Description
Author: Prof. Ram Bilas Misra
© 2019 | Publication: Sep 2019
ISBN: 978-1-925823-72-1 | 398 Pages
About the Book and Audience
The present book is the second issue of a series explaining various terms and concepts in Mathematics. Introducing the topics in concise form of definitions, main results, theorems and examples, it may serve as a reference book. The topics arranged in alphabetical order starting from Algebra (Classical) and covering up to Geometry (3-dimensional Coordinate) were included in the first volume. Further topics from Differential Geometry up to Jacobians are included in the present volume.
The subject matter is presented here in sixteen chapters of which the first one lists few results referred to in the later discussion. The next five chapters cover the material on main topics of Differential Geometry such as Curves in Space, Envelopes and Ruled surfaces, Curvature of surfaces, Gauss and Mainardi-Codazzi equations, Special curves on a surface. All of these chapters in D.G. are supplemented with number of unsolved problems with necessary hints. Finite Geometry is discussed in Chapter 7, while Chapter 8 deals with the Historical development of Euclidean geometry. The next four chapters deal with the Plane, Solid, Spherical and Transformation geometries. Improper integrals, Evaluation of Improper integrals with limits and Uniform convergence of Improper integrals is taken up in Chapters 13-15. The last chapter deals with Jacobians and their properties.
About the Author
Prof. Dr. Ram Bilas Misra, a former Vice-Chancellor of Avadh University, Faizabad (Ayodhya), India, has a long experience of teaching the subject since 1962 at different universities in India and abroad. He published 64 original research papers in Diff. Geom. of Finslerian Manifolds and Mathematical Physics in the leading research journals of international repute. As a regular reviewer, he published reviews of over 100 research papers in “Mathl. Reviews” and “Zentralblatt für Mathematik”. He has been frequently quoted both at home and abroad; notably, in the research monographs “Foundations of Finsler Geometry and Special Finsler Spaces” by Prof. Makoto Matsumoto of Kyoto Univ., Japan and “Finsler Geometry, Relativity and Gauge Theories” by Prof. G.S. Asanov of Moscow State Univ., Russia.
Prof. Misra is widely travelled and experienced academician. He has been a frequent visitor to the universities at Turin, Padua and ICTP, Trieste (all in Italy) and a visiting professor to the universities at Sopron (Hungary), Wroclaw (Poland) and Mahatma Gandhi Kashi Vidyapith, Varanasi (India).
Chapters
- Preliminaries, pp. 1-12
- Geometry (Differential): Part 1 (Curves in E3), pp. 13-76
- Geometry (Differential): Part 2 (Enveolpes and Ruled Surfaces), pp. 77-118
- Geometry (Differential): Part 3 (Curvature of Surfaces), pp. 119-168
- Geometry (Differential): Part 4 (Gauss and Mainardi-Codazzi Equations), pp. 169-184
- Geometry (Differential): Part 5 (Special Curves on a Surface), pp. 185-228
- Geomtry (Finite), pp. 229-248
- Historical Development of Euclidean Geometry, pp. 249-256
- Geometry (Plane), pp. 257-270
- Geometry (Solid), pp. 271-280
- Geometry (Spherical), pp. 281-282
- Geometry (Transformation), pp. 283-318
- Improper Integrals, pp. 319-338
- Evaluation of Limits, pp. 339-348
- Uniform Convergence of Improper Integrals, pp. 349-358
- Jacobians, pp. 359-366
Numerous Figures and Illustrations
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