Rates of change calculus pdf introduction

Calculus i or needing a refresher in some of the early topics in calculus. Instead here is a list of links note that these will only be active links in the web. Rates of change application of rates of change to get a better approximation, lets zoom in on the graph and move point q towards point p at intervals of 0. The right way to begin a calculus book is with calculus. As noted in the text for this section the purpose of this section is only to remind you of certain types of applications that were discussed in the previous chapter.

For example, if you own a motor car you might be interested in how much a change in the amount of fuel used a. Below is a walkthrough for the test prep questions. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the. Pdf produced by some word processors for output purposes only. Introduction to rates of change mit opencourseware. Today well see how to interpret the derivative as a rate of change, clarify the idea of a limit, and use this notion of limit to describe continuity a property functions need. Introduction to differential calculus the university of sydney. Rates of change the point of this section is to remind us of the. These concepts are also referred to as the average rate of change and the instantaneous rate of change. Rates of change 1 introduction 2 key issues and common. Calculus rates of change aim to explain the concept of rates of change. Other rates of change may not have special names like fuel consumption or velocity, but are nonetheless important.

Calculus table of contents calculus i, first semester chapter 1. As such there arent any problems written for this section. Despite the fact that these are my class notes they. Understand that the instantaneous rate of change is given by the average rate of change over the shortest possible interval and that this is calculated using the limit of the average rate of change as the interval approaches zero. Recognise the notation associated with differentiation e. You will see what the questions are, and you will see an important part of the answer. Learning outcomes at the end of this section you will. This calculus video tutorial provides a basic introduction into related rates. Here are my online notes for my calculus i course that i teach here at lamar university. These few pages are no substitute for the manual that comes with a calculator.

Derivatives and rates of change in this section we return. It explains how to use implicit differentiation to find dydt and dxdt. There are plenty of good things left for the other chapters, so why not get started. If y fx, then fx is the rate of change of y with respect to x. Definition when fx is defined in an open interval containing a, the tangent line to the curve y fx at the point. The problems are sorted by topic and most of them are accompanied with hints or solutions. If the dependence of p jx on x is not linear, we can still introduce the notion of the average. Try them on your own first, then watch if you need help. Module c6 describing change an introduction to differential calculus. Today well see how to interpret the derivative as a rate of change, clarify the idea of a limit, and use this notion of limit to describe continuity a property functions need to have in order for us to work with them. Its easy to determine the gradient or rate of change of a function if it is a linear. This chapter will jump directly into the two problems that the subject was invented to solve. The definition of derivative, in chapter 1, is presented in the context of a discussion of average rates of change see p. Calculus, known in early history as infinitesimal calculus, is based on finding limits to determine the rates of change of functions.