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Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers
| Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers |
| Autore | Croft Anthony |
| Edizione | [4th ed.] |
| Pubbl/distr/stampa | [Place of publication not identified], : Pearson Education Limited, 2012 |
| Descrizione fisica | 1 online resource (983 pages) |
| Disciplina | 510.2462 |
| Soggetto topico |
Engineering & Applied Sciences
Applied Mathematics |
| Soggetto genere / forma | Libros electrónicos. |
| ISBN |
1-283-68373-3
0-273-71987-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Engineering Mathematics -- Contents -- Preface -- Acknowledgements -- Review of algebraic techniques -- Introduction -- Laws of indices -- Number bases -- Polynomial equations -- Algebraic fractions -- Solution of inequalities -- Partial fractions -- Summation notation -- Review exercises 1 -- Engineering functions -- Introduction -- Numbers and intervals -- Basic concepts of functions -- Review of some common engineering functions and techniques -- Review exercises 2 -- The trigonometric functions -- Introduction -- Degrees and radians -- The trigonometric ratios -- The sine, cosine and tangent functions -- The sinc x function -- Trigonometric identities -- Modelling waves using sin t and cos t -- Trigonometric equations -- Review exercises 3 -- Coordinate systems -- Introduction -- Cartesian coordinate system - two dimensions -- Cartesian coordinate system - three dimensions -- Polar coordinates -- Some simple polar curves -- Cylindrical polar coordinates -- Spherical polar coordinates -- Review exercises 4 -- Discrete mathematics -- Introduction -- Set theory -- Logic -- Boolean algebra -- Review exercises 5 -- Sequences and series -- Introduction -- Sequences -- Series -- The binomial theorem -- Power series -- Sequences arising from the iterative solution of non-linear equations -- Review exercises 6 -- Vectors -- Introduction -- Vectors and scalars: basic concepts -- Cartesian components -- Scalar fields and vector fields -- The scalar product -- The vector product -- Vectors of n dimensions -- Review exercises 7 -- Matrix algebra -- Introduction -- Basic definitions -- Addition, subtraction and multiplication -- Robot coordinate frames -- Some special matrices -- The inverse of a 2 × 2 matrix -- Determinants -- The inverse of a 3 × 3 matrix -- Application to the solution of simultaneous equations -- Gaussian elimination.
Eigenvalues and eigenvectors -- Analysis of electrical networks -- Iterative techniques for the solution of simultaneous equations -- Computer solutions of matrix problems -- Review exercises 8 -- Complex numbers -- Introduction -- Complex numbers -- Operations with complex numbers -- Graphical representation of complex numbers -- Polar form of a complex number -- Vectors and complex numbers -- The exponential form of a complex number -- Phasors -- De Moivre's theorem -- Loci and regions of the complex plane -- Review exercises 9 -- Differentiation -- Introduction -- Graphical approach to differentiation -- Limits and continuity -- Rate of change at a specific point -- Rate of change at a general point -- Existence of derivatives -- Common derivatives -- Differentiation as a linear operator -- Review exercises 10 -- Techniques of differentiation -- Introduction -- Rules of differentiation -- Parametric, implicit and logarithmic differentiation -- Higher derivatives -- Review exercises 11 -- Applications of differentiation -- Introduction -- Maximum points and minimum points -- Points of inflexion -- The Newton--Raphson method for solving equations -- Differentiation of vectors -- Review exercises 12 -- Integration -- Introduction -- Elementary integration -- Definite and indefinite integrals -- Review exercises 13 -- Techniques of integration -- Introduction -- Integration by parts -- Integration by substitution -- Integration using partial fractions -- Review exercises 14 -- Applications of integration -- Introduction -- Average value of a function -- Root mean square value of a function -- Review exercises 15 -- Further topics in integration -- Introduction -- Orthogonal functions -- Improper integrals -- Integral properties of the delta function -- Integration of piecewise continuous functions -- Integration of vectors -- Review exercises 16. Numerical integration -- Introduction -- Trapezium rule -- Simpson's rule -- Review exercises 17 -- Taylor polynomials, Taylor series and Maclaurin series -- Introduction -- Linearization using first-order Taylor polynomials -- Second-order Taylor polynomials -- Taylor polynomials of the nth order -- Taylor's formula and the remainder term -- Taylor and Maclaurin series -- Review exercises 18 -- Ordinary differential equations I -- Introduction -- Basic definitions -- First-order equations: simple equations and separation of variables -- First-order linear equations: use of an integrating factor -- Second-order linear equations -- Review exercises 19 -- Ordinary differential equations II -- Introduction -- Analogue simulation -- Higher order equations -- State-space models -- Numerical methods -- Euler's method -- Improved Euler method -- Runge-Kutta method of order 4 -- Review exercises 20 -- The Laplace transform -- Introduction -- Definition of the Laplace transform -- Laplace transforms of some common functions -- Properties of the Laplace transform -- Laplace transform of derivatives and integrals -- Inverse Laplace transforms -- Using partial fractions to find the inverse Laplace transform -- Finding the inverse Laplace transform using complex numbers -- The convolution theorem -- Solving linear constant coefficient differential equations using the Laplace transform -- Transfer functions -- Poles, zeros and the s plane -- Laplace transforms of some special functions -- Review exercises 21 -- Difference equations and the z Transform -- Introduction -- Basic definitions -- Rewriting difference equations -- Block diagram representation of difference equations -- Design of a discrete-time controller -- Numerical solution of difference equations -- Definition of the z transform -- Sampling a continuous signal. The relationship between the z transform and the Laplace transform -- Properties of the z transform -- Inversion of z transform -- The z transform and difference equations -- Review exercises 22 -- Fourier series -- Introduction -- Periodic waveforms -- Odd and even functions -- Orthogonality relations and other useful identities -- Fourier series -- Half-range series -- Parseval's theorem -- Complex notation -- Frequency response of a linear system -- Review exercises 23 -- The Fourier transform -- Introduction -- The Fourier transform - definitions -- Some properties of the Fourier transform -- Spectra -- The t−ω duality principle -- Fourier transforms of some special functions -- The relationship between the Fourier transform and the Laplace transform -- Convolution and correlation -- The discrete Fourier transform -- Derivation of the d.f.t. -- Using the d.f.t. to estimate a Fourier transform -- Matrix representation of the d.f.t. -- Some properties of the d.f.t. -- The discrete cosine transform -- Discrete convolution and correlation -- Review exercises 24 -- Functions of several variables -- Introduction -- Functions of more than one variable -- Partial derivatives -- Higher order derivatives -- Partial differential equations -- Taylor polynomials and Taylor series in two variables -- Maximum and minimum points of a function of two variables -- Review exercises 25 -- Vector calculus -- Introduction -- Partial differentiation of vectors -- The gradient of a scalar field -- The divergence of a vector field -- The curl of a vector field -- Combining the operators grad, div and curl -- Vector calculus and electromagnetism -- Review exercises 26 -- Line integrals and multiple integrals -- Introduction -- Line integrals -- Evaluation