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Basic Engineering Mathematics 6th Edition John Bird [PDF]

Basic Engineering Mathematics (6E) by John Bird

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Basic Engineering Mathematics (6E) written by John Bird , BSc(Hons), CMath, CEng, FIMA, MIEE, FIIE(Elec), FCollP
Basic Engineering Mathematics 6th Edition introduces and then consolidates basic mathematical principles and promotes awareness of mathematical concepts for students needing a broad base for further vocational studies. In this sixth edition, new material has been added to some of the chapters, together with around 40 extra practical problems interspersed throughout the text. The four chapters only available on the website in the previous edition have been included in this edition.
In addition, some multiple choice questions have been included to add interest to the learning.
The text covers:
(i) Basic mathematics for a wide range of introductory/access/foundation mathematics courses
(ii) ‘Mathematics for Engineering Technicians’ for BTEC First NQF Level 2; chapters 1 to 12, 16 to 18, 20, 21, 23, and 25 to 27 are needed for this module.
(iii) The mandatory ‘Mathematics for Technicians’ for BTEC National Certificate and National Diploma in Engineering, NQF Level 3; chapters 7 to 10, 14 to 17, 19, 20 to 23, 25 to 27, 31, 32, 34 and 35 are needed for this module. In addition, chapters 1 to 6, 11 and 12 are helpful revision for this module.
(iv) GCSE revision, and for similar mathematics courses in English-speaking countries worldwide.
Basic Engineering Mathematics 6th Edition provides a lead into Engineering Mathematics 7th Edition.
Each topic considered in the text is presented in a way that assumes in the reader little previous knowledge of that topic.
Theory is introduced in each chapter by a brief outline of essential theory, definitions, formulae, laws and procedures. However, these are kept to a minimum, for problem solving is extensively used to establish and exemplify the theory. It is intended that readers will gain real understanding through seeing problems solved and then solving similar problems themselves.
This textbook contains some 750 worked problems, followed by over 1600 further problems (all with answers – at the end of the book). The further problems are contained within 161 Practice Exercises; each Practice Exercise follows on directly from the relevant section of work. 420 line diagrams enhance the understanding of the theory. Where at all possible the problems mirror potential practical situations found in engineering and science.
(John Bird, University of Portsmouth)

Book Detail :-
Title: Engineering Mathematics
Edition: 6th
Author(s): John Bird
Publisher: Newnes
Series:
Year: 2010
Pages: 705
Type: PDF
Language: English
ISBN: 185617767X,9781856177672,9780080962122
Country: UK
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About Author :-
Author John Bird is from Defence College of Technical Training, HMS Sultan, formerly of University of Portsmouth and Highbury College, Portsmouth.
John Bird is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with Examiner responsibilities for Advanced Mathematics with City and Guilds, and examining for the International Baccalaureate Organization. He is the author of some 125 textbooks on engineering and mathematical subjects, with worldwide sales of 1 million copies. He is currently a Senior Training Provider at the Defence School of Marine Engineering in the Defence College of Technical Training at HMS Sultan, Gosport, Hampshire, UK.

All Famous Books of this Author :-
Here is Solution Manual/Text Books of this book, We recomended you to download both.
