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Advanced Calculus A Geometric View by James J. Callahan



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Advanced Calculus A Geometric View by James J. Callahan , Department of Mathematics and Statistics, Smith College, Northampton, MA 01063, USA. ISSN: 0172-6056, ISBN 978-1-4419-7331-3, e-ISBN: 978-1-4419-7332-0.
The premise of this book is that these changes create the opportunity for a new geometric and visual approach to advanced calculus. More than forty years ago—and long before the curriculum had evolved to its present state—Andrew Gleason outlined a modern geometric approach in a series of lectures, “The Geometric Content of Advanced Calculus” [8]. (In a companion piece [17], Norman Steenrod made a similar assessment of the earlier courses in the calculus sequence.) Because undergraduate analysis bifurcated around the same time, Gleason’s insights have not been implemented to the extent that they might have been; nevertheless, they fit naturally into the approach.

Advanced Calculus A Geometric View by James J. Callahan cover the following topics.

  • 1. Starting Points
    2. Geometry of Linear Maps
    3. Approximations
    4. The Derivative
    5. Inverses
    6. Implicit Functions
    7. Critical Points
    8. Double Integrals
    9. Evaluating Double Integrals
    10. Surface Integrals
    11. Stokes’ Theorem

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