Essentials Engineering Mathematics: 2nd Edition (Paperback) book cover

Essentials Engineering Mathematics

2nd Edition

By Alan Jeffrey

Chapman and Hall/CRC

896 pages | 233 B/W Illus.

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pub: 2004-08-12
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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.

  • 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

    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


    One-sided limits


    Leibniz's formula


    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


    Infinite numerical series

    Power series

    Taylor and Maclaurin series

    Taylor's theorem for functions of two variable: stationary points and their identification

    Fourier series



    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



    Subject Categories

    BISAC Subject Codes/Headings:
    MATHEMATICS / Applied