Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics)

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9780387903576: Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics)
Reseña del editor:

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.

Reseña del editor:

This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.

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Thorpe, John A.
ISBN 10: 0387903577 ISBN 13: 9780387903576
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John A. Thorpe
Editorial: Springer-Verlag New York Inc. 1994-10-27, New York, NY (1994)
ISBN 10: 0387903577 ISBN 13: 9780387903576
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Descripción Springer-Verlag New York Inc. 1994-10-27, New York, NY, 1994. hardback. Estado de conservación: New. Nº de ref. de la librería 9780387903576

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Editorial: Springer-Verlag New York Inc., United States (1994)
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Descripción Springer-Verlag New York Inc., United States, 1994. Hardback. Estado de conservación: New. 1st ed. 1979. Corr. 4th printing 1994. 239 x 160 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AAZ9780387903576

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John A. Thorpe
Editorial: Springer-Verlag New York Inc., United States (1994)
ISBN 10: 0387903577 ISBN 13: 9780387903576
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Descripción Springer-Verlag New York Inc., United States, 1994. Hardback. Estado de conservación: New. 1st ed. 1979. Corr. 4th printing 1994. 239 x 160 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AAZ9780387903576

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John A. Thorpe
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Descripción Springer-Verlag New York Inc., 1994. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería GB-9780387903576

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Thorpe, John A.
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Descripción Estado de conservación: New. Bookseller Inventory # ST0387903577. Nº de ref. de la librería ST0387903577

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Descripción Springer, 1994. Estado de conservación: New. Series: Undergraduate Texts in Mathematics. Num Pages: 256 pages, biography. BIC Classification: PBMP. Category: (UU) Undergraduate. Dimension: 243 x 166 x 21. Weight in Grams: 534. . 1994. Fir. Hardcover. . . . . . Nº de ref. de la librería V9780387903576

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John A. Thorpe
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Descripción Hardback. Estado de conservación: New. Not Signed; 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 algeb. book. Nº de ref. de la librería ria9780387903576_rkm

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Thorpe, John A.
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97803879035760000000

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Descripción Springer. Estado de conservación: New. Series: Undergraduate Texts in Mathematics. Num Pages: 256 pages, biography. BIC Classification: PBMP. Category: (UU) Undergraduate. Dimension: 243 x 166 x 21. Weight in Grams: 534. . 1994. Fir. Hardcover. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780387903576

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