Differential Calculus of Multivariable Functions

This chapter focuses on differential calculus of multivariable functions. We generalize the definition of differentiation to such functions. The limit and continuity in a point on a plane will be defined as we had in Chapter 4. The rules of differentiations of the functions which are introduced in Chapter 5, can also be used for multivariable functions with the difference that we call them partial derivatives. After definition of degree for homogeneity the Euler's Theorem we found a relation between partial derivatives of a multi-valued function and degree of homogeneity. Several applications of partial differentiation will be given through this chapter. We mention that the Taylor's formula for single-valued function can also be generalized to multi-valued functions.