Advanced Calculus of Several Variables
Modern conceptual treatment of multivariable calculus, emphasizing interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. Over 400 well-chosen problems. 1973 edition.
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61 function 61 mapping absolutely integrable approximation ball boundary bounded calculus chain rule column vectors compute contented set continuous function converges coordinate patch Corollary critical point curve deﬁned deﬁnition denote differentiable function differential form divergence theorem dx dy equation Example Exercise exists f and g Figure ﬁnd ﬁnite ﬁrst following theorem function f given gives graph Green’s theorem Hint implies inﬁnite inverse k-dimensional k-form Lemma Let f linear mapping linearly independent mapping f matrix maximum mean value theorem multiplication neighborhood nice region normed vector space notation obtain one-to-one open set open subset oriented 2-cells orthogonal partial derivatives path positive-deﬁnite problem proof of Theorem prove quadratic form real numbers real-valued functions satisﬁes Section sequence single-variable smooth k-manifold subset of Q subspace of Q Suppose tangent plane Taylor polynomial Theorem 5.4 variables vector ﬁeld vectors v1 veriﬁed zero