2.4 Bracket keys A way of forcing a calculator to perform a calculation in a different order to that given in Section 2.3 is to use the bracket keys. For example the following sequence, on a scientific or graphics calculator: 7
2
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2.3 Some calculator conventions Your calculator will interpret the order in which you press the keys, in a particular way. For example if you press the key sequence: 2
3
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Points to note Here are a few points from the Exercise 1: The negative or minus sign for the answer −2 maybe slightly smaller and higher than the one used for subtraction in 5 − 7. There maybe two minus keys on your calculator keypad, as there are on the TI-84. The one which means do the operation subtract is
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1.3 Home screen Some calculators, like the TI-84, provide you with several different screens for menus, drawing graphs, writing programs and so on. The most important screen, where calculations are carried out, is called the Home Screen. If you should find yourself trapped on another screen, the ‘panic’ buttons to return ‘home’ are usually one or other of the following: Author(s): 1.1 Setting up your scientific or graphics calculator First have a look at your calculator keyboard. Some of the main features are described below. The screen (also called the display) is at the top. This is where calculations and so on are displayed. The remainder of the calculator, where the various keys are located, is called the keyboard. The number keys are usually in the bottom part of the keyboard and there are also the four operation keys: Author(s): 3.1 Spotlight on study As you have been working through this unit, have you thought about how you are studying, and what this process involves? Do you feel confident or concerned about whether you will be able to learn mathematics and use it in the future? Put your study methods under the spotlight now, before moving on with your studies. Learning rarely happens passively. A number of aspects of this unit have been designed to encourage your more active participation and involvement. However, even that Introduction This unit lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit – Modelling static problems – considers why objects stay put.
Please note that this unit assumes you have a good working knowledge of vectors. This is an adapted extract from the Open University course Author(s): Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is used under licence. All materials included in this unit are derived from content originated at the Open University. 1 Using vectors to model The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Click 'View document' to open the workbook (PDF, 1 MB). Learning outcomes After studying this unit you should: know some basic definitions and terminology associated with scalars and vectors and how to represent vectors in two dimensions; understand how vectors can be represented in three (or more) dimensions and know both plane polar and Cartesian representations; know ways to operate on and combine vectors. Introduction This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane. This is an adapted extract from the Open University course Mathematical methods and models (MST209) Learning outcomes After studying this unit you should: be able to solve homogeneous second-order equations; know a general method for constructing solutions to inhomogeneous linear constant-coefficient second-order equations; know about initial and boundary conditions to obtain particular values of constants in the general solution of second-order differential equations. Introduction This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers. This unit is an adapted extract from the course Author(s): Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is used under licence. All materials included in this unit are derived from content originated at the Open University. Learning outcomes After studying this unit you should be able to: understand how the wave and diffusion partial differential equations can be used to model certain systems; determine appropriate simple boundary and initial conditions for such models; find families of solutions for the wave equation, damped wave equation, diffusion equation and similar homogeneous linear second-order partial differential equations, subject to simple boundary conditions, using the meth Learning outcomes During this unit you will: learn some basic definitions and terminology associated with differential equations and their solutions; be able to visualize the direction field associated with a first-order differential equation and be able to use a numerical method of solution known as Euler's method; be able to use analytical methods of solution by direct integration; separation of variables; and the integrating factor method. First-order differential equations This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration. This unit is an adapted extract from the course Mathematical methods and Acknowledgements All materials included in this unit are derived from content originated at the Open University. 1.5 Exercises A vector a has magnitude
|a|Â =Â 7 and direction
θ = −70°.
Calculate the component form of a, giving the components
correct to two decimal places. 1.4.3 Velocity Another vector quantity which crops up frequently in
applied mathematics is velocity. In everyday English, the
words ‘speed’ and
‘velocity’ mean much the same as each other,
but in scientific parlance there is a significant difference between
them.
Exercise 1
Velocity and speed
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