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The evolution of advanced calculus in undergraduate mathematics reveals a significant shift in curriculum focus over the past fifty years. Initially a core subject, it gradually gave way to real analysis as educators prioritized rigorous foundations. This led to a bifurcation in calculus courses, with one path exploring complex topics like calculus on n-manifolds and another simplifying to two- and three-dimensional calculus. However, the traditional depth of advanced calculus is often lost, particularly in addressing the complexities of several functions of several variables within limited course time.
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Advanced Calculus, James J. Callahan
- Language
- Released
- 2010
- product-detail.submit-box.info.binding
- (Hardcover)
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- Title
- Advanced Calculus
- Subtitle
- A Geometric View
- Language
- English
- Authors
- James J. Callahan
- Publisher
- Springer-Verlag New York Inc.
- Released
- 2010
- Format
- Hardcover
- Pages
- 526
- ISBN13
- 9781441973313
- Category
- Mathematics
- Description
- The evolution of advanced calculus in undergraduate mathematics reveals a significant shift in curriculum focus over the past fifty years. Initially a core subject, it gradually gave way to real analysis as educators prioritized rigorous foundations. This led to a bifurcation in calculus courses, with one path exploring complex topics like calculus on n-manifolds and another simplifying to two- and three-dimensional calculus. However, the traditional depth of advanced calculus is often lost, particularly in addressing the complexities of several functions of several variables within limited course time.