Linear Integral Equations By Shanti Swarup Pdf Download

A. Nakdzi and W. Sanković, Multiplication, integration and fractional integral operators arising in linear integral equations on two pages : I, Inter. Journal of Math. Meth. Appl. Sci. 41 (2010), 1107 1127, DOI: 10.1080/00207160802537279.

M. E. Luna and A. Carpinteri, Existence of exact solutions for a nonlinear Volterra integral equation of fractional order, Integral Transf. Spec. Funct. 22 (2011), 45 47, DOI: 10.1080/10656011003730552.

S.K. Pant, An application of the theory of generalized integral operators and fractional differential equations to a nonlinear Volterra integral equation of second kind, Advances in difference Equations. 3 (2007), 569 587, DOI: 10.1186/1541-6560-3-5.

L. M. Fernandez, F. Gazzola and B. Ripani, Fractional calculus approach to linear non-autonomous Volterra integral equations of the first kind, J. Math. Anal. Appl. (2014), 39 376, DOI: 10.1016/j.jmaa.2014.03.005.

S. Swaminathan and V. Prasad, On the Reciprocal Potentials with a Negative Superfractional Integral, Advances in Difference Equations, 2013 (2013), Article ID 127049, 1 page, ISSN 0926-0290, doi: 10.1155/2013/127049.

J. Sanchez, Existence of least energy solutions to a nonlinear integral equation, Advances in Difference Equations, 2011 (2011), Article ID 266304, 4 pages, ISSN 0926-0290, doi: 10.1155/2011/266304.

R. R. Yavshits, Existence and asymptotics of solutions of some nonlinear Volterra integral equation of the first kind, Applied Mathematics and Computation, 218, (2012), pages 1469-1473, doi: 10.

Linear Algebra:Vector spaces, algebra of linear transformations. Algebra of matrices, determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms.Quadratic forms, reduction, and classification of quadratic forms

Linear Functions:Multiplication, vectors, domain, range, span, linear combination, independent, dependent variables, elementary functions, absolute value, polynomials, integer powers, logarithms, factorial, indefinite integrals, definite integrals, exponential functions, natural logarithms, logarithms, inverse functions, tangents, derivatives, integrals, hyperbolas, parabolas, inverse functions, hyperbolic functions, second-order linear equations, rational expressions, polynomials, indefinite integrals, derivative. Taylor polynomials, series solutions, tables, power series, indefinite integrals, analytical functions, second-order linear differential equations, integral form, and differential equations. Differential equations, Laplace transformations, applications, solution methods, algebraic solutions, homogeneous solutions, solutions of second-order differential equations.

Vector Algebra:Exponentials, matrices, matrix algebra, change of basis, direct sum, inverse, direct product, rank, direct products, eigen vectors, eigen values, principal matrices, characteristic polynomials, diagonal matrices, first-order equations, second-order equations, Gaussian elimination, Jordan canonical form, linear equations, least squares, matrix decomposition, linear independence, eigenvalues, Hessian, first-order linear systems, second-order linear systems, simultaneous equations, matrix representation, conditional probability.

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