## Matlab Tutorial 6: Analysis of Functions, Interpolation, Curve Fitting, Integrals and Differential Equations

In this tutorial we will deal with analysis of functions, interpolation, curve fitting, integrals and differential equations. Firstly, we will need to use polynomials and therefore we have to be familiar with the representation of these. A general polynomial looks like: p(x)=a_{n}x^{n} + a_{n-1}x^{n-1} +……….+ a_{1}x + a_{0 }and is represented by a vector in Matlab:

p=[ a^{n} a^{n-1} ……. a^{1} a^{0} ]

Here we have a list of basic commands dealing with polynomials.

**polyval(p,x):** Calculates the value of polynomial p for different x. If x is a vector then the polynomial is evaluated for each element in the vector x.

**poly(A):** Gives a vector that represents the characteristic polynomial for the matrix A.

**roots(p):** Gives a vector with the zeros for the polynomial p(x)=0.

**polyder(p):** Gives a vector that represents the time-derivative of the polynomial p(x). The coefficients are sored in the vector p.

**conv(p,q):** Multiplies the polynomials p and q with each other. Returns a coefficient vector.

**polyint(p):** Integrates the polynomial p analytically and uses the constant of the integration c. The constant c is assigned to 0, if it is not explicitly given.

**residue(p,q):** Makes a partial fraction expansion of p(x)/q(x).