Global Calculus
Ramanan, S.
Global Calculus - 1st ed. - Rhode Island: American Mathematical Society, c2005 - xi, 306p. : ill. ; 23cm. - Graduate Studies in Mathematics ; Vol. 65 .
Analysis, topology and algebra brought new power to geometry, revolutionizing the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.
Also includes bibliography and index.
9780821848609
Mathematics
Differential Operators
Analytic Spaces
Differential Geometry
515.94 / RAM
Global Calculus - 1st ed. - Rhode Island: American Mathematical Society, c2005 - xi, 306p. : ill. ; 23cm. - Graduate Studies in Mathematics ; Vol. 65 .
Analysis, topology and algebra brought new power to geometry, revolutionizing the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.
Also includes bibliography and index.
9780821848609
Mathematics
Differential Operators
Analytic Spaces
Differential Geometry
515.94 / RAM