Mathematical review_fall2009

Mathematical review_fall2009 - Mathematical review for...

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1 Mathematical review for ECO200 Microeconomic Theory * Familiarity with mathematics and especially calculus will allow you to understand better the economics concepts we will discuss during the course. In the past, people who took a calculus course before or during ECO200 enjoyed the material and performed better in term tests. I don’t expect you to be an expert in math, but I assume that you will know the basics. As a matter of fact, if you think that your level of math is outstanding, then I would recommend you to take ECO206 rather than ECO200. ECO206 is a calculus intensive version of ECO200. I expect, however, that your knowledge with the “basic level math” (as defined below) is proficient. I also expect that you are familiar with “medium level math” (as defined below). I do not expect you to be familiar with “advanced level math” material. The advanced level material will not be used during this course, but it might be useful in other courses. Having said that, independently of your current level of calculus, the TA or myself will explain in detail all you need to know to do very well in this course (*) Means “basic level” (**) Means “medium level” (***) Means “advanced level” * Thanks to Michael Bar for initially compiling this review.
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2 1. Sets (*) A set is any collection of elements. Examples: a. } 10 , 8 , 6 , 4 , 2 , 0 { = A - the set of even numbers between zero and 10. b. } , , { bule white red B = - the set of colors on the national flag. c. } 2 . 3 , | { = GPA feamale students M of U C - the set of U of M students that satisfy the conditions listed after the vertical bar. d. } | ) , {( 2 y x R y x D = = - the set of vectors in the two dimensional Euclidean space, such that the x-coordinate is equal to the y-coordinate. e. } , 1 0 , 1 0 | ) , {( 2 y x y x R y x E = - the set of vectors in the two dimensional Euclidean space such that both coordinates are between 0 and 1 and the x-coordinate is greater or equal to the y-coordinate. It is useful to illustrate this set graphically. The set E is colored blue. Cartesian product of A and B is sets the set of all ordered pairs such that the first element belongs to A and the second belongs to B. We denote the Cartesian product by B A × . Example: } 3 , 2 , 1 { = A , } 8 , 7 { = B , then )} 8 , 3 ( ), 7 , 3 ( ), 8 , 2 ( ), 7 , 2 ( ), 8 , 1 ( ), 7 , 1 {( = × B A . Convex sets: A set B is convex if ] 1 , 0 [ ) 1 ( , + α B y x B y x . In words, a linear combination of any two elements in the set also belongs to the set. 0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.3 0.5 0.7 0.9 1 x y E
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3 2. Functions of one variable. (*) A function B A f : consists of the domain set (A) the range set (B) and a rule that assigns to every element in the domain, a unique 1 element in the range. We can say that the function f maps from A into B. Examples: a. Let } 100 0 | { = x R x A . Let } , , , , , , , , , , { F D D C C C B B B A A B + + + = . The grading scale at the end of the syllabus is a rule that assigns a unique element in B (a letter grade) to every numerical grade between 0 and 100. We can give this grading function a name - G , and write B A G : , where A is the domain and B is the range.
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This note was uploaded on 04/10/2010 for the course ECO ECO200 taught by Professor Carlosserrano during the Spring '10 term at University of Toronto.

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Mathematical review_fall2009 - Mathematical review for...

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