Theory and Application of Infinite Series

Author: Konrad Knopp
Publisher: Courier Corporation
ISBN: 9780486318615
Release Date: 2013-04-26
Genre: Mathematics

Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Includes exercises.

Theory and Application of Infinite Series

Author: Konrad Knopp
Publisher: Courier Corporation
ISBN: 9780486661650
Release Date: 1951
Genre: Mathematics

This unusually clear and interesting classic offers a thorough and reliable treatment of an important branch of higher analysis. The work covers real numbers and sequences, foundations of the theory of infinite series, and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, and other topics). Exercises throughout. Ideal for self-study.

Infinite Sequences and Series

Author: Konrad Knopp
Publisher: Courier Corporation
ISBN: 9780486152042
Release Date: 2012-09-14
Genre: Mathematics

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.

Real Infinite Series

Author: Daniel D. Bonar
Publisher: MAA
ISBN: 0883857456
Release Date: 2006-04-06
Genre: Mathematics

An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.

Summation of Series

Author: L.B. W. Jolley
Publisher: Courier Corporation
ISBN: 9780486153384
Release Date: 2012-05-04
Genre: Mathematics

More than 1,200 common series appear here. Collected, summed, and grouped for easy reference, they constitute an immensely useful handbook for mathematicians, physicists, computer technicians, engineers, and students.

Real Analysis and Applications

Author: Frank Morgan
Publisher: American Mathematical Soc.
ISBN: 0821886118
Release Date:
Genre: Mathematics

Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis.

A Student s Guide to Infinite Series and Sequences

Author: Bernhard W. Bach, Jr.
Publisher: Cambridge University Press
ISBN: 9781107059825
Release Date: 2018-05-17
Genre: Mathematics

An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.

A Course in the Theory of Groups

Author: Derek Robinson
Publisher: Springer Science & Business Media
ISBN: 9781468401288
Release Date: 2012-12-06
Genre: Mathematics

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.

Infinite Series

Author: Isidore Isaac Hirschman
Publisher: Courier Corporation
ISBN: 9780486798240
Release Date: 2014-08-18
Genre: Mathematics

Text for advanced undergraduate and graduate students examines Taylor series, Fourier series, uniform convergence, power series, and real analytic functions. Appendix covers set and sequence operations and continuous functions. 1962 edition.

Infinite Dimensional Optimization and Control Theory

Author: Hector O. Fattorini
Publisher: Cambridge University Press
ISBN: 0521451256
Release Date: 1999-03-28
Genre: Computers

Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.