目录 Preface and Acknowledgments Notations 1 Basic Features of Euclidean Space, Rn 1.1 Real numbers 1.1.1 Convergence of sequences of real numbers 1.2 Rn as a vector space 1.3 Rn as an inner product space 1.3.1 The inner product and norm in Rn 1.3.2 Orthogonality 1.3.3 The cross product in R3 1.4 Rn as a metric space 1.5 Convergence of sequences in Rn 1.6 Compactness 1.7 Equivalent norms (*) 1.8 Solved problems for Chapter 1 2 Functions on Euclidean Spaces 2.1 Functions from Rn to Rm 2.2 Limits of functions 2.3 Continuous functions 2.4 Linear transformations 2.5 Continuous functions on compact sets 2.6 Connectedness and convexity 2.6.1 Connectedness 2.6.2 Path-connectedness 2.6.3 Convex sets 2.7 Solved problems for Chapter 2 3 Differential Calculus in Several Variables 3.1 Differentiable functions 3.2 Partial and directional derivatives, tangent space 3.3 Homogeneous functions and Euler's equation 3.4 The mean value theorem 3.5 Higher order derivatives 3.5.1 The second derivative 3.6 Taylor's theorem 3.6.1 Taylor's theorem in one variable 3.6.2 Taylor's theorem in several variables 3.7 Maxima and minima in several variables 3.7.1 Local extrema for functions in several variables 3.7.2 Degenerate critical points 3.8 The inverse and implicit function theorems 3.8.1 The Inverse Function theorem 3.8.2 The Implicit Function theorem 3.9 Constrained extrema, Lagrange multipliers 3.9.1 Applications to economics 3.10 Functional dependence 3.11 Morse's leInma (*) 3.12 Solved problems for Chapter 3 4 Integral Calculus in Several Variables 4.1 The integral in Rn 4.1.1 Darboux sums. Integrability condition
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