Multivariate Calculus and Geometry

2. Auflage 2001
ISBN: 978-1-85233-472-7
Verlag: Springer

Buch, Englisch, 254 Seiten, Format (B × H): 178 mm x 235 mm, Gewicht: 1040 g

Reihe: Springer Undergraduate Mathematics Series

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Dineen, Sean

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.