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2nd Edition

Essentials Engineering Mathematics





ISBN 9781584884897
Published August 12, 2004 by Chapman and Hall/CRC
896 Pages 233 B/W Illustrations

 
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Book Description

First published in 1992, Essentials of Engineering Mathematics is a widely popular reference ideal for self-study, review, and fast answers to specific questions. While retaining the style and content that made the first edition so successful, the second edition provides even more examples, new material, and most importantly, an introduction to using two of the most prevalent software packages in engineering: Maple and MATLAB. Specifically, this edition includes:

  • Introductory accounts of Maple and MATLAB that offer a quick start to using symbolic software to perform calculations, explore the properties of functions and mathematical operations, and generate graphical output
  • New problems involving the mean value theorem for derivatives
  • Extension of the account of stationary points of functions of two variables
  • The concept of the direction field of a first-order differential equation
  • Introduction to the delta function and its use with the Laplace transform

    The author includes all of the topics typically covered in first-year undergraduate engineering mathematics courses, organized into short, easily digestible sections that make it easy to find any subject of interest. Concise, right-to-the-point exposition, a wealth of examples, and extensive problem sets at the end each chapter--with answers at the end of the book--combine to make Essentials of Engineering Mathematics, Second Edition ideal as a supplemental textbook, for self-study, and as a quick guide to fundamental concepts and techniques.
  • Table of Contents

    Real numbers, inequalities and intervals
    Function, domain and range
    Basic coordinate geometry
    Polar coordinates
    Mathematical induction
    Binomial theorem
    Combination of functions
    Symmetry in functions and graphs
    Inverse functions
    Complex numbers; real and imaginary forms
    Geometry of complex analysis
    Modulus-argument form of a complex number
    Roots of complex numbers
    Limits
    One-sided limits
    Derivatives
    Leibniz's formula
    Differentials
    Differentiation of inverse trigonometric functions
    Implicit differentiation
    Parametrically defined curves and parametric differentiation
    The exponential function
    The logarithmic function
    Hyperbolic functions
    Inverse hyperbolic functions
    Properties and applications of differentialability
    Functions of two variables
    Limits and continuity of functions of two real variables
    Partial differentiation
    The total differential
    The chain rule
    Change of variable in partial differentiation
    Antidifferentiation (integration)
    Integration by substitution
    Some useful standard forms
    Integration by parts
    Partial fractions and integration of rational functions
    The definite integral
    The fundamental theorem of integral calculus and the evaluation of definite integrals
    Improper integrals
    Numerical integration
    Geometrical applications of definite integrals
    Centre of mass of a plane lamina
    Applications of integration to he hydrostatic pressure on a plate
    Moments of inertia
    Sequences
    Infinite numerical series
    Power series
    Taylor and Maclaurin series
    Taylor's theorem for functions of two variable: stationary points and their identification
    Fourier series
    Determinants
    Matrices
    Matrix multiplication
    The inverse matrix
    Solution of a system of linear equations: Gaussian elimination
    The Gauss-Seidel iterative method
    The algebraic eigenvalue problem
    Scalars, vectors and vector addition
    Vectors in component form
    The straight line
    The scalar product (dot product)
    The plane
    The vector product (cross product)
    Applications of the vector product
    Differentiation and integration of vectors
    Dynamics of a particle and the motion of a particle in a plane
    Scalar and vector fields and the gradient of a scalar function
    Ordinary differential equations: order and degree, initial and boundary conditions
    First order differential equations solvable by separation of variables
    The method of isoclines and Euler's methods
    Homogeneous and near homogeneous equations
    Exact differential equations
    The first order linear differential equation
    The Bernoulli equation
    The structure of solutions of linear differential equations of any order
    Determining the complementary function for constant coefficient equations
    Determining particular integrals of constant coefficient equations
    Differential equations describing oscillations
    Simultaneous first order linear constant coefficient different equations
    The Laplace transform and transform pairs
    The Laplace transform of derivatives
    The shift theorems and the Heaviside step function
    Solution of initial value problems
    The Delta function and its use in initial value problems with the Laplace transform
    Enlarging the list of Laplace transform pairs
    Symbolic Algebraic Manipulation by Computer Software
    Answers
    References

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    Reviews

    "The book is intended for first year engineering students and presumably this choice of subjects is a reflection of the course on which the author lectured. The book fulfills this purpose in a very satisfactory manner and can be warmly recommended for this purpose. The explanations are good and there is an adequacy of worked examples. …A welcome feature is that indefinite integrals mentioned in the text all have included an arbitrary constant. …Much of the book would be found useful for those in the last years at school."
    -Zentralblatt MATH

    "Each of the short sections covers the amount of material one would hope to get through in a lecture or two, typically giving a short introduction to the relevant theory and several worked examples. …Jeffrey's book could be easily adopted as a course text, and the sections can be divided naturally into groups for shorter modules."
    -Times Higher Education Supplement

    ead> Concise explanations and a wealth of examples form an ideal study guide and reference