多元微積分教程

《多元微積分教程》是2014年世界圖書出版公司出版的著作，作者是[印] 戈培德（Ghorpade S.R.）。

基本介紹

• 書名：《多元微積分教程》
• 作者：[印]戈培德（Ghorpade S.R.）
• 出版社：世界圖書出版公司
• 出版時間：2014年05月01日
• ISBN：9787510075926 

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.

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