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by Ram Bilas Misra (Author)
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.
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