6th Edition

Mathematics for Engineers and Scientists





ISBN 9781584884880
Published August 10, 2004 by Chapman and Hall/CRC
242 B/W Illustrations

USD $105.00

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Book 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

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