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Introduction to differentiation
This free course is an introduction to differentiation. Section 1 looks at gradients of graphs and introduces differentiation from first principles. Section 2 looks at finding derivatives of simple functions. Section 3 introduces rates of change by looking at real life situations. Section 4 looks at using the derivative of a function to deduce useful facts for sketching its graph. Section 5 covers the second derivative test, used to determine the nature of stationary points and ends by looking a
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2.4 Homeomorphic surfaces

As we stated in Section 1, our aim is to classify surfaces up to homeomorphism. So it is worthwhile spending a little time examining what sorts of transformations of surfaces are homeomorphisms. We shall restrict the description to surfaces in space, as these are easier to deal with, though the result at the end of this subsection applies to all surfaces.

Recall that a homeomorphism between two topological spaces (such as surfaces in space) is a bijection with the property that b
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2.3.6 Torus with 1 hole

We need not restrict ourselves to rectangles: we can also build surfaces by identifying edges of other polygons. For example, if we start with a pentagon and identify two pairs of its edges as shown in Figure 33, what do we get? Identifying the edges labelled a and c in the directions indicated, we obtain a cylinder with
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Téléinformatique. T1, Bases techniques pour les réseaux ( diapos )
Sommaire : Page d'accueil - Communiquer - Informatique - Télécommunications - Télématique et téléinformatique - Portée des réseaux - réseaux académiques - Réseaux du département informatique de l' INSA - Cours IF - Les métiers - Bases techniques pour les réseaux - Bibliogr. - Spécifications opérationnelles , fonctionnelles - Architecture des logiciels de communications - Modèle de référence OSI - Services application OSI - Services - Fonctionnement du modèle de référence -
Author(s): Beuchot, Gerard

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Electronique internet . Cette ressource est la propriété de ses auteurs et de l'INSA de Lyon.

2.3.3 Torus

Let us now return to the cylinder we obtained in Figure 27. What happens if we bend it around and glue the two ends? Now, continuing with our idea of identifying edges of our original rectangle, we want to bend the cylinder round and glue its ends in such a way that the points A and B are identified. Furthermore, bending
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2.2.3 Surfaces with boundary

Examples of surfaces with boundary are a cylinder and a Möbius band. Other examples are the following:

Surfaces with holes

We can obtain a surface with boundary by taking any surface without boundary and punching some holes in it by removing open discs. For example, Figure 19 shows a sphere with 3 holes. The boun
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2.2.2 Hollow tubing surfaces

In their doughnut-shaped representation, toruses can be thought of as being hollow tubes. Many other surfaces in space can also be drawn as if they were made of hollow tubing. Figure 15 shows two such examples.

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2.2.1 Surfaces without boundary

Examples of surfaces without boundary are a sphere and a torus. Other examples are the following:

n-fold toruses

Figure 13 depicts a 2-fold torus and a 3-fold torus, with two and three rings respectively. An n-fold torus, for any positive integer n has n rings. (A 1-fold torus is
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3.3 What can genres do for you?

Think of it like this: each genre novel suggests certain char
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Learning outcomes

After studying this course, you should be able to:

  • identify strengths and weaknesses as a writer of fiction

  • demonstrate a general awareness of fiction writing

  • discuss fiction using basic vocabulary.


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Asset allocation in investment
This course looks at how to take investor objectives and constraints and turn them into a portfolio which aims at achieving an expected return and level of risk appropriate for the investor. In this free course, Asset allocation in investment, portfolio optimisation techniques such as portfolio theory can be used to determine how much of an investor’s portfolio to put in each asset class. Portfolio theory can also be used to determine so-called model portfolios which offer optimised benchmarks
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Learning outcomes

After studying this course, you should be able to:

  • list the skills and knowledge needed to conduct full and fair recruitment and selection

  • undertake full and fair recruitment and selection systematically.


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Population ageing: a global health crisis?
This free course, Population ageing: a global health crisis?, focuses on two major issues of our time – ageing societies and global health. It provides you with an introduction to ageing societies and their implications for global health – implications which are only just beginning to be fully understood. The course will help you to deepen your understanding of ageing societies across the globe and the different components of the concept of global health. You will also explore the ways in wh
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Digital forensics
Digital evidence features in just about every part of our personal and business lives. Legal and business decisions hinge on having timely data about what people have actually done. This free course, Digital forensics, is an introduction to computer forensics and investigation, and provides a taster in understanding how to conduct investigations to correctly gather, analyse and present digital evidence to both business and legal audiences. It also outlines the tools to locate and analyse digital
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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to c
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4.3 IP over ATM

You have seen that the IP protocol supports a connectionless service, and the ATM and TCP protocols support a connection-oriented service.

SAQ 8 (Revision)

What are the relative advantages and disadvantages of connect
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4.2 ATM layers

In this section I shall briefly review some of the main functions of the ATM layers but I shall not go into too much detail because at this stage we are interested in only the general points about protocols.


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3.4 Transmission control protocol (TCP)

As I outlined in the previous section, peer entities in clients and servers exchange HTTP protocol data units when they wish to transfer a resource over the web. I gave very little detail about this because I wanted to focus on the general features of protocols in the application layer of the TCP/IP model. The HTTP protocol data units are transferred from the sender host to the receiver host by calling on the services of the transport layer. In the case we are considering, the transport layer
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7.1 Introduction

Earlier on I indicated that in order for a processor to perform a defined function it needs to be supplied with a list of instructions called a program. In this section I shall explore this idea a little further.

Software can be split into two categories, application software and operating systems. Application software is the name given to programs which enable a computer to perform specific tasks. The program that processes the image in the digital camera is one example; a word
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Learning outcomes

After studying this course, you should be able to:

  • understand what all the terms highlighted in bold in the text mean

  • understand the fundamental hardware components that make up a computer’s hardware and the role of each of these components

  • understand the difference between an operating system and an application program, and what each is used for in a computer

  • describe some examples of computers and state the effect that the use of
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