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Basic Engineering Mathematics Sixth Edition by John Bird




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Basic Engineering Mathematics Sixth Edition written by John Bird This is an other great mathematics book 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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