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Krishna's Integral Equations (&Boundary Value Problems) | Edition-27 B | Pages-480 | Code-227 (Mathematics Book 29)

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Title: Krishna's Integral Equations (&Boundary Value Problems) | Edition-27 B | Pages-480 | Code-
227 (Mathematics Book 29)
Language : ENGLISH
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CONTENTS- INTEGRAL EQUATIONS, Chapter-1: Basic Concepts1.1 Integral Equation1.2

Differentiation of a Function Under an Integral Sign1.3 Relation Between Differential and Integral
EquationsChapter-2: Solution of Integral Equations2.1 Solution of Nonhomogeneous Volterra's
Integral Equation of Second kind by the Method of Successive Substitution2.5 Solution of the
Fredholm Integral Equation by the Method of Successive Substitutions2.6 Iterated Kernels2.7
Solution of the Fredholm Integral Equation by the Method of Successive Approximation2.8
Reciprocal Functions2.9 Volterra's Solution of Fredholm's EquationChapter-3: Fredholm Integral
Equations3.1 Fredholm First Theorem3.2 Prove that the solution3.3 Every Zero of Fredholm
Function D(l) is a Pole of the Resolvent Kernel3.4 If a Real Kernel K (x, ) has a Complex Eigen
Value &#61548#61488&#61472#61501&#61472#61549&#61472#61483&#61472i, then it Also
Contains the Conjugate Eigen Value to
&#615480#61472&#61501#61472&#61549#61472&#8211iv3.5 Hadamard's Lemma3.6
Convergence Proof3.7 Fredholm Second Theorem3.8 Fredholm's Associated Equation3.9
Characteristic Solutions3.10 Fredholm's Third Theorem3.11 Solution of the Homogeneous Integral
Equation3.12 If D(&#615480 &#61501#614720 and D (x,
&#61560&#615480&#61472#61626/&#614720 then for a Proper Choice of
&#615600&#61472#61542&#61472x) &#61501#61472D (x, 0 &#615480&#61472ia Continuous
Solution of the Homogeneous Integral Equation3.13 Fundamental Functions3.14 Integral
Equations with Degenerate KernelsChapter-4: Hilbert Schmidt Theory4.1 All Iterated Kernels of a
Symmetric Kernel are also Symmetric4.2 Orthogonality4.3 Orthogonality of Fundamental
Functions4.4 Eigen Values of Symmetric Kernel are Real4.10 Fourier Series of Power of the Eigen
Values of the Iterated Kernel4.11 Hilbert-Schmidt Theorem4.12 The inequalities of Schwarz and
Minkowski4.13 Hilbert's Theorem4.14 Complete Normalized Orthogonal System of Characteristic
Functions4.15 Coefficients of the Continuous Function f (x)4.16 Complete Normalized Orthogonal
System of Fundamental Functions4.17 Bessel Inequality4.18 Riesz-Fischer Theorem4.19
Representation by a linear Combination of the Characteristic Functions4.20 Schmidt's Solution of
the Non-Homogeneous Integral Equation4.21 Solution of the Fredholm Integral Equation of first
KindChapter-5: Application of Integral Equations5.1 Introduction5.2 Initial Value Problem5.3
Boundary Value Problems5.4 Deformation of a Rod5.5 Determination of Periodic Solutions5.6
Green's Function5.7 Construction of Green's Function5.8 Particular Case5.9 Influence
Function5.10 Construction of Green's Function when the Boundary Value Problem Contains a
Parameter5.11 Longitudinal Vibrations of a RodChapter-6: Singular Integral Equations6.1
Introduction6.2 Abel Integral Equation6.3 Particular Case6.4 Weakly Singular Kernel6.5 Iteration
of the Singular Equation6.6 Fredholm Operator6.7 Equivalence of the Fredholm Integral Equation
and the Iterated Equation6.8 Prove that the Eigenvalues &#615480and &#61548pof the Kernels k
and kp are of the Same Rank6.9 If a Number &#61549#61472is an Eigenvalue of the Iterated
Kernel kp (x, &#61560, then atleast one of the Distinct Numbers6.10 Integral Equation in an
Infinite Interval6.11 Cauchy Principal Integral6.12 Cauchy Type Integral6.13 Cauchy Integral on
the Path of Integration6.14 Plemelj Formulae6.15 The Plemelj &#8211Prvalov Theorem6.16
Poincare'-Bertrand Transformation Formula for Iterated Singular Integrals6.17 Application of the
Calculus of Residues6.18 Hilbert Kernel6.19 Solution of the Cauchy-type Singular Integral
EquationChapter-7: Integral