Refresher and Functions

IMPORTANT Some of these functions require the Symbolic Math Toolbox to work. Make sure it is installed before trying to use them.

Refresher

partfrac(expr,var) expresses expr as partial fractions, relative to a variable var. Full documentation
```
  syms x;
  partfrac(x^2/(x^3-3*x+2),x)
```
diff(f(x),x,n) computes the nth derivative of f(x) which is a symbolic expression with respect to x. If n is omitted it will be the first order derivative. Full documentation
```
  syms x;
  f = x^3-4*x;
  diff(f,x,2)
```
int(expr,var,a,b) computes the definite integral of symbolic expr with respect to var from a to b. If a and b are omitted then it will return a symbolic expression of the indefinite integral. Full documentation
```
  syms x;
  expr = sin(x) - x^4;
  int(expr,x)
```
integral(f(x),a,b) can only compute numerical integrations of functions, unlike int() which uses symbolic expressions. It computes the definite integral from a to b of function f(x). Full documentation
```
  f = @(x) x.^3 -6;
  integral(f,-5,2)
```

limit(f(x), x, value) computes the limit of a function when the variable x of a symbolic function (which is different from the normal functions) tends to the value. Full Documentation
```
  syms x;
  f = 3*x^-2 + 5;
  limit(f,x,Inf)
```
solve(eqn1,eqn2,var1,var2) solves a or a system of symbolic equations. The equations can be inputed in a matrix or separetly and so can the variables that you desire to solve for. Full Documentation
```
  syms x
  eq1 = 4*x^2 + 8 == -4;
  solve(eq1,x)
```
```
  syms x y;
  eq1 = x + y - 5 == 0;
  eq2 = x^2 - y == 3;
  [xsol ysol] = solve(eq1,eq2,x,y)  
```

plot(X, Y) generates a 2D plot of X values against Y values. X and Y have to be equal-sized Row/Column matrices. Full Documentation
```
  X = [1, 2, 3, 4, 5];
  Y = [1, 4, 9, 16, 25];
  plot(X,Y)
```

fplot(f(x),Range) similar to plot() but instead it takes a symbolic function and a range as [xmin xmax] to plot the function through. If the Range argument is omited the range is [-5 to 5]. Full Documentation
```
  f = @(x) sin(x)^-3;
  fplot(f)
```

fsurf(f(x,y),xyinterval) generates a 3D plot of a symbolic function of 2 variables, the second argument is a matrix that contains the following values [xmin xmax ymin ymax]. By default it’s interval is [-5 to 5] for both x and y. Full Documentation
```
  f = @(x,y) cos(x)*y^3;
  fsurf(f)
```