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E-raamat: Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

(Technical University Prague, Prague, Czech Republic)
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Solving Ordinary and Partial Boundary Value Problems in Science and EngineeringSuurem pilt
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Provides an accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, covering fundamental properties and methods of constructing solutions and approximations. Presents special remarks for mathematical readers, demonstrating the possibility of generalizations of obtained results and showing connections between them. For non-mathematicians, material provides functional-analytical results needed in the theory of variational methods without proofs. Contains chapter problems. Annotation c. by Book News, Inc., Portland, Or.

This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations.
Discussions include:
  • ordinary differential equations
  • classical theory of partial differential equations
  • Laplace and Poisson equations
  • heat equation
  • variational methods of solution of corresponding boundary value problems
  • methods of solution for evolution partial differential equations
    The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary.
    Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.

    • Arvustused

    "Numerous technical and physical examples explained in a very clear manner help to understand better theoretical material and motivate further exploration of the subject. Accumulating many years of the author's teaching experience at the Technical University of Prague, this excellent book will be of benefit for engineers, scientists, and mathematicians dealing with boundary value problems, as well as students of science and engineering." -Yuri V. Rogovchenko (Famagusta), Zentralblatt Math, Vol. 1078, April 2006 "A very nice text...addressed to the non-mathematician." - Ivo Babuska, Professor of Engineering and Mathematics, University of Texas "This book is unusual in that it sits at the intersection of differential equations and numerical analysis, and in this regard it represents a modern approach to the subject. A good discussion" -CHOICE, May 1999

    Introduction 1(4)
    1 Ordinary Differential Equations with Boundary Conditions; Eigen-value Problems
    		5(50)
    1.1 Technical Motivation
    		5(5)
    1.2 Relation Between the Problem (1.1.3) and (1.1.4) and the Problem Corresponding to the Zero Vertical Loading of the Bar
    		10(1)
    1.3 Brief Summary of the Space L(2)(a,b)
    		11(7)
    1.4 Eigenvalue Problems
    		18(2)
    1.5 Basic Properties of Eigenvalues and Eigenfunctions
    		20(7)
    1.6 Nonhomogeneous Equations with Boundary Conditions
    		27(10)
    1.7 The Finite-Difference Method for Ordinary Differential Equations
    		37(3)
    1.8 Convergence of the Finite-Difference Method
    		40(1)
    1.9 Application of the Finite-Difference Method in Eigenvalue Problems
    		41(2)
    1.10 Problems 1.10.1 to 1.10.15
    		43(12)
    2 Partial Differential Equations: Classical Approach
    		55(30)
    2.1 Basic Concepts; Examples of Equations Frequently Encountered in Applications; The Heat-Conduction Equation Derived
    		55(7)
    2.2 Boundary Value Problems (Equations with Boundary Conditions); The Dirichlet Problem for Laplace and Poisson Equations; The Maximum Principle for Harmonic Functions and its Consequences
    		62(9)
    2.3 The Heat-Conduction Equation
    		71(6)
    2.4 Problems 2.4.1 to 2.4.12
    		77(8)
    3 Variational Methods of Solution of Elliptical Boundary Value Problems; Generalized Solutions and Their Approximations; Weak Solutions
    		85(70)
    3.1 The Equation Au = f
    		85(5)
    3.2 Comparison Functions, Domain of Definition of Operator A; Symmetrical, Positive, and Positive-Definite Operators
    		90(14)
    3.3 Theorem on Minimum of Functional of Energy
    		104(7)
    3.4 Generalized Derivatives; The Energetic Space, the Sobolev Space; Generalized Solutions, Weak Solutions
    		111(1)
    3.4.1 Functions of One Variable
    		111(11)
    3.4.2 Functions of Several Variables
    		122(1)
    3.5 The Ritz and Galerkin Methods; The Finite-Element Method
    		122(15)
    3.6 Eigenvalue Problems for Equations of Order 2k
    		137(4)
    3.7 Problems 3.7.1 to 3.7.16
    		141(14)
    4 The Finite-Difference Method for Partial Differential Equations; The Method of Discretization in Time (the Rothe Method)
    		155(28)
    4.1 The Finite-Difference Method (the Method of Finite Differences, the Net Method) for Partial Differential Equations
    		155(5)
    4.2 The Finite-Difference Method for the Heat Equation
    		160(1)
    4.2.1 The Explicit Scheme
    		160(3)
    4.2.2 The Implicit Scheme
    		163(3)
    4.3 The Method of Discretization in Time (the Rothe Method, the Method of Lines)
    		166(5)
    4.4 Problems 4.4.1 to 4.4.9
    		171(12)
    5 The Fourier Method
    		183(14)
    5.1 The Fourier Method for One-Dimensional Vibration Problems
    		183(5)
    5.2 Problems 5.2.1 to 5.2.8
    		188(9)
    References 197(2)
    Index 199
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