Essential Math For Economics Dianna DaSilva-Glasgow Department of Economics University of Guyana September 7, 2017

Basic Algebra and percentages Wk Lecture 1 . . . Basic Algebra and percentages

Equation of a linear relationship If we know the intercept and slope we can describe the line succinctly in equation form. In its general form the equation of a straight line is Where b = intercept m = slope y = dependent variable x = independent variable

Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable x-values y-values Domain Range Input Output x f(x)

The input of a function is the independent variable The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

Exercise: Equation of a linear relationship  Interpreting the Slope Given the equation y= 2x + 6 What is the slope of the line? What is the value of y, when x = 1 Interpret the slope;

Exercise: Equation of a linear relationship  Since y = mx + c Y = 2(1) +6 What is the slope? Y = 2+6 It is m = 2. Y = 8   What is the value of y, when x = 1 Y = 2x + 6

Exercise: Equation of a linear relationship Interpreting the slope of the line ( Y = 2x +6) This value tells us that, for every increase of 1 unit in the input variable of Y or (x in this case), the value of the output variable Y will increase by 2.

Equation of a linear relationship Solving simultaneous equations 2x+3y=6 3x -2y = 2 solve for x and y

Percentages

What does % mean? per for every cent 100

Percentages A percentage is a fraction converted to a decimal, and then multiplied by 100 and add percent sign (%). For example,

(move all digits 2 places to the right) To find 1% of a number ÷ by 100 Find 1% of 225 225. 225 ÷ 100 (move all digits 2 places to the right) 2 . 2 5 1% of 225 = 2.25

(move all digits 1 place to the right) To find 10% of a number ÷ by 10 Find 10% of 376 376. 376 ÷ 10 (move all digits 1 place to the right) 3 7 . 6 10% of 376 = 37.6

How to change percentages, into fractions and decimals A percentage is a special fraction. The % says, “per hundred.” For example, 47%, is simply another way of writing the fraction 47/100

You can almost see the 100 in the percentage sign % The noughts The 1 Percentage Fraction 7% 7/100 19% 19/100 83% 83/100 Etc.

So to write a percentage as a fraction, you simply put it over 100 like this: 24% = 24/100 Yes, but remember to try to write the fraction in its simplest terms 24% = 24/100 12/50 6/25

To change decimal into a percentage To change a decimal into a percentage, you X by 100 X 100 0.23 23%

Percentage Change When an original value is changed to a new value, the percentage change of the value can be measured in the following way.  

Percentage Change Example Peter’s weight decreases from 60 kg to 48 kg. Find the percentage change of his weight.

Percentage Change Example Solution :  Percentage decrease of weight is 20%.

Lecture 2 . . . Basic calculus

Basic Differentiation Rules Lesson 3.2A

Basic Derivatives Constant function Then f’(x) = 0 Power Function Then Given f(x) = k Then f’(x) = 0 Power Function Given f(x) = x n Then

Exercises Use combinations of the two techniques to take derivatives of the following

Basic Rules Constant multiple Sum Rule Difference Rule

Exercises Determine the following

Lecture 3 . . . Presentation of Data

The Presentation of Scientific Data: Results, Tables and Graphs

Data Individual facts, statistics, or items of information. Generated from experiment, observation or research. How do we convey Data to others? Data Table (Visual/Organizer). Graphs (Visual).

Data Tables A Data Table is a mode of visual communication and means of arranging data (organization). Age Table: First Name Last Name Age (yrs) Bill Davolio 33 Nancy Klondike 43 Sarah Obesanjo 23 Justin Saunders 37 Mike Timberlake 26 Paulo Ilustre 11 Variable “B” or “Y” Variable “A” or “X” Independent Variable Dependent Variable

Graphs A diagram (visual) showing the relationship between sets of numbers, or topics, that represents how one set depends or changes with another. Different graphs can show different things. Examples…...

Bar Graph Used to show relationships between variables that may be “fixed” in time or space. A “snap shot”. Bars can help to give a sense of quantity. http://teachertech.rice.edu/Participants/sboone/Lessons/Fish/bargraph.jpg

Line Graph Used to show relationships, such as rates. Changes over time or given variable. http://www.earthjustice.org/news/press/006/federal-agencies-admit-yellowstone-grizzly-bear-population.html

Scatter Plot Points “plotted” between to axis (the variables). Add trendlines to see correlations in the data. Trendlines or lines of best fit. Part of linear regressions for statistical analysis. http://upload.wikimedia.org/wikipedia/commons/0/0f/Oldfaithful3.png

Pie Chart (Circle Graph) A circular chart that illustrates relative magnitudes or frequencies (Example Percentages) Pie chart of populations of English native speakers

How do you draw a graph? Important skill, to draw it means you can read a graph. Remember, it’s a visual expression, or picture, of data.

1st - A graph – Basic Terms Number Line “Y” “Y” Axis Plot/Data Area Number Line “X” “X” Axis

Using Microsoft Excel Steps In excel file, highlight data Go to ‘Insert’ Select chart type Edit chart