Multivariate calculus and geometry
著者
書誌事項
Multivariate calculus and geometry
（Springer undergraduate mathematics series）
Springer, c1998
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注記
Includes index
内容説明・目次
内容説明
Aimed primarily at higher-level undergraduates, this book seeks to provide a deeper understanding of multivariate calculus and geometry, which will enable the reader to appreciate the uses and limitations of multivariate analysis when applying them to new problems. It provides a description of the basic concepts, via familiar explanations, which are then tested in technically demanding examples. The author assumes a minimal amount of prerequisite knowledge.
目次
Preface.- Introduction to Differentiable Functions.- Level Sets and Tangent Spaces.- Lagrange Multipliers.- Maxima and Minima on Open Sets.- Curves in bbR.- Line Integrals.- The Frenet-Serret Equations.- Geometry of Curves in bbR.- Double Integration.- Parametrized Surfaces in bbR.- Surface Area.- Surface Integrals.- Stokes' Theorem.- Triple Integration.- Divergence Theorem.- Geometry of Surfaces bbR.- Gaussian Curvature.- Geodesic Curvature.- Solutions.- Index.
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