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wylie c barrett l advanced engineering mathematics 5ed 1982

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Textbook in PDF format This book has been written to help you in your development as an applied scientist, whether engineer, physicist, chemist, or mathematician. It contains material which you will find of great use, not only in the technical courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. We have tried to write a book which you will find not only useful but also easy to study, at least as easy as a book on advanced mathematics can be. There is a good deal of theory in it, for it is the theoretical portion of a subject which is the basis for the nonroutine applications of tomorrow. But nowhere will you find theory for its own sake, interesting and legitimate as this may be to a pure mathematician. Our theoretical discussions are designed to illuminate principles, to indicate generalizations, to establish limits within which a given technique may or may not be safely used, or to point out pitfalls into which one might otherwise stumble. On the other hand, there are many applications illustrating, with the material at hand, the usual steps in the solution of a physical problem: formulation, manipulation, and interpretation. These examples are, without exception, carefully set up and completely worked, with all but the simplest steps included. Study them carefully, with paper and pencil at hand, for they are an integral part of the text. If you do this, you should find the exercises, though challenging, still within your ability to work. Preface To the Student Ordinary Differential Equations of the First Order Functions and Equations Classification of Differential Equations Solutions of Differential Equations Solution Curves and Integral Curves Differential Equations with Prescribed Solutions Existence and Uniqueness of Solutions Exact First-Order Equations Integrating Factors for First-Order Equations Separable First-Order Equations Homogeneous First-Order Equations Linear First-Order Equations Special First-Order Equations Second-Order Equations of Reducible Order Orthogonal Trajectories Applications of First-Order Differential Equations Linear Differential Equations A Fundamental Existence and Uniqueness Theorem Families of Solutions Solutions of Nonhomogeneous Equations Variation of Parameters and Reduction of Order Homogeneous Second-Order Equations with Constant Coefficients Homogeneous Equations of Higher Order Nonhomogeneous Equations with Constant Coefficients The Euler-Cauchy Differential Equation Applications of Linear Differential Equations with Constant Coefficients Green’s Functions Introduction to Linear Algebra The Algebra of Vectors The Algebra of Matrices Special Matrices Determinants Systems of Linear Algebraic Equations Special Linear Systems, Inverses, Adjoints, and Cramer’s Rule Characteristic-Value Problems Simultaneous Linear Differential Equations Solutions, Consistency, and Equivalence of Linear Differential Systems The Reduction of a Differential System to an Equivalent System Fundamental Concepts and Theorems Concerning First-Order Systems Complementary Functions and Particular Integrals of Linear Differential Systems Linear Differential Systems with Constant Coefficients Finite Differences The Differences of a Function Interpolation Formulas Numerical Differentiation and Integration The Numerical Solution of Differential Equations Difference Equations Difference Equations and the Numerical Solution of Differential Equations Mechanical Systems and Electric Circuits Systems with One Degree of Freedom The Translational Mechanical System The Series Electric Circuit Systems with Several Degrees of Freedom Fourier Series and Integrals Periodic Functions The Euler Coefficients Alternative Formulas for the Fourier Coefficients Half-Range Expansions Alternative Forms of Fourier Series Applications of Fourier Series The Fourier Integral as the Limit of a Fourier Series Applications of Fourier Integrals From the Fourier Integral to the Laplace Transform The Laplace Transformation Theoretical Preliminaries The General Method The Transforms of Special Functions Further General Theorems The Heaviside Expansion Theorems The Transforms of Periodic Functions Convolution and the Duhamel Formulas Partial Differential Equations The Derivation of Equations The d’Alembert Solution of the Wave Equation Characteristics and the Classification of Partial Differential Equations Separation of Variables Orthogonal Functions and the General Expansion Problem Further Applications Laplace Transform Methods The Numerical Solution of Partial Differential Equations Bessel Functions and Legendre Polynomials Theoretical Preliminaries The Series Solution of Bessel’s Equation Modified Bessel Functions Equations Solvable in Terms of Bessel Functions Identities for the Bessel Functions The Orthogonality of the Bessel Functions Applications of Bessel Functions Legendre Polynomials Vector Spaces and Linear Transformations Vector Spaces Subspaces, Linear Dependence, and Linear Independence Bases and Dimension Linear Transformations Sums, Products, and Inverses of Linear Transformations Linear Operator Equations Applications and Further Properties of Matrices Transition Probabilities and a Mass-Spring System Rank and the Equivalence of Matrices The Existence of Green’s Functions and Their Use in Solving Nonhomogeneous Differential Systems Quadratic Forms Characteristic Values and Characteristic Vectors of a Matrix The Transformation of Matrices Functions of a Square Matrix Vector Analysis The Algebra of Vectors Vector Functions of One Variable The Operator V Line, Surface, and Volume Integrals Integral Theorems Further Applications The Calculus of Variations Systems of Euler-Lagrange Equations The Extrema of Integrals under Constraints Sturm-Liouville Problems Variations Hamilton’s Principle and Lagrange Equations of Motion Analytic Functions of a Complex Variable Algebraic Preliminaries The Geometric Representation of Complex Numbers Absolute Values Functions of a Complex Variable Analytic Functions The Elementary Functions of z Integration in the Complex Plane Analytic Functions and Two-Dimensional Field Theory Infinite Series in the Complex Plane Series of Complex Terms Taylor’s Expansion Laurent’s Expansion The Theory of Residues The Residue Theorem The Evaluation of Real Definite Integrals The Complex Inversion Integral Stability Criteria Conformal Mapping The Geometrical Representation of Functions of z Conformal Mapping The Bilinear Transformation The Schwarz-Christoffel Transformation Answers to Odd-Numbered Exercises Index

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wylie c barrett l advanced engineering mathematics 5ed 1982