Professor A.N. Tikhonov was the founder of nonlinear ill-posed problem theory. This two-volume book introduces the reader to the theory and shows its applications in the natural sciences.The first volume introduces the foundations of the theory and provides the background necessary for the design of numerical methods. The second volume presents the finite-dimensional variants and modification of these methods to help readers use current computer software. It considers applications in linear algebra, vibrational spectroscopy, astrophysics, and medicine.

Nonlinear Ill-Posed Problems (Applied Mathematics)

Science & Math

Tikhonov, A.N.

Leonov, A.S.

Yagola, A.G.

Mathematics

Chapman and Hall/CRC

Based on practical work with mathematical physics done in the Physics Department of Moscow State University, this outstanding text by three of the Faculty's distinguished members focuses on a wide range of problems. Chapters are divided according to the method of solution — thereby giving students the opportunity, through independent work, to gain elementary problem-solving skills where mathematical physics equations are concerned. In addition, there is a supplement devoted to the special coordinate systems of mathematical physics, together with a section devoted to special functions. Designed not only for students but for engineers and research workers, this volume includes an exceptionally useful selection of problems, a number of which are accompanied by detailed instructions and solutions.

A Collection of Problems in Mathematical Physics (Dover Books on Physics)

Samarskii, A.

Budak, B. M.

Physics

Dover Publications

Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.

Equations of Mathematical Physics (Dover Books on Physics)

Samarskii, A.A.

This is the sixth edition of a text that has been in use since the 1950s; it has been substantially revised and reflects developments in mathematical physics at the end of the 20th century.

Equations of Mathematical Physics (Russian Research in Mathematics and Science)

Reference

Foreign Language Study & Reference

The Edwin Mellen Press Ltd

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.

Numerical Methods for the Solution of Ill-Posed Problems (Mathematics and Its Applications, 328)

Computers & Technology

Goncharsky, A.

Stepanov, V.V.

Yagola, Anatoly G.

Programming

Springer

The proposed book is one of a series called "A Course of Higher Mathematics and Mathematical Physics" edited by A. N. Tikhonov, V. A. Ilyin and A. G. Sveshnikov. The book is based on a lecture course which, for a number of years now has been taught at the Physics Department and the Department of Computational Mathematics and Cybernetics of Moscow State University. The exposition reflects the present state of the theory of differential equations, as far as it is required by future specialists in physics and applied mathematics, and is at the same time elementary enough. An important part of the book is devoted to approximation methods for the solution and study of differential equations, e.g. numerical and asymptotic methods, which at the present time play an essential role in the study of mathematical models of physical phenomena. Less attention is paid to the integration of differential equations in elementary functions than to the study of algorithms on which numerical solution methods of differential equations for computers are based.

Differential Equations (Springer Series in Soviet Mathematics)

Vasil'eva, A.B.

Sveshnikov, A.G.

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and Rhs approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a Fortran program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.

Numerical Methods for the Solution of Ill-Posed Problems (Mathematics and Its Applications)

Professor A.N. Tikhonov was the founder of nonlinear ill-posed problem theory. This two-volume book introduces the reader to the theory and shows its applications in the natural sciences.The first volume introduces the foundations of the theory and provides  the background necessary for the design of numerical methods. The second volume presents the finite-dimensional variants and modification of these methods to help readers use current computer software. It considers applications in linear algebra, vibrational spectroscopy, astrophysics, and medicine.

Nonlinear Ill-Posed Problems (Applied Mathematical Sciences)

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