Advanced Calculus of Several Variables
Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.
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2ero absolutely integrable approximation ball boundary bounded calculus cellulation chain rule column vectors compute contented set continuous function continuously differentiable converges coordinate patch Corollary critical point curve defined definition denote differentiable function differential form dimensional equation Euler-Lagrange equation Example Exercise exists fact Figure following theorem fundamental theorem generali2ation given gives graph Green's theorem Hint implicit mapping theorem implies inductively inner product inverse Lemma limit point linear mapping linearly independent matrix maximum mean value theorem minimum value multiplication n x n n-dimensional neighborhood nice region normed vector space notation obtain one-to-one open set open subset oriented 2-cell orthogonal partial derivatives path problem PROOF Let proof of Theorem prove quadratic form real numbers real-valued functions Section sequence single-variable smooth manifold Stokes subspace Suppose tangent plane Theorem 5.4 variables vector field verify