Partial Differentiation Second EditionPDF电子书下载

CHAPTER Ⅰ PARTIAL DERIVATIVES 1

1．Functions of Two Variables 1

2．Functions of Three or More Variables 6

3．Higher Partial Derivatives 8

CHAPTER Ⅱ CHANGE OF VARIABLE IN PARTIAL DIFFERENTIATION 13

4．Total Derivatives 13

5．Second Derivatives 17

6．Derivatives in Any Direction 26

7．Euler＇s Theorems on Homogeneous Functions 28

8．Jacobians 31

9．Differentials 86

10．Functional Dependence 43

11．Problems on Change of Variable 46

Examples 50

CHAPTER Ⅲ TAYLOR＇S THEOREM AND GEOMETRICAL APPLICATIONS 57

12．Taylor＇s Theorem for a Function of Several Variables 57

13．Applications to the Theory of Plane Curves 61

14．Applications to Curves and Surfaces in Space 68

15．Curvilinear Coordinates 73

16．Vectors 76

CHAPTER Ⅳ MAXIMA AND MINIMA 80

17．Functions of a Single Variable 80

18．Functions of Two Variables 81

19．Functions of n Variables 88

20．Lagrange＇s Method of Undetermined Multipliers 89

Examples 101

APPENDIX IMPLICIT FUNCTIONS 104

Index 107