(*  This file of Mathematica commands can be executed by Mathematica  *)
(*  Lines that begin and end like this one are ignored by Mathematica *)
(*  For best results put this file in your home directory             *)
(*  Start Mathimatica from Unix by typing "math"                      *)
(*  When you get a Mathimatica prompt type: "<<mathin                 *)
(*  I've added Mathimatica "Print commands because Mathematica only   *)
(*  the results of the last command in a file like this.  They also   *)
(*  make results look a little better for a situation like this.      *)
(*  However, you would normally not use them in an interactive session *)
(*  Try typing variations on any other command you see here  *)
(*                                                                     *)
Print [" Find Solutions to the Equation: a x^2 + b x + c = 0"]
(*                                                                     *)
(*  In the line below "eqn1 = " just gives a name to the equation that *)
(*  will abbreiviate later commands  *)
(*                                                                     *)
eqn1= a*x^2+b*x+c==0.
(*                                                                     *)
(*   Now generate a solution and name it soln1 *)
(*                                                                     *)
soln1= Solve[eqn1,x]
(*                                                                     *)
(*   In an interactive session "Solve[a*x^2+b*x+c==0,x]" would be fine *)
(*  Print to display the equation and solution *)
(*                                                                     *)
Print ["For the equation   ", eqn1]
Print ["The solutions are:",soln1]
(*                                                                     *)
(* I can now go back and set values for a, b, and c and solve again  *)
(*                                                                     *)
a = 1
b = -1
c = -1
(*                                                                     *)
Print ["For ", eqn1]
Print ["The solutions are:", N[soln1]]
(*                                                                     *)
(* In the above print the Mathematica function N[ ], gives a decimal  *)
(* answer for x.   Depending on how your defaults are set, you may    *)
(* see answers that aren't too helpful without using N[ ]             *)
(*   Solve is an algebraic solver and at some point in equation       *)
(*   difficulty will give up.  Then you need to try NSolve or FindRoot *)
(*   NSolve works for polynomial equations   *)
(*                                                                     *)
soln1= NSolve[eqn1,x]
Print ["For the equation   ", eqn1]
Print ["The solutions are:",soln1]
(*                                                                     *)
(*   For more complicated equations Mathematica will apply Newton's method *)
(*   Remember that this requires an initial guess, and only finds one      *)
(*   solution near the guess   *)
(*   For a first guess of x = 3, the solution is obtained as follows:      *)
(*                                                                     *)
soln1=FindRoot[eqn1,{x,3}]
Print ["Newton solution starting from 3 is:",soln1]
(*                                                                     *)
(*   Mathematica does an amazing number of things,  take a look at a book  *)
(*   on the program for detailed information   *)
(*   One useful function is integration:       *)
(*                                                                     *)
answer1=Integrate[x^2*Sin[x],x]
Print["Indefinate integral of x**2 sin(x) is"]
Print[answer1]
(*                                                                     *)
(*   You can also do definate integrals   *)
(*                                                                     *)
answer2=Integrate[x^2*Sin[x],{x,0,Pi/2}]
Print["Integral of x**2 sin(x) from 0.0 to pi is"]
Print[answer2," = ",N[answer2]]
(*                                                                     *)
(*   If Mathematica refuses to use Integrate to evaluate a definate Integral *)
(*   try the numerical integrator NIntegrate  *)
(*                                                                     *)
answer2=NIntegrate[x^2*Sin[x],{x,0,Pi/2}]
Print["Numerical Integral of x**2 sin(x) from 0.0 to pi is"]
Print[answer2]
(*                                                                     *)
(*   Another useful operation is symbolic differentiation    *)
(*                                                                     *)
answer3=D[x^2*Sin[x],x]
Print["Derivative of x**2 sin(x) with respect to x is"]
Print[answer3]
(*                                                                     *)
(*  Check you course notes for more mathematica commands and play with them *)