)
• 16.6 Construction of triangles (p. 125)
• Assignment 8 (p. 126)
• 17. Introduction to trigonometry (p. 128)
• 17.1 Trigonometry (p. 128)
• 17.2 The theorem of Pythagoras (p. 128)
• 17.3 Trigonometric ratios of acute angles (p. 129)
• 17.4 Solution of right-angled triangles (p. 131)
• 17.5 Angles of elevation and depression (p. 132)
• 17.6 Evaluating trigonometric ratios of any angles (p. 134)
• 18. Trigonometric waveforms (p. 137)
• 18.1 Graphs of trigonometric functions (p. 137)
• 18.2 Angles of any magnitude (p. 138)
• 18.3 The production of a sine and cosine wave (p. 140)
• 18.4 Sine and cosine curves (p. 141)
• 18.5 Sinusoidal form A sin([omega]t [plus or minus] [alpha]) (p. 144)
• Assignment 9 (p. 146)
• 19. Cartesian and polar co-ordinates (p. 148)
• 19.1 Introduction (p. 148)
• 19.2 Changing from Cartesian into polar co-ordinates (p. 148)
• 19.3 Changing from polar into Cartesian co-ordinates (p. 150)
• 19.4 Use of R [right arrow] P and P [right arrow] R functions on calculators (p. 151)
• 20. Areas of plane figures (p. 152)
• 20.1 Mensuration (p. 152)
• 20.2 Properties of quadrilaterals (p. 152)
• 20.3 Worked problems on areas of plane figures (p. 153)
• 20.4 Further worked problems on areas of plane figures (p. 157)
• 20.5 Areas of similar shapes (p. 158)
• Assignment 10 (p. 159)
• 21. The circle (p. 160)
• 21.1 Introduction (p. 160)
• 21.2 Properties of circles (p. 160)
• 21.3 Arc length and area of a sector (p. 161)
• 21.4 The equation of a circle (p. 164)
• 22. Volumes of common solids (p. 166)
• 22.1 Volumes and surface areas of regular solids (p. 166)
• 22.2 Worked problems on volumes and surface areas of regular solids (p. 166)
• 22.3 Further worked problems on volumes and surface areas of regular solids (p. 168)
• 22.4 Volumes and surface areas of frusta of pyramids and cones (p. 172)
• 22.5 Volumes of similar shapes (p. 175)
• Assignment 11 (p. 175)
• 23. Irregular areas and volumes and mean values of waveforms (p. 177)
• 23.1 Areas of irregular figures (p. 177)
• 23.2 Volumes of irregular solids (p. 179)
• 23.3 The mean or average value of a waveform (p. 180)
• 24. Triangles and some practical applications (p. 184)
• 24.1 Sine and cosine rules (p. 184)
• 24.2 Area of any triangle (p. 184)
• 24.3 Worked problems on the solution of triangles and their areas (p. 184)
• 24.4 Further worked problems on the solution of triangles and their areas (p. 186)
• 24.5 Practical situations involving trigonometry (p. 187)
• 24.6 Further practical situations involving trigonometry (p. 190)
• Assignment 12 (p. 192)
• 25. Vectors (p. 193)
• 25.1 Introduction (p. 193)
• 25.2 Vector addition (p. 193)
• 25.3 Resolution of vectors (p. 195)
• 25.4 Vector subtraction (p. 196)
• 25.5 Relative velocity (p. 198)
• 26. Number sequences (p. 200)
• 26.1 Simple sequences (p. 200)
• 26.2 The n'th term of a series (p. 200)
• 26.3 Arithmetic progressions (p. 201)
• 26.4 Worked problems on arithmetic progression (p. 202)
• 26.5 Further worked problems on arithmetic progressions (p. 203)
• 26.6 Geometric progressions (p. 204)
• 26.7 Worked problems on geometric progressions (p. 205)
• 26.8 Further worked problems on geometric progressions (p. 206)
• Assignment 13 (p. 207)
• 27. Presentation of statistical data (p. 208)
• 27.1 Some statistical terminology (p. 208)
• 27.2 Presentation of ungrouped data (p. 209)
• 27.3 Presentation of grouped data (p. 212)
• 28. Measures of central tendency and dispersion (p. 217)
• 28.1 Measures of central tendency (p. 217)
• 28.2 Mean, median and mode for discrete data (p. 217)
• 28.3 Mean, median and mode for grouped data (p. 218)
• 28.4 Standard deviation (p. 219)
• 28.5 Quartiles, deciles and percentiles (p. 221)
• 29. Probability (p. 223)
• 29.1 Introduction to probability (p. 223)
• 29.2 Laws of probability (p. 223)
• 29.3 Worked problems on probability (p. 224)
• 29.4 Further worked problems on probability (p. 225)
• Assignment 14 (p. 227)
• List of formulae (p. 229)
• Answers to exercises (p. 233)
• Index (p. 247)