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Ebook Mathematics for economics and business (8th edition): Part 2

(BQ) Part 2 book "Mathematics for economics and business" has contents: Partial differentiation, integration, matrices, linear programming, dynamics, answers to problems. | www.downloadslide.com CHAPTER 5 Partial Differentiation This chapter continues the topic of calculus by describing how to differentiate functions of more than one variable. In many ways this chapter can be regarded as the climax of the whole book. It is the summit of the mathematical mountain that we have been merrily climbing. Not only are the associated mathematical ideas and techniques quite sophisticated, but also partial differentiation provides a rich source of applications. In one sense there is no new material presented here. If you know how to differentiate a function of one variable then you also know how to partially differentiate a function of several variables because the rules are the same. Similarly, if you can optimise a function of one variable then you need have no fear of unconstrained and constrained optimisation. Of course, if you cannot use the elementary rules of differentiation or cannot find the maximum and minimum values of a function as described in Chapter 4 then you really are fighting a lost cause. Under these circumstances you are best advised to omit this chapter entirely. There is no harm in doing this, because it does not form the prerequisite for any of the later topics. However, you will miss out on one of the most elegant and useful branches of mathematics. There are six sections. It is important that Sections 5.1 and 5.2 are read first, but the remaining sections can be studied in any order. Sections 5.1 and 5.2 follow the familiar pattern. We begin by looking at the mathematical techniques and then use them to determine marginal functions and elasticities. Section 5.3 describes the multiplier concept and completes the topic of national income determination which you studied in Chapter 1. The final three sections are devoted to optimisation. For functions of several variables, optimisation problems are split into two groups, unconstrained and constrained. Unconstrained problems, tackled in Section 5.4, involve the .