Advanced Calculus: A Course in Mathematical Analysis
Advanced Calculus: A Course in Mathematical Analysis
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发表时间：
1995-08
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通讯作者：
P. Fitzpatrick
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作者：
P. Fitzpatrick
真实的数字。序列的连续函数与极限分化作为微分方程解的初等函数。一体化第二基本定理及其结果泰勒多项式的近似。序列的收敛性和函数的级数。欧几里得空间连续性、紧密性和连通性。度量空间多元实值函数的偏微分性。实值函数的局部逼近。用线性映射逼近非线性映射。图像与逆：反函数定理。隐函数定理及其应用。多元函数的积分。
Real Numbers. Sequences. Continuous Functions And Limits. Differentiation. The Elementary Functions As Solutions Of Differential Equations. Integration. The Second Fundamental Theorem And Its Consequences. Approximation By Taylor Polynomials. The Convergence Of Sequences And Series Of Functions. The Euclidian Space. Continuity, Compactness And Connectedness. Metric Spaces. Partial Differentiability Of Real-Valued Functions Of Several Variables. Local Approximation Of Real-Valued Functions. Approximating Nonlinear Mappings By Linear Mappings. Images And Inverses: The Inverse Function Theorem. The Implicit Function Theorem And Its Applications. Integration For Functions Of Several Variables.