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+# Functions
+This directory contains the functions written throught the course.
+* days.m
+* falsePositive.m
+* heun.m
+* luFactor.m
+* simpson.m
+* spacialMatrix.m
+
+---
+
+## [days.m](days.m)
+Function to count the total days elapsed in a year according to a given date.
+The syntax of the function is `days(<months>, <days>, <leap>)` where `<months>` is a integer (1-12). `<days>` is an integer from 1-31 and `<leap>` accounts for leap years.
+
+### Input
+* `months` - month number (1-12). Example: `8` represents August.
+* `days` - day number of the month.
+* `leap` - indicates if the year is a leapyear or a regular year. `0` for regular and `1` for leap year.
+
+### Output
+`nd` - number of days elapsed in the year.
+
+### Example:
+`days(8,4,0)` represents August 8th in a regular year (non-leap year).
+
+---
+
+## [falsePositive.m](falsePositive.m)
+Function finds the root of an anonymous function using the false position method.
+Synopsis: `[root, fx, ea, iter] = falsePosition(func, xl, xu, es, maxit, varargin)`.
+
+### Input
+`func` - the function being evaluated.
+`xl` - lower bound guess.
+`xu` - upper bound guess.
+`es` - desired relative error (default 0.0001%)
+`maxit` - maximum number of iterations (default 200)
+`varargin` - any additional parameters used by the function
+
+### Output
+`root` - estimated root location.
+`fx` - function evaluated at root location.
+`ea` - approximated relative error (%).
+`iter` - number of iterations performed.
+
+### Notes:
+Known issue: the output of `iter` needs fixing. The output is incorrect.
+
+---
+
+## [heun.m](heun.m)
+Uses the heun method to integrate an ODE.
+Synopsis: `[t,y] = Heun(dydt,tspan,y0,h)`.
+
+### Input
+`dydt` -the differential equation of interest (must be anonymous function).
+`tspan` - the initial and final values of the independent variable as a vector with length=2 [ti,tf].
+`y0` - the initial value of the dependent variable.
+`h` - step size.
+`es` - stopping criterion (%), optional (default = 0.001).
+`maxit` - maximum iterations of corrector, optional (default = 50).
+
+### Output
+`t` - vector of independent variable values
+`y` - vector of solution for dependent variable
+
+### Notes:
+This function needs some working on to compute a correct solution when using multiple steps with an irregular step size at the end.
+
+---
+
+## [luFactor.m](luFactor.m)
+
+Performs LU decomposition with pivoting.
+Synopsis: `[L, U, P] = luFactor(A)`.
+
+### Input
+`A` - a coefficient matrix.
+
+### Output
+`L` - lower triangular matrix, with 1's along the diagonals.
+`U` - upper triangular matrix.
+`P` - the permutation matrix.
+
+### Notes:
+Be cautious when using this function on bigger matrices. The `L` variable is known to be incorrect.
+
+---
+
+## [simpson.m](simpson.m)
+Evaluates the integral of two vectors by Simpsons 1/3 rule.
+Synopsis: `[I] = Simpson(x, y)`
+
+### Input
+`x` - the vector of equally spaced independent variable.
+`y` - the vector of function values with respect to x.
+
+### Output
+`I` - numerical calculated integral.
+
+### Notes:
+The current state of this function is **deprecated**. The algorithm fails compute the correct trapeziodal rule given 2 data points as well as 3 data points. Thus, failing to solve real problem. Pull requests are welcomed.
+
+---
+
+## [specialMatrix.m](specialMatrix.m)