Certain qualitative and approximate methods are needed to solve problems of differential equations with maxima, which depend on the maximum value of a state on past time intervals. One of the few up-to-date references on the topic, this book develops these qualitative and approximate methods of analysis for nonlinear differential equations with maxima. It explains the underlying theory of differential equations; how to accurately model real-world applications, including automatic control systems; and how to solve initial value and boundary value problems of differential equations with...

This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration no generalized Riemann integrals of Henstock Kurzweil variety are involved.

In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy Riemann, Laplace, and minimal surface equations.

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Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations.

After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions...

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.

The book highlights the connection between Gauss's theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and...

This book provides a thorough, self-contained explanation of Galois theory of commutative rings. Requiring some background in commutative algebra and algebraic geometry, the book gives complete proofs of the main results of separable Galois theory. This edition includes a new chapter that offers background on separability and a new chapter on categorical Galois theory that incorporates many developments in the field. The book also covers Boolean spectrum theory and the fundamental groupoid.