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The need to support his family meant that George Boole (1815-64) was a largely self-educated mathematician. Widely recognised for his ability, he became the first professor of mathematics at Cork. Boole belonged to the British school of algebra, which held what now seems to modern mathematicians to be an excessive belief in the power of symbolism. However, in Boole's hands symbolic algebra became a source of novel and lasting mathematics. Also reissued in this series, his masterpiece was An Investigation of the Laws of Thought (1854), and his two later works A Treatise on Differential Equations (1859) and A Treatise on the Calculus of Finite Differences (1860) exercised an influence which can still be traced in many modern treatments of differential equations and numerical analysis. The beautiful and mysterious formulae that Boole obtained are among the direct ancestors of the theories of distributions and of operator algebras.

Differential equations.

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Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Differential equations

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This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis. Contents: Introduction and Overview; Volterra Models of Evolving Dynamical Systems: Volterra Equations of the First Kind with Piecewise Continuous Kernels; Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels; Volterra Op

Nonlinear integral equations. --- Volterra equations. --- Equations, Volterra --- Integral equations --- Integral equations, Nonlinear --- Nonlinear theories

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This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried

Fractional differential equations. --- Extraordinary differential equations --- Differential equations --- Fractional calculus

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Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

Difference equations. --- Differential equations. --- Difference equations --- Numerical solutions.