CubicFormula (p)
Compute roots of a cubic (degree 3) polynomial using the cubic formula. The polynomial should be given as a vector of coefficients. That is 4*x^3 + 2*x + 1 corresponds to the vector [1,2,0,4]. Returns a column vector of the three solutions. The first solution is always the real one as a cubic always has one real solution.
See Planetmath, Mathworld, or Wikipedia for more information.
EulersMethod (f,x0,y0,x1,n)
Use classical Euler's method to numerically solve y'=f(x,y) for
initial x0, y0 going to
x1 with n increments,
returns y at x1.
Systems can be solved by just having y be a
(column) vector everywhere. That is, y0 can
be a vector in which case f should take a number
x and a vector of the same size for the second
argument and should return a vector of the same size.
FindRootBisection (f,a,b,TOL,N)
Find root of a function using the bisection method.
FindRootFalsePosition (f,a,b,TOL,N)
Find root of a function using the method of false position.
FindRootMullersMethod (f,x1,x2,x3,TOL,N)
Find root of a function using the Muller's method.
FindRootSecant (f,a,b,TOL,N)
Find root of a function using the secant method.
PolynomialRoots (p)
Compute roots of a polynomial (degrees 1 through 4) using one of the formulas for such polynomials. The polynomial should be given as a vector of coefficients. That is 4*x^3 + 2*x + 1 corresponds to the vector [1,2,0,4]. Returns a column vector of the solutions.
The function calls QuadraticFormula, CubicFormula, and QuarticFormula.
QuadraticFormula (p)
Compute roots of a quadratic (degree 2) polynomial using the quadratic formula. The polynomial should be given as a vector of coefficients. That is 3*x^2 + 2*x + 1 corresponds to the vector [1,2,3]. Returns a column vector of the two solutions.
See Planetmath or Mathworld for more information.
QuarticFormula (p)
Compute roots of a quartic (degree 4) polynomial using the quartic formula. The polynomial should be given as a vector of coefficients. That is 5*x^4 + 2*x + 1 corresponds to the vector [1,2,0,0,5]. Returns a column vector of the four solutions.
See Planetmath, Mathworld, or Wikipedia for more information.
RungeKutta (f,x0,y0,x1,n)
Use classical non-adaptive fourth order Runge-Kutta method to
numerically solve
y'=f(x,y) for initial x0, y0
going to x1 with n
increments, returns y at x1.
Systems can be solved by just having y be a
(column) vector everywhere. That is, y0 can
be a vector in which case f should take a number
x and a vector of the same size for the second
argument and should return a vector of the same size.