# Maclaurin series and Euler's identity

8 videos

2 skills

In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun.
If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.

### Maclaurin and Taylor series intuition

VIDEO
12:59 minutes

Approximating a function at 0 using a polynomial

### Cosine Taylor series at 0 (Maclaurin)

VIDEO
5:37 minutes

Approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0)

### Taylor series at 0 (Maclaurin) for e to the x

VIDEO
6:10 minutes

Taylor Series at 0 (Maclaurin) for e to the x

### Euler's formula and Euler's identity

VIDEO
11:27 minutes

Rationale for Euler's Formula and Euler's Identity

### Maclaurin series based on cos x

VIDEO
8:01 minutes

### Evaluating power series for mystery function

VIDEO
6:09 minutes

### Maclaurin series for sin x, cos x, and eˣ

PRACTICE PROBLEMS

### Finding power series through integration

VIDEO
11:06 minutes

### Integration and differentiation of power series

PRACTICE PROBLEMS

Integration and differentiation of power series