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內容簡介

　　Calculus of real-valued functions of several real variables， also known as multivariable calculus， is a rich and fascinating subject. On the one hand， it seeks to extend eminently useful and immensely successful notions in one-variable calculus such as limit， continLuty， derivative， and integral to "higher dimensions." On the other hand， the fact that there is much more room to move about in the 'n space Rn than on the real line R brings to the fore deeper geometric and topological notions that play a significant role in the study of functions of two or more variables.

內頁插圖

目錄

1Vectors and Functions
1.1 Preliminaries
Algebraic Operations
Order Properties
Intervals, Disks, and Bounded Sets
Line Segments and Paths
1.2 Functions and Their Geometric Properties
Basic Notions
Bounded Functions
Monotonicity and Bimonotonicity
Functions of Bounded Variation
Functions of Bounded Bivariation
Convexity and Concavity
Local Extrema and Saddle Points
Intermediate Value Property
1.3 Cylindricaj and Spherical Coordinates
Cylindrical Coordinates
Spherical Coordinates
Notes and Comments
Exercises

2 Sequences, Continuity, and Limits
2.1 Sequences in R2
, Subsequences and Cauchy Sequences
Closure, Boundary, and Interior
2.2 Continuity
Composition of Continuous Functions
Piecing Continuous Functions on Overlapping Subsets
Characterizations of Continuity
Continuity and Boundedness
Continuity and Monotonicity
Continuity, Bounded Variation, and Bounded Bivariation
Continuity and Convexity
Continuity and Intermediate Value Property
Uniform Continuity
Implicit Function Theorem
2.3 Limits
Limits and Continuity
Limit from a Quadrant
Approaching Infinity
Notes and Comments
Exercises

3 Partial and Total Differentiation
3.1 Partial and Directional Derivatives
Partial Derivatives
Directional Derivatives
Higher-Order Partial Derivatives
Higher-Order Directional Derivatives
3.2 Differentiability
Differentiability and Directional Derivatives
Implicit Differentiation
3.3 Taylor's Theorem and Chain Rule
Bivariate Taylor Theorem
Chain Rule
3.4 Monotonicity and Convexity
Monotonicity and First Partials
Bimonotonicity and Mixed Partials
Bounded Variation and Boundedness of First Partials
Bounded Bivariation and Boundedness of Mixed Partials
Convexity and Monotonicity of Gradient
Convexity and Nonnegativity of Hessian
3.5 Functions of Three Variables. ,
Extensions and Analogues
Tangent Planes and Normal Lines to Surfaces
Convexity and Ternary Quadratic Forms
Notes and Comments
Exercises

4 Applications of Partial Differentiation
4.1 Absolute Extrema
Boundary Points and Critical Points
4.2 Constrained Extrema
Lagrange Multiplier Method
Case of Three Variables
4.3 Local Extrema and Saddle Points
……
5 Multiple Integration
6 Applications and Approximations of Multiple Integrals
7Double Series and Improper Double Integrals
References
List of Symbols and Abbreviations
Index

前言/序言

經典數學叢書（影印版）：多元微積分教程 [A Course in Multivariable Calculus and Analysis] 下載 mobi epub pdf txt 電子書

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評分☆☆☆☆☆

joli

評分☆☆☆☆☆

學習微積分的好教材，多看數學，養生~~

評分☆☆☆☆☆

學習微積分的好教材，多看數學，養生~~

評分☆☆☆☆☆

joli

評分☆☆☆☆☆

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評分☆☆☆☆☆

我為什麼喜歡在京東買東西，因為今天買明天就可以送到。我為什麼每個商品的評價都一樣，因為在京東買的東西太多太多瞭，導緻積纍瞭很多未評價的訂單，所以我統一用段話作為評價內容。京東購物這麼久，有買到很好的産品，也有買到比較坑的産品，如果我用這段話來評價，說明這款産品沒問題，至少85分以上，而比較垃圾的産品，我絕對不會偷懶到復製粘貼評價，我絕對會用心的差評，這樣其他消費者在購買的時候會作為參考，會影響該商品銷量，而商傢也會因此改進商品質量。

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