NEKG33 Mathematical methods for economists
by Lund University
A course for students at Lund University.
Do you remember your high school algebra (adding fractions and all that fun stuff)? If not, lets do a review! We focus on real numbers, rules for real numbers and fractions. Pay particular attention to the distributive law and the quadratic identities.
You also did square root-stuff in high school. Come on in if you need to review. Focus today will be on powers, inequalities and sign diagrams.
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.
Enough of algebra for now. Let's move on to analysis, specifically to linear and quadratic function. Remember the y=kx+m? That's the focus of today.
Have you had the pleasure of working with logarithms? You may find them a bit nasty, but they are actually quite nice. We will cram in some other stuff as well such as power- and exponential functions.
Economists love derivatives. Will you?
Derivatives are fun so let's go one step further and do derivatives of derivatives. Convex and concave functions will also fit nicely into todays program.
We know how to differentiate a function. Let's use these mad skills to optimize a function.
Ordinary derivatives are for newbies. Today we move on from functions of a single variable to functions of several variables and do partial derivatives.
Final day of the first part of the course. We will look at the most "advanced" topic of the course, constrained optimization and the method of Lagrange.
First day of the second part of the course. A fresh start is always nice. We do a complete reboot and start from the begining.
Today we will admire the pretty summation sign ∑.
You have been working with functions since sixth grade (or thereabouts). Let's learn what a function really is!
Today we study composite functions, when two functions become one. Then we learn how to make a graph of an equation.
Inverse functions are like Jeopardy. If y = f(x), i will tell you y and you and go and find your x.
Today we will learn about limits. Do you remember how the "lim" appeared in the definition of the derivative? Well, it's time to take it on. Oh yeah, a bit on continuity as well.
No point postponing it - we must do the full definition of the derivative. With some limit-skills, this should work out fine. In addition to this, we will do the chain rule which will allow us to differentiate more complex functions.
Want to find the derivative when you have no function? Then implicit differentiation is for you. Want to find the derivative of the inverse without finding the inverse? Let's see how.
The function y = x^3 has a kind of funky behaviour at the origin - thats's because it is an infection point.
OK, so we know what ∫ are. Let's learn how to calculate them.
Welcome to the matrix!
Not as simple as multiplying two numbers but not too hard either.
Mathematicians love to invert things and matrices are no exception. Determinants will help us figure out when we can invert a matrix.
We have been working with functions of two variables a bit. But wait, there is more!
Once we know how to do partial derivatives, optimizing a function of two variables is the next step.