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浪漫地理學(xué):追尋崇高景觀
多變量數(shù)學(xué)入門(英文) 版權(quán)信息
- ISBN:9787560394329
- 條形碼:9787560394329 ; 978-7-5603-9432-9
- 裝幀:一般膠版紙
- 冊數(shù):暫無
- 重量:暫無
- 所屬分類:>
多變量數(shù)學(xué)入門(英文) 內(nèi)容簡介
本書共包括四章,**章內(nèi)容圍繞線性代數(shù)展開,具體包括子空間與向量的線性相關(guān)、高斯消元法和線性相關(guān)引理、矩陣、秩和秩零化度定理、正交補和正交投影、矩陣的行階梯形和非齊次方程組等;第二章為歐幾里得空間中的分析學(xué),具體包括歐幾里得空間中的開集和閉集、可微性等;第三章主題為線性代數(shù),包括排列、行列式、方陣的逆矩陣、計算逆、標(biāo)準(zhǔn)正交基和克萊姆-施密特、線性變換的矩陣表示以及特征值和譜定理;第四章是分析學(xué)的內(nèi)容,介紹了壓縮映射原理、反函數(shù)定理以及隱函數(shù)定理。
多變量數(shù)學(xué)入門(英文) 目錄
Contents
Preface
1 Linear Algebra
1 Vectors in Rn
2 Dot product and angle between vectors in Rn
3 Subspaces and linear dependence of vectors
4 Gaussian Elimination and the Linear Dependence Lemma
5 The Basis Theorem
6 Matrices
7 Rank and the Rank-Nullity Theorem
8 Orthogonal complements and orthogonal projection
9 Row Echelon Form of a Matrix
10 Inhomogeneous systems
2 Analysis in Rn
1 Open and closed sets in Euclidean Space
2 Bolzano-Weierstrass, Limits and Continuity in Rn
3 Differentiability
4 Directional Derivatives, Partial Derivatives, and Gradient
5 Chain Rule
6 Higher-order partial derivatives
7 Second derivative test for extrema of multivariable function
8 Curves in Rn
9 Submanifolds of Rn and tangential gradients
3 More I,inear Algebra
1 Permutations
2 Determinants
3 Inverse of a Square Matrix
4 Computing the Inverse
5 Orthonormal Basis and Gram-Schmidt
6 Matrix Representations of Linear Transformations
7 Eigenvalues and the Spectral Theorem
4 More Analysis in Rn
1 Contraction Mapping Principle
2 Inverse Function Theorem
3 Implicit Function Theorem
A Introductory Lectures on Real Analysis
Lecture 1: The Real Numbers
Lecture 2: Sequences of Real Numbers and the Bolzano-Weierstrass Theorem
Lecture 3: Continuous Functions
Lecture 4: Series of Real Numbers
Lecture 5: Power Series
Lecture 6: Taylor Series Representations
Lecture 7: Complex Series, Products of Series, and Complex Exponential Series
Lecture 8: Fourier Series
Lecture 9: Pointwise Convergence of Trigonometric Fourier Series
Index
編輯手記
Preface
1 Linear Algebra
1 Vectors in Rn
2 Dot product and angle between vectors in Rn
3 Subspaces and linear dependence of vectors
4 Gaussian Elimination and the Linear Dependence Lemma
5 The Basis Theorem
6 Matrices
7 Rank and the Rank-Nullity Theorem
8 Orthogonal complements and orthogonal projection
9 Row Echelon Form of a Matrix
10 Inhomogeneous systems
2 Analysis in Rn
1 Open and closed sets in Euclidean Space
2 Bolzano-Weierstrass, Limits and Continuity in Rn
3 Differentiability
4 Directional Derivatives, Partial Derivatives, and Gradient
5 Chain Rule
6 Higher-order partial derivatives
7 Second derivative test for extrema of multivariable function
8 Curves in Rn
9 Submanifolds of Rn and tangential gradients
3 More I,inear Algebra
1 Permutations
2 Determinants
3 Inverse of a Square Matrix
4 Computing the Inverse
5 Orthonormal Basis and Gram-Schmidt
6 Matrix Representations of Linear Transformations
7 Eigenvalues and the Spectral Theorem
4 More Analysis in Rn
1 Contraction Mapping Principle
2 Inverse Function Theorem
3 Implicit Function Theorem
A Introductory Lectures on Real Analysis
Lecture 1: The Real Numbers
Lecture 2: Sequences of Real Numbers and the Bolzano-Weierstrass Theorem
Lecture 3: Continuous Functions
Lecture 4: Series of Real Numbers
Lecture 5: Power Series
Lecture 6: Taylor Series Representations
Lecture 7: Complex Series, Products of Series, and Complex Exponential Series
Lecture 8: Fourier Series
Lecture 9: Pointwise Convergence of Trigonometric Fourier Series
Index
編輯手記
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