Mathematical Methods e-bog

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions. The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed. The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.