NEKG33 Mathematical methods for economists
Chapter 3 : Day 03: Equations
By Lund University
Who doesn't enjoy finding our x? Day 3 is equation day. Remember the pesky formula for solving quadratic equations? We will do this one and some other fun stuff like systems of equations. Lots of stuff today. If overwhelmed, focus on the lectures and get back to exercises when you have the time.
Equations: Rules and terminology
In this section, we will look at the basic terminology for equations and the rules that you can use to solve equations. We will look at the distinction between a variable and a constant in an equation and we will learn how to classify an equation allowing us to apply the appropriate methods to solve the equation.
Equivalent equations and inequalities
Equations, terminology
Equations, constants and variables
Classification of equations
Solving equations
Quadratic equations
Quadratic equations is an important class of equations. We will review the formula for solving a general quadratic equation and a reduced quadratic equation (which is a quadratic equation where the constant in front of the x-square term is one). In this section we will also look at how to factor a quadratic expression and learn how to completing the square of a quadratic expression.
Reduced quadratic equations
Quadratic equations
Factoring a reduced quadratic expression and completing the square
Factoring a quadratic expression and completing the square
Single equations: Problems
Exercises on quadratic equations and other equations
Problem: Solve linear and quadratic equations
Problem: Understanding the quadratic formula
Problem: Solve linear and nonlinear equations
Problem: Simplify by factoring
Problem: Solve equations
Problem: Factor expressions
Problem: Solve inequalities
Problem: Solve text-equations
Problem: Solve equations containing constants
Problem: Solve equations containing constants
Problem: Solve quadratic equations
Problem: Solve quadratic equations
Problem Solve quadratic text-equations
Problem: Solve equations containing square roots
Systems of linear equations
This section is an introduction to systems of linear equations. We will restrict the study to two linear equations and look at two methods for solving such a system. The first method is called the substitution method and the second is the elimination method.