of line integrals in two dimensions -- Evaluation of line integrals in three dimensions. Conservative fields and potential functions -- Double and triple integrals -- Some simple volume and surface integrals -- The divergence theorem and Stokes' theorem -- Maxwell's equations in integral form -- Review exercises 27 -- Probability -- Introduction -- Introducing probability -- Mutually exclusive events: the addition law of probability -- Complementary events -- Concepts from communication theory -- Conditional probability: the multiplication law -- Independent events -- Review exercises 28 -- Statistics and probability distributions -- Introduction -- Random variables -- Probability distributions - discrete variable -- Probability density functions - continuous variable -- Mean value -- Standard deviation -- Expected value of a random variable -- Standard deviation of a random variable -- Permutations and combinations -- The binomial distribution -- The Poisson distribution -- The uniform distribution -- The exponential distribution -- The normal distribution -- Reliability engineering -- Review exercises 29 -- Appendix I Representing a continuous function and a sequence as a sum of weighted impulses -- Appendix II The greek alphabet -- Appendix III SI units and prefixes -- Appendix IV The binomial expansion of (n−N/n)n -- Index. |
| Altri titoli varianti | Engineering mathematics |
| Record Nr. | UNINA-9910150233903321 |
Croft Anthony
|
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| [Place of publication not identified], : Pearson Education Limited, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mathematics for engineers / / Anthony Croft, Robert Davison
| Mathematics for engineers / / Anthony Croft, Robert Davison |
| Autore | Croft Anthony |
| Edizione | [Fourth edition.] |
| Pubbl/distr/stampa | Harlow, England : , : Pearson Prentice Hall, , 2015 |
| Descrizione fisica | 1 online resource (1,217 pages) : illustrations (some color), tables, graphs |
| Disciplina | 624.076 |
| Soggetto topico | Engineering mathematics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title -- Copyright -- Contents -- Publisher's acknowledgements -- Preface -- Using mathematical software packages -- 1 Arithmetic -- Block 1 Operations on numbers -- Block 2 Prime numbers and prime factorisation -- End of chapter exercises -- 2 Fractions -- Block 1 Introducing fractions -- Block 2 Operations on fractions -- End of chapter exercises -- 3 Decimal numbers -- Block 1 Introduction to decimal numbers -- Block 2 Significant figures -- End of chapter exercises -- 4 Percentage and ratio -- Block 1 Percentage -- Block 2 Ratio -- End of chapter exercises -- 5 Basic algebra -- Block 1 Mathematical notation and symbols -- Block 2 Indices -- Block 3 Simplification by collecting like terms -- Block 4 Removing brackets -- Block 5 Factorisation -- Block 6 Arithmetic of algebraic fractions -- Block 7 Formulae and transposition -- End of chapter exercises -- 6 Functions and mathematical models -- Block 1 Basic concepts of functions -- Block 2 The graph of a function -- Block 3 Composition of functions -- Block 4 One-to-one functions and inverse functions -- Block 5 Parametric representation of a function -- Block 6 Describing functions -- Block 7 The straight line -- Block 8 Common engineering functions -- End of chapter exercises -- 7 Polynomial equations, inequalities, partial fractions and proportionality -- Block 1 Solving linear equations -- Block 2 Solving quadratic equations -- Block 3 Factorising polynomial expressions and solving polynomial equations -- Block 4 Solving simultaneous equations -- Block 5 Solution of inequalities -- Block 6 Partial fractions -- Block 7 Proportionality -- End of chapter exercises -- 8 Logarithms and exponentials -- Block 1 The exponential function -- Block 2 Logarithms and their laws -- Block 3 Solving equations involving logarithms and exponentials -- Block 4 Applications of logarithms.
