Lecture: Derivatives - Summary

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Из курса от партнера University of London

Quantitative Foundations for International Business

156 оценки

University of London

Quantitative Foundations for International Business

156 оценки

Курс 3 из 6 — Specialization International Business Essentials

This course provides the essential mathematics required to succeed in the finance and economics related modules of the Global MBA, including equations, functions, derivatives, and matrices. You can test your understanding with quizzes and worksheets, while more advanced content will be available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

Из урока

Derivatives

An important topic in many scientific disciplines- including economics- is the study of how quickly quantities change. The concept used to describe the rate of change of a function is known as the derivative. In this lecture, we will define the derivative of a function, and share some of the important rules for calculating it.

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George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

Equations and functions are clearly related to change in one variable

when another variable or other variables change.

This week dealt with this concept in detail

by introducing the concept of a derivative.

This is a crucial topic in many scientific disciplines,

including finance, business, and economics.

We want to know either how much the variable costs change if the inputs

change or how much revenue changes if production level changes or

how much consumption changes if income changes.

Or how quickly some or even all of these quantities change over time.

For computing the future position of a planet in space, or to predict the growth

in population of a species, or to calculate how the demand for

a commodity changes if the population changes, or finally,

how much capital we will have to repay because of interest payment.

We need information about rates of change, all variables and functions.

So this week, we have defined the concept of the derivative

as the rate of change of a function.

The week has been focused on the basic definition of the derivative, and

we have been giving the geometrical interpretation for this concept.

This representation is very intuitive.

And it gives insights on why.

When we started the graph of a function, we would like to have a precise

measure of its steepness at a given point in the graph.

From this graphical intuition of a derivative,

we have built the idea of incremental ratios.

And have been seeing the derivative can be seen

as the limit of this ratio in a given point of the function.

From this very general definition of a derivative,

we have presented some important rules for calculating derivatives.

And we have shown how to compute the derivatives of a function.

In more detail, we went through rules of differentiation,

such as the product rule and the quotient rule and the chain and power rules.

We also focused on the idea of calculating the derivative

to measure the rate of change of a variable or a function.

Finally, we introduced the concept of higher order derivatives and

presented all of these concepts using some examples.

These examples have been taken from business, economics, and finance.

Through these examples, we saw in detail how to interpret the derivative and

why it became a mathematical tool of crucial importance to the development of

modern modelling for finance and economics.

Up to this point, the material presented has dealt with mathematical models but

have a relatively low number of variables and functions.

The next week, we'll present a tool that allows

a generalization of the concepts we have been presenting so far.

Thank you very much.

[MUSIC]

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