Bird’s Engineering Mathematics, 9th Edition
- Length: 758 pages
- Edition: 9
- Language: English
- Publisher: Routledge
- Publication Date: 2021-03-16
- ISBN-10: 0367643782
- ISBN-13: 9780367643782
- Sales Rank: #2522471 (See Top 100 Books)
Now in its ninth edition, Bird’s 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 1,300 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 topic coverage makes this a great text for a range of level 2 and 3 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 and A-level revision.
Its companion website at www.routledge.com/cw/bird provides resources for both students and lecturers, including full solutions for all 2,000 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 Section 1 Number and algebra 1 Revision of fractions, decimals and percentages 1.1 Fractions 1.2 Ratio and proportion 1.3 Decimals 1.4 Percentages 2 Indices, engineering notation and metric conversions 2.1 Indices 2.2 Worked problems on indices 2.3 Engineering notation and common prefixes 2.4 Metric conversions 2.5 Metric - US/imperial conversions 3 Binary, octal and hexadecimal numbers 3.1 Introduction 3.2 Binary numbers 3.3 Octal numbers 3.4 Hexadecimal numbers 4 Calculations and evaluation of formulae 4.1 Errors and approximations 4.2 Use of calculator 4.3 Conversion tables and charts 4.4 Evaluation of formulae Revision Test 1 5 Algebra 5.1 Basic operations 5.2 Laws of indices 5.3 Brackets and factorisation 5.4 Fundamental laws and precedence 5.5 Direct and inverse proportionality 6 Further algebra 6.1 Polynomial division 6.2 The factor theorem 6.3 The remainder theorem 7 Partial fractions 7.1 Introduction to partial fractions 7.2 Partial fractions with linear factors 7.3 Partial fractions with repeated linear factors 7.4 Partial fractions with quadratic factors 8 Solving simple equations 8.1 Expressions, equations and identities 8.2 Worked problems on simple equations 8.3 Further worked problems on simple equations 8.4 Practical problems involving simple equations 8.5 Further practical problems involving simple equations Revision Test 2 9 Transposition of formulae 9.1 Introduction to transposition of formulae 9.2 Worked problems on transposition of formulae 9.3 Further worked problems on transposition of formulae 9.4 Harder worked problems on transposition of formulae 10 Solving simultaneous equations 10.1 Introduction to simultaneous equations 10.2 Worked problems on simultaneous equations in two unknowns 10.3 Further worked problems on simultaneous equations 10.4 More difficult worked problems on simultaneous equations 10.5 Practical problems involving simultaneous equations 11 Solving quadratic equations 11.1 Introduction to quadratic equations 11.2 Solution of quadratic equations by factorisation 11.3 Solution of quadratic equations by ‘completing the square’ 11.4 Solution of quadratic equations by formula 11.5 Practical problems involving quadratic equations 11.6 The solution of linear and quadratic equations simultaneously 12 Inequalities 12.1 Introduction to inequalities 12.2 Simple inequalities 12.3 Inequalities involving a modulus 12.4 Inequalities involving quotients 12.5 Inequalities involving square functions 12.6 Quadratic inequalities 13 Logarithms 13.1 Introduction to logarithms 13.2 Laws of logarithms 13.3 Indicial equations 13.4 Graphs of logarithmic functions Revision Test 3 14 Exponential functions 14.1 Introduction to exponential functions 14.2 The power series for ex 14.3 Graphs of exponential functions 14.4 Napierian logarithms 14.5 Laws of growth and decay 15 Number sequences 15.1 Arithmetic progressions 15.2 Worked problems on arithmetic progressions 15.3 Further worked problems on arithmetic progressions 15.4 Geometric progressions 15.5 Worked problems on geometric progressions 15.6 Further worked problems on geometric progressions 15.7 Combinations and permutations 16 The binomial series 16.1 Pascal’s triangle 16.2 The binomial series 16.3 Worked problems on the binomial series 16.4 Further worked problems on the binomial series 16.5 Practical problems involving the binomial theorem Revision Test 4 Section 