Quiz: Symbolic Math in Python
1. What are some of the SymPy Python package capabilities for symbolic math operations? Check all that apply.
A. Analytic (exact) derivatives
- Correct.
B. Analytic (exact) definite integrals
- Correct.
C. Analytic (exact) indefinite integrals
- Correct.
D. Simplification
- Correct.
2. In order to use the symbolic features of SymPy (import sympy as sp), a variable such as x must first be declared as follows (see help video):
A. x = sp.Variable('x')
- Incorrect. Use sp.Symbol('x').
B. x = sp.Parameter('x')
- Incorrect. Use sp.Symbol('x')
C. x = sp.Symbol('x')
- Correct.
3. Analytic solutions are not exact.
A. True
- Incorrect. Numerical solutions are not exact. Analytic solutions are exact.
B. False
- Correct. Numerical solutions are not exact. Analytic solutions are exact.
4. Numerical solutions are typically an approximation of an exact solution.
A. True
- Correct. One example is to use a finite difference to calculate a derivative such as df(x)/dx = f(x1)-f(x0) / (x1-x0). As the difference between x1 and x0 decreases, the approximation become more exact until the limits of machine precision (number of decimal places that can be stored by a computer) introduces round-off or truncation error.
B. False
- Incorrect. The exact analytic solution is often not possible, but the numeric error can be approximated and reduced to a specified level.
