Chapter 2 - Univariate and multivariate calculus

Abstract

This chapter introduces the essential techniques for the numerical standard calculus that will be used throughout the whole book. It represents therefore the basis, to understand the way the static optimization in Part II, the dynamic modeling, as well as the dynamic optimization in Part III have been applied with Excel. This chapter will try to execute and grasp with Excel the geometric interpretation of the differentiation and integration, so that the way calculus is applied to economics will be somehow easier to understand. This chapter has been divided into numerical differentiation, partial differentiation, and numerical integration. The last paragraph describes some applications to economics, even though the whole book will be covering examples where the univariate and multivariate calculus is applied. The univariate and multivariate calculus has a vast range of applications in economics and essentially the whole book is going to apply, one way or another, all that has been discussed within this chapter. Chapter 4, dedicated to the differential equations, uses the similar techniques for the numerical integration. We will see again the differential calculus to find the extreme points of a function, within Chapter 5, dedicated to the optimization techniques for univariate and multivariate functions. Chapter 6 will show all these concepts applied to the theory of microeconomics. In Part II of the book, within the calculus of variations and the optimal control theory, we will always resort to numerical differentials and numerical integration, in a context of finding an optimizing function, also called the optimal path or optimal trajectory.