多元微积分教程（英文 影印本）

多元微积分教程（英文 影印本）
出版时间：2014年版
丛编项： 经典数学丛书
内容简介
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.
目录
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