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Global Calculus
 
S. Ramanan Chennai Mathematics Institute, Chennai, India
Global Calculus
Hardcover ISBN:  978-0-8218-3702-3
Product Code:  GSM/65
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2107-6
Product Code:  GSM/65.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-3702-3
eBook: ISBN:  978-1-4704-2107-6
Product Code:  GSM/65.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Global Calculus
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Global Calculus
S. Ramanan Chennai Mathematics Institute, Chennai, India
Hardcover ISBN:  978-0-8218-3702-3
Product Code:  GSM/65
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2107-6
Product Code:  GSM/65.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-3702-3
eBook ISBN:  978-1-4704-2107-6
Product Code:  GSM/65.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 652005; 316 pp
    MSC: Primary 14; 32; 53;

    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.

    Readership

    Graduate students and research mathematicians interested in differential or algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Sheaves and differential manifolds: Definitions and examples
    • Chapter 2. Differential operators
    • Chapter 3. Integration on differential manifolds
    • Chapter 4. Cohomology of sheaves and applications
    • Chapter 5. Connections on principal and vector bundles; Lifting of symbols
    • Chapter 6. Linear connections
    • Chapter 7. Manifolds with additional structures
    • Chapter 8. Local analysis of elliptic operators
    • Chapter 9. Vanishing theorems and applications
    • Appendix
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 652005; 316 pp
MSC: Primary 14; 32; 53;

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.

Readership

Graduate students and research mathematicians interested in differential or algebraic geometry.

  • Chapters
  • Chapter 1. Sheaves and differential manifolds: Definitions and examples
  • Chapter 2. Differential operators
  • Chapter 3. Integration on differential manifolds
  • Chapter 4. Cohomology of sheaves and applications
  • Chapter 5. Connections on principal and vector bundles; Lifting of symbols
  • Chapter 6. Linear connections
  • Chapter 7. Manifolds with additional structures
  • Chapter 8. Local analysis of elliptic operators
  • Chapter 9. Vanishing theorems and applications
  • Appendix
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.