Author | Craven, B. D. author |
---|---|
Title | Functions of several variables [electronic resource] / by B. D. Craven |
Imprint | Dordrecht : Springer Netherlands, 1981 |
Connect to | http://dx.doi.org/10.1007/978-94-010-9347-7 |
Descript | VIII, 138 p. online resource |
1. Differentiable Functions -- 1.1 Introduction -- 1.2 Linear part of a function -- 1.3 Vector viewpoint -- 1.4 Directional derivative -- 1.5 Tangent plane to a surface -- 1.6 Vector functions -- 1.7 Functions of functions -- 2. Chain Rule and Inverse Function Theorem -- 2.1 Norms -- 2.2 Frรฉchet derivatives -- 2.3 Chain rule -- 2.4 Inverse function theorem -- 2.5 Implicit functions -- 2.6 Functional dependence -- 2.7 Higher derivatives -- 3. Maxima and Minima -- 3.1 Extrema and stationary points -- 3.2 Constrained minima and Lagrange multipliers -- 3.3 Discriminating constrained stationary points -- 3.4 Inequality constraints -- 3.5 Discriminating maxima and minima with inequality constraints 62 Further reading -- 4. Integrating Functions of Several Variables -- 4.1 Basic ideas of integration -- 4.2 Double integrals -- 4.3 Length, area and volume -- 4.4 Integrals over curves and surfaces -- 4.5 Differential forms -- 4.6 Stokesโs theorem -- Further reading -- Appendices -- A. Background required in linear algebra and elementary calculus -- B. Compact sets, continuous functions and partitions of unity -- C. Answers to selected exercises -- Index (including table of some special symbols)