1.2 Chemical elements Atoms of the same atomic number behave virtually identically in chemical reactions. They are therefore given the same chemical name and chemical symbol. For example, the atom of atomic number 6, which is shown in Figure 1, is a carbon atom, whose symbol is C. All materials are made of atoms, but there is a special class of substan
Introduction This unit is an adapted extract from the course The molecular world
(S205) This unit will provide you with a detailed understanding of some of the important problems and topics that are being studied by the chemists of today, and of the ways in which associated problems might be solved by chemical methods. But to acquire this understanding you must have a good grasp of fundamental chemic
4.1 Overview One of the most surprising aspects of quantum physics is the ability of particles to pass through regions that they are classically forbidden from entering. This is the phenomenon of quantum-mechanical tunnelling that was mentioned in Session 1. In Session 4 we first demonstrate the phenomenon of tunnelling with the ai
2.1 Overview Session 2 discusses the scattering of a particle using wave packets. We shall restrict attention to one dimension and suppose that the incident particle is initially free, described by a wave packet of the form This is a superposition of de Broglie waves, with the function
Learning outcomes By the end of this unit you should be able to: explain the meanings of the emboldened terms and use them appropriately; describe the behaviour of wave packets when they encounter potential energy steps, barriers and wells; describe how stationary-state solutions of the Schrödinger equation can be used to analyse scattering and tunnelling; for a range of simple potential energy functions, obtain the solution of the time-independent Sc
4.3 Education, education, education We have already listed some of the main modifiable risk factors, such as smoking and excessive alcohol consumption. Question: Try to recall two ot 1.3.1 Who is affected by cardiovascular diseases? Cardiovascular diseases are the main cause of premature death (before the age of 75) in the UK, across Europe and the USA – indeed, across many parts of the world (Figures 3 and Author(s): 2.5 Expressing probability According to Equation 1, probability is defined as a fraction. However a fraction such as  Complex numbers Numbers Interpreting data: Boxplots and tables Surfaces 5.3 Powers Having discussed nth roots, we are now in a position to define the expression ax, where a is positive and x is a rational power (or exponent). If a > 0, m Introduction This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics.
In order to complete this unit you will need 6 Solutions to the exercises Section 6 contains solutions to the exercises that appear throughout sections 1-5. Click 'View document' below to open the solutions (15 pages, 468KB). Acknowledgements All written material contained within this unit originated at the Open University. Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence 1. Join the 200,000 students currently studyi 3.2.1 Try some yourself 1 Use the method outlined in Example 9 to estimate each of the following, and then use yo 2.2.1 Try some yourself 1 Find the following powers by hand, as estimates for calculator work. (a) 107 (b) 108 (c) 34 (d) (−2)2 1.3 Square roots Given any number, you now know how to find its square. But, given the squared number, how do you find the original number? If the gardener in Author(s): Learning outcomes By the end of this unit you should be able to: evaluate the squares, cubes and other powers of positive and negative numbers with or without your calculator; estimate square roots and calculate them using your calculator; describe the power notation for expressing numbers; use your calculator to find powers of numbers; multiply and divide powers of the same number; understand and apply negative powers, t
SAQ 1.2
may also be expressed as a decimal number or as a percentage:
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.Author(s):
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property. First published on Wed, 2
This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. Boxplots can also be useful for drawing attention to possible outliers in a dat
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces. First published on Thu, 18 Aug 2011 as <
Definition
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Example 3
