## NEKG33 Mathematical methods for economists

### by Lund University

A course for students at Lund University.

## Chapter 1: Day 01: Real numbers and fractions

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.

## Chapter 2: Day 02: Powers, inequalities and sign diagrams

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.

## Chapter 3: Day 03: Equations

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.

## Chapter 4: Day 04: Linear and quadratic functions

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.

## Chapter 5: Day 05: Power- exponential and logarithmic functions

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.

## Chapter 6: Day 06: Derivatives

Economists love derivatives. Will you?

## Chapter 7: Day 07: Higher order derivatives

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.

## Chapter 8: Day 08: Optimizing a function of one variable

We know how to differentiate a function. Let's use these mad skills to optimize a function.

## Chapter 9: Day 09: Partial derivatives

Ordinary derivatives are for newbies. Today we move on from functions of a single variable to functions of several variables and do partial derivatives.

## Chapter 10: Day 10: Lagrange

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.

## Chapter 11: Day 11: Logic and sets

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.

## Chapter 12: Day 12: Summation sign

Today we will admire the pretty summation sign ∑.

## Chapter 13: Day 13: Functions

You have been working with functions since sixth grade (or thereabouts). Let's learn what a function really is!

## Chapter 14: Day 14: Composite functions and graphs of equations

Today we study composite functions, when two functions become one. Then we learn how to make a graph of an equation.

## Chapter 15: Day 15: Inverse functions

Inverse functions are like Jeopardy. If y = f(x), i will tell you y and you and go and find your x.

## Chapter 16: Day 16

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.

## Chapter 17: Day 17: More on derivatives

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.

## Chapter 18: Day 18: Implicit differentiation and the derivative of the inverse

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.

## Chapter 19: Day 19: Inflections points

The function y = x^3 has a kind of funky behaviour at the origin - thats's because it is an infection point.

∫!

## Chapter 21: Day 21: Computing integrals

OK, so we know what ∫ are. Let's learn how to calculate them.

## Chapter 22: Day 22: Matrices

Welcome to the matrix!

## Chapter 23: Day 23: Matrix multiplication

Not as simple as multiplying two numbers but not too hard either.

## Chapter 24: Day 24: Matrix inverse and determinants

Mathematicians love to invert things and matrices are no exception. Determinants will help us figure out when we can invert a matrix.

## Chapter 25: Day 25: Function of several variables.

We have been working with functions of two variables a bit. But wait, there is more!

## Chapter 26: Day 26

Once we know how to do partial derivatives, optimizing a function of two variables is the next step.

Chain rule