2 Trigonometry 17 Introduction to trigonometry 17.1 Trigonometry 17.2 The theorem of Pythagoras 17.3 Trigonometric ratios of acute angles 17.4 Fractional and surd forms of trigonometric ratios 17.5 Evaluating trigonometric ratios of any angles 17.6 Solution of right-angled triangles 17.7 Angle of elevation and depression 17.8 Trigonometric approximations for small angles 18 Trigonometric waveforms 18.1 Graphs of trigonometric functions 18.2 Angles of any magnitude 18.3 The production of a sine and cosine wave 18.4 Sine and cosine curves 18.5 Sinusoidal form Asin(ωt±α) 18.6 Waveform harmonics 19 Cartesian and polar co-ordinates 19.1 Introduction 19.2 Changing from Cartesian into polar co-ordinates 19.3 Changing from polar into Cartesian co-ordinates 19.4 Use of Pol/Rec functions on calculators Revision Test 5 20 Triangles and some practical applications 20.1 Sine and cosine rules 20.2 Area of any triangle 20.3 Worked problems on the solution of triangles and their areas 20.4 Further worked problems on the solution of triangles and their areas 20.5 Practical situations involving trigonometry 20.6 Further practical situations involving trigonometry 21 Trigonometric identities and equations 21.1 Trigonometric identities 21.2 Worked problems on trigonometric identities 21.3 Trigonometric equations 21.4 Worked problems (i) on trigonometric equations 21.5 Worked problems (ii) on trigonometric equations 21.6 Worked problems (iii) on trigonometric equations 21.7 Worked problems (iv) on trigonometric equations 22 Compound angles 22.1 Compound angle formulae 22.2 Conversion of asinωt+bcos ωt into R sin(ωt+α) 22.3 Double angles 22.4 Changing products of sines and cosines into sums or differences 22.5 Changing sums or differences of sines and cosines into products Revision Test 6 Section 3 Areas and volumes 23 Areas of common shapes 23.1 Introduction 23.2 Properties of quadrilaterals 23.3 Areas of common shapes 23.4 Worked problems on areas of common shapes 23.5 Further worked problems on areas of plane figures 23.6 Worked problems on areas of composite figures 23.7 Areas of similar shapes 24 The circle and its properties 24.1 Introduction 24.2 Properties of circles 24.3 Radians and degrees 24.4 Arc length and area of circles and sectors 24.5 Worked problems on arc length and area of circles and sectors 24.6 The equation of a circle 25 Volumes and surface areas of common solids 25.1 Introduction 25.2 Volumes and surface areas of regular solids 25.3 Worked problems on volumes and surface areas of regular solids 25.4 Further worked problems on volumes and surface areas of regular solids 25.5 Volumes and surface areas of frusta of pyramids and cones 25.6 The frustum and zone of a sphere 25.7 Prismoidal rule 25.8 Volumes of similar shapes 26 Irregular areas and volumes and mean values of waveforms 26.1 Area of irregular figures 26.2 Volumes of irregular solids 26.3 The mean or average value of a waveform Revision Test 7 Section 4 Graphs 27 Straight line graphs 27.1 Introduction to graphs 27.2 The straight line graph 27.3 Practical problems involving straight line graphs 28 Reduction of non-linear laws to linear form 28.1 Determination of law 28.2 Determination of law involving logarithms 29 Graphs with logarithmic scales 29.1 Logarithmic scales 29.2 Graphs of the form y=axn 29.3 Graphs of the form y=abx 29.4 Graphs of the form y=aekx 30 Graphical solution of equations 30.1 Graphical solution of simultaneous equations 30.2 Graphical solution of quadratic equations 30.3 Graphical solution of linear and quadratic equations simultaneously 30.4 Graphical solution of cubic equations 31 Functions and their curves 31.1 Standard curves 31.2 Simple transformations 31.3 Periodic functions 31.4 Continuous and discontinuous functions 31.5 Even and odd functions 31.6 Inverse functions Revision Test 8 Section 5 Complex numbers 32 Complex numbers 32.1 Cartesian complex numbers 32.2 The Argand diagram 32.3 Addition and subtraction of complex numbers 32.4 Multiplication and division of complex numbers 32.5 Complex equations 32.6 The polar form of a complex number 32.7 Multiplication