Advanced Calculus

Written by: Lynn H. Loomis (Harvard) & Shlomo Sternberg (Harvard)

Two members of the Department of Mathematics at Harvard University put this large, free online calculus textbook together in 1990. It was based on an honors course that was offered in the 1960s.

The preface of the text indicates that this text could be used for a two-semester course in advanced calculus or a three-semester course in analysis.

Prerequisites for the course included calculus, linear algebra and partial derivatives.

Chapter Titles from Advanced Calculus Online Textbook

  1. Vector Spaces
  2. Finite-Dimensional Vector Spaces
  3. The Differential Calculus
  4. Compactness and Completeness
  5. Scalar Product Spaces
  6. Differential Equations
  7. Multilinear Functionals
  8. Integration
  9. Differentiable Manifolds
  10. The Integral Calculus on Manifolds
  11. Exterior Calculus
  12. Potential Theory in E^n
  13. Classical Mechanics

View this Free Online Material at the source:
Advanced Calculus

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