End of chapter exercises -- 9 Trigonometry -- Block 1 Angles -- Block 2 The trigonometrical ratios -- Block 3 The trigonometrical ratios in all quadrants -- Block 4 Trigonometrical functions and their graphs -- Block 5 Trigonometrical identities -- Block 6 Trigonometrical equations -- Block 7 Engineering waves -- End of chapter exercises -- 10 Further trigonometry -- Block 1 Pythagoras's theorem and the solution of right-angled triangles -- Block 2 Solving triangles using the sine rule -- Block 3 Solving triangles using the cosine rule -- Block 4 Surveying -- Block 5 Resolution and resultant of forces -- End of chapter exercises -- 11 Complex numbers -- Block 1 Arithmetic of complex numbers -- Block 2 The Argand diagram and polar form of a complex number -- Block 3 The exponential form of a complex number -- Block 4 De Moivre's theorem -- Block 5 Solving equations and finding roots of complex numbers -- Block 6 Phasors -- End of chapter exercises -- 12 Matrices and determinants -- Block 1 Introduction to matrices -- Block 2 Multiplication of matrices -- Block 3 Determinants -- Block 4 The inverse of a matrix -- Block 5 Computer graphics -- End of chapter exercises -- 13 Using matrices and determinants to solve equations -- Block 1 Cramer's rule -- Block 2 Using the inverse matrix to solve simultaneous equations -- Block 3 Gaussian elimination -- Block 4 Eigenvalues and eigenvectors -- Block 5 Iterative techniques -- Block 6 Electrical networks -- End of chapter exercises -- 14 Vectors -- Block 1 Basic concepts of vectors -- Block 2 Cartesian components of vectors -- Block 3 The scalar product, or dot product -- Block 4 The vector product, or cross product -- Block 5 The vector equation of a line and a plane -- End of chapter exercises -- 15 Differentiation -- Block 1 Interpretation of a derivative -- Block 2 Using a table of derivatives. Block 3 Higher derivatives -- End of chapter exercises -- 16 Techniques and applications of differentiation -- Block 1 The product rule and the quotient rule -- Block 2 The chain rule -- Block 3 Implicit differentiation -- Block 4 Parametric differentiation -- Block 5 Logarithmic differentiation -- Block 6 Tangents and normals -- Block 7 Maximum and minimum values of a function -- End of chapter exercises -- 17 Integration -- Block 1 Integration as differentiation in reverse -- Block 2 Definite integrals -- Block 3 The area bounded by a curve -- Block 4 Computational approaches to integration -- Block 5 Integration by parts -- Block 6 Integration by substitution -- Block 7 Integration using partial fractions -- Block 8 Integration of trigonometrical functions -- End of chapter exercises -- 18 Applications of integration -- Block 1 Integration as the limit of a sum -- Block 2 Volumes of revolution -- Block 3 Calculating centres of mass -- Block 4 Moment of inertia -- Block 5 The length of a curve and the area of a surface of revolution -- Block 6 The mean value and root-mean-square value of a function -- End of chapter exercises -- 19 Sequences and series -- Block 1 Sequences and series -- Block 2 Sums of whole numbers, their squares and cubes -- Block 3 Pascal's triangle and the binomial theorem -- Block 4 Taylor series and Maclaurin series -- End of chapter exercises -- 20 Differential equations -- Block 1 Basic concepts of differential equations -- Block 2 Separation of variables -- Block 3 Solving first-order linear equations using an integrating factor -- Block 4 Computational approaches to differential equations -- Block 5 Second-order linear constant-coefficient equations I -- Block 6 Second-order linear constant-coefficient equations II -- End of chapter exercises -- 21 Functions of more than one variable and partial differentiation. Block 1 Functions of two independent variables, and their graphs -- Block 2 Partial differentiation -- Block 3 Higher-order derivatives -- Block 4 Stationary values of a function of two variables -- End of chapter exercises -- 22 The Laplace transform -- Block 1 The Laplace transform -- Block 2 The inverse Laplace transform -- Block 3 Solving differential equations using the Laplace transform -- End of chapter exercises -- 23 Statistics and probability -- Block 1 Data -- Block 2 Data averages -- Block 3 Variation of data -- Block 4 Elementary probability -- Block 5 Laws of probability -- Block 6 Probability distributions -- Block 7 The binomial distribution -- Block 8 The Poisson distribution -- Block 9 The normal distribution -- End of chapter exercises -- 24 An introduction to Fourier series and the Fourier transform -- Block 1 Periodic waveforms and their Fourier representation -- Block 2 Introducing the Fourier transform -- End of chapter exercises -- Typical examination papers -- Appendix 1: SI units and prefixes -- Index. |
| Record Nr. | UNINA-9910154772003321 |
|
Croft Anthony
|
||
| Harlow, England : , : Pearson Prentice Hall, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||