Author | Guzman, Alberto. author |
---|---|
Title | Derivatives and Integrals of Multivariable Functions [electronic resource] / by Alberto Guzman |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0035-2 |
Descript | X, 319 p. 30 illus. online resource |
1 Differentiability of Multivariate Functions -- 1.1 Differentiability -- 1.2 Derivatives and Partial Derivatives -- 1.3 The Chain Rule -- 1.4 Higher Derivatives -- 2 Derivatives of Scalar Functions -- 2.1 Directional Derivatives and the Gradient -- 2.2 The Mean Value Theorem -- 2.3 Extreme Values and the Derivative -- 2.4 Extreme Values and the Second Derivative -- 2.5 Implicit Scalar Functions -- 2.6 Curves, Surfaces, Tangents, and Normals -- 3 Derivatives of Vector Functions -- 3.1 Contractions -- 3.2 The Inverse Function Theorem -- 3.3 The Implicit Function Theorem -- 3.4 Lagrangeโs Method -- 4 Integrability of Multivariate Functions -- 4.1 Partitions -- 4.2 Integrability in a Box -- 4.3 Domains of Integrability -- 4.4 Integrability and Sets of Zero Volume -- 5 Integrals of Scalar Functions -- 5.1 Fubini's Theorem -- 5.2 Properties of Integrals -- 5.3 Change of Variable -- 5.4 Generalized Integrals -- 5.5 Line Integrals -- 5.6 Surface Integrals -- 6 Vector Integrals and the Vector-Field Theorems -- 6.1 Integrals of the Tangential and Normal Components -- 6.2 Path-Independence -- 6.3 On the Edge: The Theorems of Green and Stokes -- 6.4 Gauss's Theorem -- Solutions to Exercises -- References