Practice question · Sort into groups
Sort each task by the kind of computation it needs.
Groups: Numerical · Symbolic
- Find a root of a messy equation by Newton's method
- Factor a polynomial into exact linear factors
- Approximate the integral of the Gaussian from 0 to 1 to six decimals
- Return an exact formula for the derivative of x cubed times sin x
- Solve a 1000 by 1000 linear system to ten decimal places
Hints
- Ask whether the answer wanted is a formula or a number.
- Anything reported 'to six decimals' has already accepted approximation.
Show the answer
Numerical: Approximate the integral of the Gaussian from 0 to 1 to six decimals, Find a root of a messy equation by Newton's method, Solve a 1000 by 1000 linear system to ten decimal places
Symbolic: Return an exact formula for the derivative of x cubed times sin x, Factor a polynomial into exact linear factors
Why
Symbolic computation manipulates expressions exactly and returns formulas; numerical computation returns approximate numbers where no closed form is available or wanted. The phrase 'to n decimals' is the giveaway that you are in the numerical world.
Practise Programming for Mathematics
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