Multivariate Calculus and Geometry
Springer London Ltd (Verlag)
978-1-4471-6418-0 (ISBN)
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.
Sean Dineen taught for many years at University College Dublin where he is now an emeritus professor. He is the author of many research articles and monographs and of a number of successful and popular textbooks including: Analysis; A Gateway to Understanding Mathematics (World Scientific, 2012) and Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula (AMS, Second Edition, 2013).
Introduction to Differentiable Functions.- Level Sets and Tangent Spaces.- Lagrange Multipliers.- Maxima and Minima on Open Sets.- Curves in Rn.- Line Integrals.- The Frenet–Serret Equations.- Geometry of Curves in R3.- Double Integration.- Parametrized Surfaces in R3.- Surface Area.- Surface Integrals.- Stokes’ Theorem.- Triple Integrals.- The Divergence Theorem.- Geometry of Surfaces in R3.- Gaussian Curvature.- Geodesic Curvature.
| Reihe/Serie | Springer Undergraduate Mathematics Series |
|---|---|
| Zusatzinfo | 103 Illustrations, black and white; XIV, 257 p. 103 illus. |
| Verlagsort | England |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Curvature and Torsion of Curves • Double and Triple Integrals • Frenet-Serret Equations • Gaussian curvature • Geodesic Curvature • Geometrie • Lagrange multipliers • line integrals • Multivariate Analyse • Stokes Theorem • surface integrals • The Hessian • The Weingarten Mapping |
| ISBN-10 | 1-4471-6418-0 / 1447164180 |
| ISBN-13 | 978-1-4471-6418-0 / 9781447164180 |
| Zustand | Neuware |
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