Linear Integral Equations By Shanti Swarup Pdf Download
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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.