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