Multivariate calculus and geometry
著者
書誌事項
Multivariate calculus and geometry
（Springer undergraduate mathematics series）
Springer, c2001
2nd ed.
- : pbk
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注記
Includes index
内容説明・目次
内容説明
This book provides the higher-level reader with a comprehensive review of all important aspects of Differential Calculus, Integral Calculus and Geometric Calculus of several variables The revised edition, which includes additional exercises and expanded solutions, and gives a solid description of the basic concepts via simple familiar examples which are then tested in technically demanding situations. Readers will gain a deep understanding of the uses and limitations of multivariate calculus.
目次
1. Introduction to Differentiable Functions.- 2. Level Sets and Tangent Spaces.- 3. Lagrange Multipliers.- 4. Maxima and Minima on Open Sets.- 5. Curves in ?n.- 6. Line Integrals.- 7. The Frenet-Serret Equations.- 8. Geometry of Curves in ?3.- 9. Double Integration.- 10. Parametrized Surfaces in ?3.- 11. Surface Area.- 12. Surface Integrals.- 13. Stokes' Theorem.- 14. Triple Integrals.- 15. The Divergence Theorem.- 16. Geometry of Surfaces in ?3.- 17. Gaussian Curvature.- 18. Geodesic Curvature.- Solutions.
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