and division in polar form 32.8 Applications of complex numbers 33 De Moivre’s theorem 33.1 Introduction 33.2 Powers of complex numbers 33.3 Roots of complex numbers Section 6 Vectors 34 Vectors 34.1 Introduction 34.2 Scalars and vectors 34.3 Drawing a vector 34.4 Addition of vectors by drawing 34.5 Resolving vectors into horizontal and vertical components 34.6 Addition of vectors by calculation 34.7 Vector subtraction 34.8 Relative velocity 34.9 i,j, and k notation 35 Methods of adding alternating waveforms 35.1 Combination of two periodic functions 35.2 Plotting periodic functions 35.3 Determining resultant phasors by drawing 35.4 Determining resultant phasors by the sine and cosine rules 35.5 Determining resultant phasors by horizontal and vertical components 35.6 Determining resultant phasors by complex numbers Revision Test 9 Section 7 Differential calculus 36 Introduction to differentiation 36.1 Introduction to calculus 36.2 Functional notation 36.3 The gradient of a curve 36.4 Differentiation from first principles 36.5 Differentiation of y=axn by the general rule 36.6 Differentiation of sine and cosine functions 36.7 Differentiation of eax and lnax 37 Methods of differentiation 37.1 Differentiation of common functions 37.2 Differentiation of a product 37.3 Differentiation of a quotient 37.4 Function of a function 37.5 Successive differentiation 38 Some applications of differentiation 38.1 Rates of change 38.2 Velocity and acceleration 38.3 Turning points 38.4 Practical problems involving maximum and minimum values 38.5 Points of inflexion 38.6 Tangents and normals 38.7 Small changes 39 Solving equations by Newton’s method 39.1 Introduction to iterative methods 39.2 The Newton--Raphson method 39.3 Worked problems on the Newton--Raphson method 40 Maclaurin’s series 40.1 Introduction 40.2 Derivation of Maclaurin’s theorem 40.3 Conditions of Maclaurin’s series 40.4 Worked problems on Maclaurin’s series Revision Test 10 41 Differentiation of parametric equations 41.1 Introduction to parametric equations 41.2 Some common parametric equations 41.3 Differentiation in parameters 41.4 Further worked problems on differentiation of parametric equations 42 Differentiation of implicit functions 42.1 Implicit functions 42.2 Differentiating implicit functions 42.3 Differentiating implicit functions containing products and quotients 42.4 Further implicit differentiation 43 Logarithmic differentiation 43.1 Introduction to logarithmic differentiation 43.2 Laws of logarithms 43.3 Differentiation of logarithmic functions 43.4 Differentiation of further logarithmic functions 43.5 Differentiation of f(x)x Revision Test 11 Section 8 Integral calculus 44 Standard integration 44.1 The process of integration 44.2 The general solution of integrals of the form axn 44.3 Standard integrals 44.4 Definite integrals 45 Integration using algebraic substitutions 45.1 Introduction 45.2 Algebraic substitutions 45.3 Worked problems on integration using algebraic substitutions 45.4 Further worked problems on integration using algebraic substitutions 45.5 Change of limits 46 Integration using trigonometric substitutions 46.1 Introduction 46.2 Worked problems on integration of sin2x,cos2x,tan2x and cot2x 46.3 Worked problems on integration of powers of sines and cosines 46.4 Worked problems on integration of products of sines and cosines 46.5 Worked problems on integration using the sin θ substitution 46.6 Worked problems on integration using the tan θ substitution Revision Test 12 47 Integration using partial fractions 47.1 Introduction 47.2 Integration using partial fractions with linear factors 47.3 Integration using partial fractions with repeated linear factors 47.4 Integration using partial fractions with quadratic factors 48 The t=tanθ2 substitution 48.1 Introduction 48.2 Worked problems on the t=tanθ2 substitution 48.3 Further worked problems on the t=tanθ2 substitution 49 Integration by parts 49.1 Introduction 49.2 Worked problems on integration by parts 49.3 Further worked problems on integration by parts 50 Numerical integration 50.1 Introduction 50.2 The trapezoidal rule 