An introduction to mathematics for economics by Akihito Asano

By Akihito Asano

''An advent to arithmetic for Economics introduces quantitative ways to scholars of economics and finance in a succinct and obtainable sort. The introductory nature of this textbook capacity a heritage in economics isn't crucial, because it goals to assist scholars savour that studying arithmetic is appropriate to their total figuring out of the topic. financial and monetary functions are defined in Read more...

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You can easily see from this expression that it is ‘a half of 2’, where it is 2 2 1 hard to observe something meaningful from the expression √ , which contains a square 2 √ 1 2 root on the denominator. The expressions √ and are value-wise identical, but in 2 2 order to facilitate communication, we tend to use a more intuitively appealing expression. √ Since we convert an irrational number on the denominator ( 2) into a rational number (2), we call this procedure rationalisation of the denominator.

2 = Therefore x = 1 ± −(−2) ± Solving a quadratic equation that has two complex roots. 22 Basic mathematics The above three examples are related to the quadratic functions we will see in the next section. 9 Functions A variable y is said to be a function of another variable x if there is a rule that associates with each possible value of x exactly one value y. For example, we can express the rule that has to hold regarding the temperature in Centigrade (x) and the temperature in Fahrenheit (y) as the following: 9 x + 32.

18 Basic mathematics What is ‘some polynomial expression’ in the above brackets? We know that the highest power x is raised to in that expression is 2, because the product of it and x − 1 must be 2x 3 − x 2 − 2x + 1, which contains an x 3 term. Hence let us denote that polynomial expression as ax 2 + bx + c: 2x 3 − x 2 − 2x + 1 = (x − 1)(ax 2 + bx + c). If we expand the right hand side (RHS) of this equation, we have: (x − 1)(ax 2 + bx + c) = ax 3 + (b − a)x 2 + (c − b)x − c. Now compare ax 3 + (b − a)x 2 + (c − b)x − c with 2x 3 − x 2 − 2x + 1, which need to be equal.

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