One Basic Material. - I Vectors. - II Differentiation of Vectors. - III Functions of Several Variables. - IV The Chain Rule and the Gradient. - Two Maxima Minima and Taylor's Formula. - V Maximum and Minimum. - VI Higher Derivatives. - Three Curve Integrals and Double Integrals. - VII Potential Functions. - VIII Curve Integrals. - IX Double Integrals. - X Green's Theorem. - Four Triple and Surface Integrals. - XI Triple Integrals. - XII Surface Integrals. - Five Mappings Inverse Mappings and Change of Variables Formula. - XIII Matrices. - XIV Linear Mappings. - XV Determinants. - XVI Applications to Functions of Several Variables. - XVII The Change of Variables Formula. - Appendix Fourier Series. - 1. General Scalar Products. - 2. Computation of Fourier Series. - Answers to Exercises. Language: English