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Multivariate calculus and geometry / Sean Dineen.

Material type: TextTextSeries: Springer undergraduate mathematics seriesPublication details: London : Springer-Verlag, 2014.Description: xiv, 257 p. ; illISBN:
  • 9781447164180
Subject(s): DDC classification:
  • 515 23 D583
Contents:
1. Introduction to Differentiable Functions -- 2. Level Sets and Tangent Spaces -- 3. Lagrange Multipliers -- 4. Maxima and Minima on Open Sets -- 5. Curves in Rn -- 6. Line Integrals -- 7. The Frenet?Serret Equations -- 8. Geometry of Curves in R3 -- 9. Double Integration -- 10. Parametrized Surfaces in R3 -- 11. Surface Area -- 12. Surface Integrals -- 13. Stokes? Theorem -- 14. Triple Integrals -- 15. The Divergence Theorem -- 16. Geometry of Surfaces in R3 -- 17. Gaussian Curvature -- 18. Geodesic Curvature-- Solutions-- Index.
Summary: This book has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515 D583 (Browse shelf(Opens below)) Available 136024
Total holds: 0

Includes index.

1. Introduction to Differentiable Functions --
2. Level Sets and Tangent Spaces --
3. Lagrange Multipliers --
4. Maxima and Minima on Open Sets --
5. Curves in Rn --
6. Line Integrals --
7. The Frenet?Serret Equations --
8. Geometry of Curves in R3 --
9. Double Integration --
10. Parametrized Surfaces in R3 --
11. Surface Area --
12. Surface Integrals --
13. Stokes? Theorem --
14. Triple Integrals --
15. The Divergence Theorem --
16. Geometry of Surfaces in R3 --
17. Gaussian Curvature --
18. Geodesic Curvature--
Solutions--
Index.

This book has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

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