Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Starting with the useful concept of an elementary integral defined (axiomatically) on a family of elementary functions, this treatment examines the general theory of the integral, Lebesque integral in n space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." - Sci-Tech Book News. 1966 edition.

This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, a detailed treatment of Markov chains, continuous Markov processes, and more. 150 problems, many with answers. Indispensable to mathematicians and natural scientists alike.

This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series and much more. Over 100 problems at ends of chapters. Answers in back of book. 1962 ed.

2013 Reprint of 1961 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers. Georgi Shilov was a Soviet mathematician and expert in the field of functional analysis, who contributed to the theory of normed rings and generalized functions. Shilov often collaborated with colleague Israel Gelfand on research that included generalized functions and partial differential equations.

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms.