Mathematics for Engineers and Scientists: 6th Edition (Paperback) book cover

Mathematics for Engineers and Scientists

6th Edition

By Alan Jeffrey

Chapman and Hall/CRC

1,016 pages | 242 B/W Illus.

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pub: 2004-08-10
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Description

Since its original publication in 1969, Mathematics for Engineers and Scientists has built a solid foundation in mathematics for legions of undergraduate science and engineering students. It continues to do so, but as the influence of computers has grown and syllabi have evolved, once again the time has come for a new edition.

Thoroughly revised to meet the needs of today's curricula, Mathematics for Engineers and Scientists, Sixth Edition covers all of the topics typically introduced to first- or second-year engineering students, from number systems, functions, and vectors to series, differential equations, and numerical analysis. Among the most significant revisions to this edition are:

  • Simplified presentation of many topics and expanded explanations that further ease the comprehension of incoming engineering students

  • A new chapter on double integrals

  • Many more exercises, applications, and worked examples

  • A new chapter introducing the MATLAB and Maple software packages

    Although designed as a textbook with problem sets in each chapter and selected answers at the end of the book, Mathematics for Engineers and Scientists, Sixth Edition serves equally well as a supplemental text and for self-study. The author strongly encourages readers to make use of computer algebra software, to experiment with it, and to learn more about mathematical functions and the operations that it can perform.

  • Table of Contents

    NUMBERS, TRIGONOMETRIC FUNCTIONS AND COORDINATE GEOMETRY

    Sets and numbers

    Integers, rationals and arithmetic laws

    Absolute value of a real number

    Mathematical induction

    Review of trigonometric properties

    Cartesian geometry

    Polar coordinates

    Completing the square

    Logarithmic functions

    Greek symbols used in mathematics

    VARIABLES, FUNCTIONS AND MAPPINGS

    Variables and functions

    Inverse functions

    Some special functions

    Curves and parameters

    Functions of several real variables

    SEQUENCES, LIMITS AND CONTINUITY

    Sequences

    Limits of sequences

    The number e

    Limits of functions -/ continuity

    Functions of several variables -/ limits, continuity

    A useful connecting theorem

    Asymptotes

    COMPLEX NUMBERS AND VECTORS

    Introductory ideas

    Basic algebraic rules for complex numbers

    Complex numbers as vectors

    Modulus -/ argument form of complex numbers

    Roots of complex numbers

    Introduction to space vectors

    Scalar and vector products

    Geometrical applications

    Applications to mechanics

    Problems

    DIFFERENTIATION OF FUNCTIONS OF ONE OR MORE REAL VARIABLES

    The derivative

    Rules of differentiation

    Some important consequences of differentiability

    Higher derivatives _/ applications

    Partial differentiation

    Total differentials

    Envelopes

    The chain rule and its consequences

    Change of variable

    Some applications of dy/dx=1/ dx/dy

    Higher-order partial derivatives

    EXPONENTIAL, LOGARITHMIC AND HYPERBOLIC FUNCTIONS AND AN INTRODUCTION TO COMPLEX FUNCTIONS

    The exponential function

    Differentiation of functions involving the exponential function

    The logarithmic function

    Hyperbolic functions

    Exponential function with a complex argument

    Functions of a complex variable, limits, continuity and differentiability

    FUNDAMENTALS OF INTEGRATION

    Definite integrals and areas

    Integration of arbitrary continuous functions

    Integral inequalities

    The definite integral as a function of its upper limit -/ the indefinite integral

    Differentiation of an integral containing a parameter

    Other geometrical applications of definite integrals

    Centre of mass and moment of inertia

    Line integrals

    SYSTEMATIC INTEGRATION

    Integration of elementary functions

    Integration by substitution

    Integration by parts

    Reduction formulae

    Integration of rational functions - partial fractions

    Other special techniques of integration

    Integration by means of tables

    Problems

    DOUBLE INTEGRALS IN CARTESIAN AND PLANE POLAR COORDINATES

    Double integrals in Cartesian coordinates

    Double integrals using polar coordinates

    Problems

    MATRICES AND LINEAR TRANSFORMATIONS

    Matrix algebra

    Determinants

    Linear dependence and linear independence

    Inverse and adjoint matrices

    Matrix functions of a single variable

    Solution of systems of linear equations

    Eigenvalues and eigenvectors

    Matrix interpretation of change of variables in partial differentiation

    Linear transformations

    Applications of matrices and linear transformations

    Problems

    SCALARS, VECTORS AND FIELDS

    Curves in space

    Antiderivatives and integrals of vector functions

    Some applications

    Fields, gradient and directional derivative

    Divergence and curl of a vector

    Conservative fields and potential functions

    Problems

    SERIES, TAYLOR'S THEOREM AND ITS USES

    Series

    Power series

    Taylor's theorem

    Applications of Taylor's theorem

    Applications of the generalized mean value theorem

    DIFFERENTIAL EQUATIONS AND GEOMETRY

    Introductory ideas

    Possible physical origin of some equations

    Arbitrary constants and initial conditions

    First-order equations - direction fields and isoclines

    Orthogonal trajectories

    First-order differential equations

    Equations with separable variables

    Homogeneous equations

    Exact equations

    The linear equation of first order

    Direct deductions

    HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS

    Linear equations with constant coefficients _/ homogeneous case

    Linear equations with constant coefficients _/ inhomogeneous case

    Variation of parameters

    Oscillatory solutions

    Coupled oscillations and normal modes

    Systems of first-order equations

    Two-point boundary value problems

    The Laplace transform

    The Delta function

    Applications of the Laplace transform

    FOURIER SERIES

    Introductory ideas

    Convergence of Fourier series

    Different forms of Fourier series

    Differentiation and integration

    NUMERICAL ANALYSIS

    Errors and efficient methods of calculation

    Solution of linear equations

    Interpolation

    Numerical integration

    Solution of polynomial and transcendental equations

    Numerical solutions of differential equations

    Determination of eigenvalues and eigenvectors

    PROBABILITY AND STATISTICS

    The elements of set theory for use in probability and statistics

    Probability, discrete distributions and moments

    Continuous distributions and the normal distribution

    Mean and variance of a sum of random variables

    Statistics - inference drawn from observations

    Linear regression

    SYMBOLIC ALGEBRAIC MANIPULATION BY COMPUTER SOFTWARE

    Maple

    MATLAB

    ANSWERS

    REFERENCE LISTS:

    Useful identities and constants

    Basic derivatives and rules

    Laplace transform pairs

    Short table of integrals

    INDEX

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT003000
    MATHEMATICS / Applied
    TEC009000
    TECHNOLOGY & ENGINEERING / Engineering (General)