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Solved Exercises in Fractional Calculus
This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.
The Many Faces of Maxwell, Dirac and Einstein Equations
This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.
Mastering Calculus through Practice
This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques. It opens with an introduction to fundamental facts of mathematical logic, set theory, and pre-calculus, extending toward functions, limits, derivatives, and integrals. Over 300 solved problems are approached with a simple, direct style, ordered in a way that positively challenges students and helps them build self-confidence as they progress. A special final chapter adds five carefully crafted problems for a comprehensive recap of the work. The book is aimed at first-year students of fields in which calculus and its applications have a role, including Science, Technology, Engineering, Mathematics, Economics, Architecture, Management, and Applied Social Sciences, as well as students of Quantitative Methods courses. It can also serve as rich supplementary reading for self-study.
The Many Faces of Maxwell, Dirac and Einstein Equations
This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.
Cálculo fracionário
O Cálculo Fraccionário (CF) remonta ao início do cálculo integro- -diferencial clássico. A comunidade científica considera que o CF decorre de uma troca de cartas entre L'Hôpital e Leibniz em 1695. A partir desse instante pode-se encontrar a contribuição de nomes famosos, tais como Euler, Fourier, Laplace, Abel, Liouville, Riemann e muitos outros matemáticos. No entanto, ao contrário do cálculo clássico (de ordem inteira), o CF manteve-se relativamente desconhecido da comunidade científica, pelo que a sua aplicação nas ciências aplicadas, como na física e na engenharia, se limita a poucas contribuições, embora relevantes, tais como as de Heaviside, ou dos irmãos Cole. A ...
