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 Fréchet 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 Stokes's 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). Language: English