Multivariate Calculus and Geometry

3rd Auflage 2014
ISBN: 978-1-4471-6418-0
Verlag: Springer

Buch, Englisch, 257 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 4161 g

Reihe: Springer Undergraduate Mathematics Series

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Dineen, Seán

Fachgebiete

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

Inhaltsverzeichnis

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.

Über Autor(innen)

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).