Based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907, this title includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions. The range of entries in the Subject Index is very wide. To mention a few out of many hundreds: Horner's method, multinomial theorem, mortality table, arithmetico-geometric series, Pellian equation, Bernoulli numbers, irrationality of e, Gudermanian, Euler numbers, continuant, Stirling's theorem,...

Presents a study of the principles of logic, with special emphasis on inference and induction.

In addition to the standard topics, this volume contains many topics not often found in an algebra book, such as inequalities, and the elements of substitution theory. Especially extensive is Chrystal's treatment of the infinite series, infinite products, and (finite and infinite) continued fractions.

Contains historical background and discussion of results for each chapter, References, and an Index.

Presents the basic features of almost periodic functions. This book describes the connections that exist between theory (pure ) of almost periodic functions and such areas of application as the theory of ordinary differential equations and partial differential equations.

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In this second English edition of Caratheodory's work (originally published in German), the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Caratheodory's work.

This second volume is a comprehensive treatment of Diophantine analysis. Besides the familiar cases of Diophantine equations, this rubric also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in artihmetical and geometrical progressions. Many important Diophantine equations, such as Pell's equation, and classes of equations, such as quadratic, cubic and quartic equations, are treated in detail.

Covers the related topics of divisibility and primality. This book describes the development of our understanding of perfect numbers. It also covers standard topics, such as Fermat's theorems, primitive roots, counting divisors, the Mobius function, and prime numbers themselves.