Basic Engineering Mathematics Sixth Edition by John Bird
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Basic Engineering Mathematics Sixth Edition written by
John Bird , BSc(Hons), CMath, CEng, FIMA, MIEE, FIIE(Elec), FCollP
John Bird's approach to mathematics, based on numerous worked examples supported by problems, is ideal for students of a wide range of abilities. Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the mathematics engineering students need to master.The book presents a logical topic progression, rather than following the structure of a particular syllabus and is suitable for all Level 3 vocational students and first year undergraduates in Engineering. However, coverage has been carefully matched to the mathematics units within the 2007 BTEC National specifications.In this fifth edition, new material on inequalities and differentiation of parametric equations, implicit and logarithmic functions as well as an introduction to differential equations has been added. The book now also includes two new revision tests and even more problems for students to work through.Additional chapters on linear correlation, linear regression and sampling and estimation theories can be downloaded for free from http://books.elsevier.com/companions/9780750685559Support material for tutors is available as a free download at http://textbooks.elsevier.com:Instructor's manual with full solutions and suggested marking scheme for all 18 revision tests in the bookSolutions manual with worked solutions for about 1,250 of the further problems in the bookElectronic files for all illustrations in the book * New colour layout helps navigation and highlights key learning points, formulae and exercises* Over 1,000 worked examples and 2,000 questions, all with answers* Fully up to date with the 2007 BTEC National specification* Free lecturer support material available via textbooks.elsevier.com
Title: Engineering Mathematics (5th Edition)
Author(s): John Bird
Publisher: Newnes
Series:
Year: 2010
Pages: 705
Type: PDF
Language: English
ISBN: 185617767X,9781856177672,9780080962122
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Basic Engineering Mathematics Sixth Edition 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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