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1st Edition

This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new Moshe Sniedovich September 10, The author emphasizes the crucial role that modeling plays in understanding this area.

He also Lawrence Narici, Edward Beckenstein July 26, With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn—Banach theorem.


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Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory.

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as Stay on CRCPress.

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MATH224: The Divergence Theorem (full)

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Norton, The Gauss-Green theorem for fractal boundaries. Duke Math. Jurkat W. Nonnenmacher, A generalized n-dimensional Riemann integral and the divergence theorem with singularities , Acta Sci. Szeged , 59 , — Katsoulakis M.

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Tzavaras, Contractive relaxation systems and the scalar multidimensional conservation law , Comm. Kruzkov S. Russian , 81 , — Lax P. Zarantonello, Academic Press, New York, , pp.


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Lions P. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations , J. Liu T. Smoller, On the vacuum state for the isentropic gas dynamics equations , Adv. Natalini R. Chapman and Hall: London, Mascia C. Terracina, Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equations , Arch. Nonnenmacher D. London Math. Otto F. Pfeffer W. Press: Cambridge. 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. The sets of finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation. The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter.

The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field.

The Divergence Theorem and Sets of Finite Perimeter

Removable Singularities Distributions Differential equations Holomorphic functions Harmonic functions The minimal surface equation Injective limits. The author starts these considerations with a nice presentation of the background of these problems. Pawlak, Mathematical Reviews , April We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.