Cohomology and Differential Forms

Title: Cohomology and Differential Forms | Author(s): Izu Vaisman |Publisher: Dover Publications | Year: 2016 | Language: English | Pages : 293 | ISBN: 0486804836, 9780486804835 | Size: 21 MB  | Extension: pdf

This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romanias University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology.

A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

Fundamental of Mathematics Co-ordinate Geometry

Title: Fundamental of Mathematics Co-ordinate Geometry | Author(s): Sanjay Mishra Pearson| Series:  Periodical: | Publisher: Pearson | Year: 2018 | Language: English | Pages : 850 | Size: 46 MB | Extension: pdf

Key Features 1. Strictly aligned with the prescribed syllabus. Written in a lucid manner to assist students to understand the concepts without the help of any guide. 2. Provides the vast subject in a structured and useful manner so as to familiarize the candidates taking the current examinations with the current trends and types of multiple-choice questions asked. 3. The multiple-choice questions have been arranged in following categories: Straight Objective Type Questions (Single Choice) Brainteasers Objective Type Questions (Single Choice) Multiple Correct Answer Type Questions (More than one choice) Linked-Comprehension Type Questions Assertion and Reasoning Questions Matrix-Match Type Questions and the IIT - JEE Corner About the Book: Fundamentals of Mathematics -CoordinateGeometry Aspiring engineers have always wanted to secure admissioninpioneering institutes such as the Indian Institute ofTechnologyand the National Institute of Technology. FundamentalsofMathematics, the complete mathematics collection, preparesstudentsfor such prestigious entrance examinations. This seriesiscustomized, class-tested and structure-driven with aconceptualapproach to the subject. The authority, command andexperience ofthe author, Sanjay Mishra, is reflected in the clearexplanationsof complex concepts and in the chapter-end exercises.Each volumeof this series is meticulously planned in a uniquestudent-friendlymanner to make the learning process easier, moreeffective andenjoyable. Contents Preface Acknowledgements Chapter 1 Point and Cartesian System Introduction Postulates of Euclidean Geometry Frame of reference Co-ordinate Systems Rectangular co-ordinate system Sign convention Oblique Co-ordinate System Polar co-ordinate system Relation between the polar and cartesian co-ordinates Distance Between Two Points Lying in a Plane When co-ordinates of two points are given in rectangularform When the co-ordinates of point are given in oblique system When the co-ordinates of points