• Download PDF Basic Engineering Mathematics (3E) by John Bird NEW
• Download PDF Basic Engineering Mathematics (4E) by John Bird NEW
• Download PDF Basic Engineering Mathematics (6E) by John Bird NEW
• Download PDF Engineering Mathematics (5E) by John Bird NEW
• Download PDF Higher Engineering Mathematics (5E) by John Bird NEW
• Download PDF Understanding Engineering Mathematics by John Bird NEW

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Basic Engineering Mathematics (6E) written by John Bird cover the following topics. Algebra
Introduction, Revision of basic laws, Revision of equations, Polynomial division, The factor theorem, The remainder theorem
Partial fractions
Introduction to partial fractions, Worked problems on partial fractions with linear factors, Worked problems on partial fractions with repeated linear factorsvWorked problems on partial fractions with quadratic factors
Logarithms
Introduction to logarithms, Laws of logarithms, Indicial equations, Graphs of logarithmic functions
Exponential functions
Introduction to exponential functions, The power series for ex, Graphs of exponential functions, Napierian logarithms, Laws of growth and decay, Reduction of exponential laws to linear form, Revision Test 1
Hyperbolic functions
Introduction to hyperbolic functions, Graphs of hyperbolic functions, Hyperbolic identities, Solving equations involving hyperbolic functions, Series expansions for cosh x and sinh x
Arithmetic and geometric progressions
Arithmetic progressions, Worked problems on arithmetic progressions, Further worked problems on arithmetic progressions, Geometric progressions, Worked problems on geometric progressions, Further worked problems on geometric progressions
The binomial series
Pascal’s triangle, The binomial series, Worked problems on the binomial series, Further worked problems on the binomial series, Practical problems involving the binomial theorem, Revision Test 2
Maclaurin’s series
Introduction, Derivation of Maclaurin’s theorem, Conditions of Maclaurin’s series, Worked problems on Maclaurin’s series, Numerical integration using Maclaurin’s series, Limiting values
Solving equations by iterative methods
Introduction to iterative methods, The bisection method, An algebraic method of successive approximations, The Newton-Raphson method
Binary, octal and hexadecimal
Introduction, Binary numbers, Octal numbers, Hexadecimal numbers, Revision Test 3
Introduction to trigonometry
Trigonometry, The theorem of Pythagoras, Trigonometric ratios of acute angles, Evaluating trigonometric ratios, Solution of right-angled triangles, Angles of elevation and depression, Sine and cosine rules, Area of any triangle, Worked problems on the solution of triangles and finding their areas, Further worked problems on solving triangles and finding their areas, Practical situations involving trigonometry, Further practical situations involving trigonometry
Cartesian and polar co-ordinates
Introduction, Changing from Cartesian into polar co-ordinates, Changing from polar into Cartesian co-ordinates, Use of Pol/Rec functions on calculators
The circle and its properties
Introduction, Properties of circles, Radians and degrees, Arc length and area of circles and sectors, The equation of a circle, Linear and angular velocity, Centripetal force, Revision Test 4
Trigonometric waveforms
Graphs of trigonometric functions, Angles of any magnitude, The production of a sine and cosine wave, Sine and cosine curves, Sinusoidal form Asin(?t ± a), Harmonic synthesis with complex waveforms 146
Trigonometric identities and equations
Trigonometric identities, Worked problems on trigonometric identities, Trigonometric equations, Worked problems (i) on trigonometric equations, Worked problems (ii) on trigonometric equations, Worked problems (iii) on trigonometric equations, Worked problems (iv) on trigonometric equations
The relationship between trigonometric and hyperbolic functions
The relationship between trigonometric and hyperbolic functions, Hyperbolic identities
Compound angles
Compound angle formulae, Conversion of a sin?t +b cos?t into R sin(?t +a), Double angles, Changing products of sines and cosines into sums or differences, Changing sums or differences of sines and cosines into products, Power waveforms in a.c. circuits, Revision Test 5
Functions and their curves
Standard curves, Simple transformations, Periodic functions, Continuous and discontinuous functions, Even and odd functions, Inverse functions, Asymptotes, Brief guide to curve sketching, Worked problems on curve sketching
Irregular areas, volumes and mean values of waveforms
Areas of irregular figures, Volumes of irregular solids, The mean or average value of a waveform, Revision Test 6
Complex numbers
Cartesian complex numbers, The Argand diagram, Addition and subtraction of complex numbers, Multiplication and division of complex numbers, Complex equations, The polar form of a complex number, Multiplication and division in polar form, Applications of complex numbers
De Moivre’s theorem
Introduction, Powers of complex numbers, Roots of complex numbers, The exponential form of a complex number
