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Advanced Calculus
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CC BY-NC-SA
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Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.

Note: this is a 57 MB PDF Document.

Subject:
Calculus
Mathematics
Material Type:
Textbook
Provider:
Harvard University
Provider Set:
Individual Authors
Author:
Sternberg Shlomo and Lynn Loomis
Date Added:
02/16/2011
Analysis II
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CC BY-NC-SA
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This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.

Subject:
Calculus
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Guillemin, Victor
Date Added:
09/01/2005
Geometry of Manifolds
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This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Auroux, Denis
Date Added:
02/01/2007
Introduction to Lie Groups
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This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001).
Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Helgason, Sigurdur
Date Added:
09/01/2004