Elementary Topics in Differential Geometry

J. A. Thorpe

ISBN 10: 0387903577 / ISBN 13: 9780387903576

Editore: Springer New York, Springer US Apr 1979, 1979

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Neuware -In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 276 pp. Englisch.

Codice articolo 9780387903576

Dati bibliografici

• Titolo: Elementary Topics in Differential Geometry
• Editore: Springer New York, Springer US Apr 1979
• Data di pubblicazione: 1979
• Lingua: Inglese
• ISBN 10: 0387903577
• ISBN 13: 9780387903576
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 21 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 21 millimetri di profondità
• Peso: 582 grammi

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Riassunto

In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under­ standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

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