The theory of matrices and determinants
Matrix notation, Addition, subtraction and multiplication of matrices, The unit matrix, The determinant of a 2 by 2 matrix, The inverse or reciprocal of a 2 by 2 matrix, The determinant of a 3 by 3 matrix, The inverse or reciprocal of a 3 by 3 matrix
The solution of simultaneous equations by matrices and determinants
Solution of simultaneous equations by matrices, Solution of simultaneous equations by determinants, Solution of simultaneous equations using Cramers rule, Solution of simultaneous equations using the Gaussian elimination method, Revision Test 7
Vectors
Introduction, Scalars and vectors, Drawing a vector, Addition of vectors by drawing, Resolving vectors into horizontal and vertical components, Addition of vectors by calculation, Vector subtraction, Relative velocity, i, j and k notation
Methods of adding alternating waveforms
Combination of two periodic functions, Plotting periodic functions, Determining resultant phasors by drawing, Determining resultant phasors by the sine and cosine rules, Determining resultant phasors by horizontal and vertical components, Determining resultant phasors by complex numbers
Scalar and vector products
The unit triad, The scalar product of two vectors, Vector products, Vector equation of a line, Revision Test 8
Methods of differentiation
Introduction to calculus, The gradient of a curve, Differentiation from first principles, Differentiation of common functions, Differentiation of a product, Differentiation of a quotient, Function of a function, Successive differentiation
Some applications of differentiation
Rates of change, Velocity and acceleration, Turning points, Practical problems involving maximum and minimum values, Tangents and normals, Small changes
Differentiation of parametric equations
Introduction to parametric equations, Some common parametric equations, Differentiation in parameters, Further worked problems on differentiation of parametric equations
Differentiation of implicit functions
Implicit functions, Differentiating implicit functions, Differentiating implicit functions containing products and quotients, Further implicit differentiation
Logarithmic differentiation
Introduction to logarithmic differentiation, Laws of logarithms, Differentiation of logarithmic functions, Differentiation of further logarithmic functions, Differentiation of [ f (x)] x Revision Test 9
Differentiation of hyperbolic functions
Standard differential coefficients of hyperbolic functions, Further worked problems on differentiation of hyperbolic functions
Differentiation of inverse trigonometric and hyperbolic functions
Inverse functions, Differentiation of inverse trigonometric functions, Logarithmic forms of the inverse hyperbolic functions, Differentiation of inverse hyperbolic functions
Partial differentiation
Introduction to partial derivatives, First order partial derivatives, Second order partial derivatives
Total differential, rates of change and small changes
Total differential, Rates of change, Small changes
Maxima, minima and saddle points for functions of two variables
Functions of two independent variables, Maxima, minima and saddle points, Procedure to determine maxima, minima and saddle points for functions of two variables, Worked problems on maxima, minima and saddle points for functions of two variables, Further worked problems on maxima, minima and saddle points for functions of two variablesSumInstallment, Revision Test 10
Standard integration
The process of integration, The general solution of integrals of the form axn, Standard integrals, Definite integrals
Some applications of integration
Introduction, Areas under and between curves, Mean and r.m.s. values, Volumes of solids of revolution, Centroids, Theorem of Pappus, Second moments of area of regular sections
Integration using algebraic substitutions
Introduction, Algebraic substitutions, Worked problems on integration using algebraic substitutions, Further worked problems on integration using algebraic substitutions, Change of limits, Revision Test 11
Integration using trigonometric and hyperbolic substitutions
Introduction, Worked problems on integration of sin2 x, cos2 x, tan2 x and cot2 x, Worked problems on powers of sines and cosines, Worked problems on integration of products of sines and cosines, Worked problems on integration using the sin ? substitution, Worked problems on integration using tan ? substitution, Worked problems on integration using the sinh ? substitution, Worked problems on integration using the cosh ? substitution
Integration using partial fractions
Introduction, Worked problems on integration using partial fractions with linear factors, Worked problems on integration using partial fractions with repeated linear factors, Worked problems on integration using partial fractions with quadratic factors
The t =tan x/2 substitution
Introduction, Worked problems on the t =tan x/2 substitution, Further worked problems on the t = tan x/2 substitution, Revision Test 12
Integration by parts
