Next: , Previous: Algebra, Up: Top


3 Calculus

3.1 Differential Operator

— Operator: differential expr
— Operator: ' expr

The Jacal command differential computes the derivative of the expression expr with respect to a generic derivation. It is generic in the sense that nothing is assumed about its effect on the individual variables. The derivation is denoted by a right quote.

          e6 : differential(x^2+y^3);
          
                          2
          e6: 2 x x' + 3 y  y'
          
          e7 : (x^2+y^3)';
          
                          2
          e7: 2 x x' + 3 y  y'

3.2 Derivative Commands

— Command: diff expr var1 ...

The Jacal command diff computes the derivative of the expression expr with respect to var1, ....

          e6 : diff(x^2+y^3,y);
          
                 2
          e6: 3 y
— Command: partial expr var1 ...

The Jacal command partial computes the partial derivative of the expression expr with respect to var1, ....

          e6 : partial(x^2+@1^3,1);
          
                  2
          e6: 3 @1
— Command: PolyDiff poly var1 ...

The Jacal command PolyDiff computes the derivative of the expression poly with respect to var1, .... It is faster than diff but poly must be a polynomial.