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Other titles in the Dover Books on Mathematics series:
Integral Equationsby F. G. Tricomi
Synopses & ReviewsPublisher Comments:This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, wellwritten treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful appendices, an excellent bibliography, and an index. A section of exercises enables the student to check his progress. Contents include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, Types of Singular or Nonlinear Integral Equations, and more. Professor Tricomi has presented the principal results of the theory with sufficient generality and mathematical rigor to facilitate theoretical applications. On the other hand, the treatment is not so abstract as to be inaccessible to physicists and engineers who need integral equations as a basic mathematical tool. In fact, most of the material in this book falls into an analytical framework whose content and methods are already traditional. Synopsis:Authoritative, wellwritten treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography. Synopsis:Authoritative, wellwritten treatment of extremely useful mathematical tool with wide applications. Volterra Equations, Fredholm Equations, much more. Advanced undergraduate to graduate level. Exercises. Bibliography.
Table of Contents1. Volterra Equations
1.1 A Mechanical Problem Leading to an Integral Equation 1.2 Integral Equations and Algebraic Systems of Linear Equations 1.3 Volterra Equations 1.4 L subscript 2Kernels and Functions 1.5 Solution of Volterra Integral Equations of the Second Kind 1.6 Volterra Equations of the First Kind 1.7 An Example 1.8 Volterra Integral Equations and Linear Differential Equations 1.9 Equations of the Faltung type (Closed Cycle Type) 1.10 Transverse Oscillations of a Bar 1.11 Application to the Bessel Functions 1.12 Some Generalizations of the Theory of Volterra Equations 1.13 NonLinear Volterra Equations 2. Fredholm Equations 2.1 Solution by the Method of Successive Approximations: Neumann's Series 2.2 An Example 2.3 Fredholm's Equations with PincherleGoursat Kernels 2.4 The Fredholm Theorem for General Kernels 2.5 The Formulae of Fredholm 2.6 Numerical Solution of Integral Equations 2.7 The Fredholm Solution of the Dirichlet Problem 3. Symmetric Kernels and Orthogonal Systems of Functions 3.1 Introductory Remarks and a Process of Orthogonalization 3.2 Approximation and Convergence in the Mean 3.3 The RieszFischer Theorem 3.4 Completeness and Closure 3.5 Completeness of the Trigonometric System and of the Polynomials 3.6 Approximation of a General L subscript 2Kernel by Means of PGKernels 3.7 Enskog's Method 3.8 The Spectrum of a Symmetric Kernel 3.9 The Bilinear Formula 3.10 The HilbertSchmidt Theorem and Its Applications 3.11 Extremal Properties and Bounds for Eigenvalues 3.12 Positive KernelsMercer's Theorem 3.13 Connection with the Theory of Linear Differential Equations 3.14 Critical Velocities of a Rotating Shaft and Transverse Oscillations of a Beam 3.15 Symmetric Fredholm Equations of the First Kind 3.16 Reduction of a Fredholm Equation to a Similar One with a Symmetric Kernel 3.17 Some Generalizations 3.18 Vibrations of a Membrane 4. Some Types of Singular or NonLinear Integral Equations 4.1 Orientation and Examples 4.2 Equations with Cauchy's Principal Value of an Integral and Hilbert's Transformation 4.3 The Finite Hilbert Transformation and the Airfoil Equation 4.4 Singular Equations of the Carleman Type 4.5 General Remarks About NonLinear Integral Equations 4.6 NonLinear Equations of the Hammerstein Type 4.7 Forced Oscillations of Finite Amplitude Appendix I. Algebraic Systems of Linear Equations Appendix II. Hadamard's Theorem Exercises; References; Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Other books you might likeRelated SubjectsReference » Science Reference » General Science and Mathematics » Mathematics » Analysis General Science and Mathematics » Mathematics » Calculus » General Science and Mathematics » Mathematics » Differential Equations 