50.3 The mid-ordinate rule 50.4 Simpson’s rule 50.5 Accuracy of numerical integration Revision Test 13 51 Areas under and between curves 51.1 Area under a curve 51.2 Worked problems on the area under a curve 51.3 Further worked problems on the area under a curve 51.4 The area between curves 52 Mean and root mean square values 52.1 Mean or average values 52.2 Root mean square values 53 Volumes of solids of revolution 53.1 Introduction 53.2 Worked problems on volumes of solids of revolution 53.3 Further worked problems on volumes of solids of revolution 54 Centroids of simple shapes 54.1 Centroids 54.2 The first moment of area 54.3 Centroid of area between a curve and the x-axis 54.4 Centroid of area between a curve and the y-axis 54.5 Worked problems on centroids of simple shapes 54.6 Further worked problems on centroids of simple shapes 54.7 Theorem of Pappus 55 Second moments of area 55.1 Second moments of area and radius of gyration 55.2 Second moment of area of regular sections 55.3 Parallel axis theorem 55.4 Perpendicular axis theorem 55.5 Summary of derived results 55.6 Worked problems on second moments of area of regular sections 55.7 Worked problems on second moments of area of composite areas Revision Test 14 Section 9 Differential equations 56 Introduction to differential equations 56.1 Family of curves 56.2 Differential equations 56.3 The solution of equations of the form dydx=f(x) 56.4 The solution of equations of the form dydx=f(y) 56.5 The solution of equations of the form dydx=f(x)·f(y) Revision Test 15 Section 10 Further number and algebra 57 Boolean algebra and logic circuits 57.1 Boolean algebra and switching circuits 57.2 Simplifying Boolean expressions 57.3 Laws and rules of Boolean algebra 57.4 De Morgan’s laws 57.5 Karnaugh maps 57.6 Logic circuits 57.7 Universal logic gates 58 The theory of matrices and determinants 58.1 Matrix notation 58.2 Addition, subtraction and multiplication of matrices 58.3 The unit matrix 58.4 The determinant of a 2 by 2 matrix 58.5 The inverse or reciprocal of a 2 by 2 matrix 58.6 The determinant of a 3 by 3 matrix 58.7 The inverse or reciprocal of a 3 by 3 matrix 59 The solution of simultaneous equations by matrices and determinants 59.1 Solution of simultaneous equations by matrices 59.2 Solution of simultaneous equations by determinants 59.3 Solution of simultaneous equations using Cramers rule 59.4 Solution of simultaneous equations using the Gaussian elimination method Revision Test 16 Section 11 Statistics 60 Presentation of statistical data 60.1 Some statistical terminology 60.2 Presentation of ungrouped data 60.3 Presentation of grouped data 61 Mean, median, mode and standard deviation 61.1 Measures of central tendency 61.2 Mean, median and mode for discrete data 61.3 Mean, median and mode for grouped data 61.4 Standard deviation 61.5 Quartiles, deciles and percentiles 62 Probability 62.1 Introduction to probability 62.2 Laws of probability 62.3 Worked problems on probability 62.4 Further worked problems on probability 62.5 Permutations and combinations 62.6 Bayes’ theorem Revision Test 17 63 The binomial and Poisson distribution 63.1 The binomial distribution 63.2 The Poisson distribution 64 The normal distribution 64.1 Introduction to the normal distribution 64.2 Testing for a normal distribution Revision Test 18 65 Linear correlation 65.1 Introduction to linear correlation 65.2 The Pearson product-moment formula for determining the linear correlation coefficient 65.3 The significance of a coefficient of correlation 65.4 Worked problems on linear correlation 66 Linear regression 66.1 Introduction to linear regression 66.2 The least-squares regression lines 66.3 Worked problems on linear regression 67 Sampling and estimation theories 67.1 Introduction 67.2 Sampling distributions 67.3 The sampling distribution of the means 67.4 The estimation of population parameters based on a large sample size 67.5 Estimating the mean of a population based on a small sample size Revision Test 19 List of essential formulae Answers to Practice Exercises Index
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