Introduction, Worked problems on integration by parts, Further worked problems on integration by parts
Reduction formulae
Introduction, Using reduction formulae for integrals of the form x^n e^x dx, Using reduction formulae for integrals of the form x^n cos x dx and x^n sin x dx, Using reduction formulae for integrals of the form sin^n x dx and cos^n x dx, Further reduction formulae
Numerical integration
Introduction, The trapezoidal rule, The mid-ordinate rule, Simpson’s rule, Revision Test 13
Solution of first order differential equations by separation of variables
Family of curves, Differential equations, The solution of equations of the form dy/dx = f (x), The solution of equations of the form dy/dx = f (y), The solution of equations of the form dy/dx = f (x) · f (y)
Homogeneous first order differential equations
Introduction, Procedure to solve differential equations of the form P dy/dx = Q , Worked problems on homogeneous first order differential equations, Further worked problems on homogeneous first order differential equations
Linear first order differential equations
Introduction, Procedure to solve differential equations of the form dy/dx + Py = Q, Worked problems on linear first order differential equations, Further worked problems on linear first order differential equations
Numerical methods for first order differential equations
Introduction, Euler’s method, Worked problems on Euler’s method, An improved Euler method, The Runge-Kutta method, Revision Test 14
Second order differential equations of the form a d^2y/dx^2 + b dy/dx + cy=0
Introduction, Procedure to solve differential equations of the form a d2y/dx2 +b dy/dx +cy = 0, Worked problems on differential equations of the form a d2y/dx2 + b dy/dx + cy = 0, Further worked problems on practical differential equations of the form a d2y/dx2 +b dy/dx +cy =0
Second order differential equations of the form a d2y/dx2 +b dy/dx +cy=f(x)
Complementary function and particular integral, Procedure to solve differential equations of the form a d2y/dx2 +b dy/dx +cy = f (x), Worked problems on differential equations of the form a d2y/dx2 +b dy/dx + cy = f (x) where f (x) is a constant or polynomial, Worked problems on differential equations of the form a d2y/dx2 +b dy/dx + cy = f (x) where f (x) is an exponential function, Worked problems on differential equations of the form a d2y/dx2 +b dy/dx + cy = f (x) where f (x) is a sine or cosine function, Worked problems on differential equations of the form a d2y/dx2 +b dy/dx + cy = f (x) where f (x) is a sum or a product
Power series methods of solving ordinary differential equations
Introduction, Higher order differential coefficients as series, Leibniz’s theorem, Power series solution by the Leibniz–Maclaurin method, Power series solution by the Frobenius method, Bessel’s equation and Bessel’s functions, Legendre’s equation and Legendre, polynomials
An introduction to partial differential equations
Introduction, Partial integration, Solution of partial differential equations by direct partial integration, Some important engineering partial differential equations, Separating the variables, The wave equation, The heat conduction equation, Laplace’s equation, Revision Test 15
Presentation of statistical data
Some statistical terminology, Presentation of ungrouped data, Presentation of grouped data
Measures of central tendency and dispersion
Measures of central tendency, Mean, median and mode for discrete data, Mean, median and mode for grouped data, Standard deviation, Quartiles, deciles and percentiles
Probability
Introduction to probability, Laws of probability, Worked problems on probability, Further worked problems on probability, Revision Test 16
The binomial and Poisson distributions
The binomial distribution, The Poisson distribution
The normal distribution
Introduction to the normal distribution, Testing for a normal distribution
Linear correlation
Introduction to linear correlation, The product-moment formula for determining the linear correlation coefficient, The significance of a coefficient of correlation, Worked problems on linear correlation
Linear regression
Introduction to linear regression, The least-squares regression lines, Worked problems on linear regression, Revision Test 17
Introduction to Laplace transforms
Introduction, Definition of a Laplace transform, Linearity property of the Laplace transform, Laplace transforms of elementary functions, Worked problems on standard Laplace transforms
Properties of Laplace transforms
The Laplace transform of eat f (t), Laplace transforms of the form eat f (t), The Laplace transforms of derivatives, The initial and final value theorems
Inverse Laplace transforms
Definition of the inverse Laplace transform, Inverse Laplace transforms of simple functions, Inverse Laplace transforms using partial fractions, Poles and zeros
The solution of differential equations using Laplace transforms
Introduction, Procedure to solve differential equations by using Laplace transforms, Worked problems on solving differential equations using Laplace transforms


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