Quiz: Symbolic Math in Python

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May 18, 2022, at 03:38 AM by 10.35.117.248 -
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Incorrect. The function returns the derivatives at the current time and state values, not the solution.
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Incorrect. Use sp.Symbol('x').
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Incorrect. The user-defined function returns the derivatives at the requested time and state values.
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Incorrect. Use sp.Symbol('x')
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May 18, 2022, at 03:37 AM by 10.35.117.248 -
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(:title Quiz: Symbolic Math in Python:) (:keywords quiz, test, Python, plot, sympy, symbolic, equations, introduction, course:) (:description Learning assessment on symbolic math solutions with Python.:)

1. What are some of the SymPy Python package capabilities for symbolic math operations? Check all that apply.

A. Analytic (exact) derivatives
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Correct.

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B. Analytic (exact) definite integrals
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Correct.

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C. Analytic (exact) indefinite integrals
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Correct.

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D. Simplification
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Correct.

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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')
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Incorrect. The function returns the derivatives at the current time and state values, not the solution.

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B. x = sp.Parameter('x')
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Incorrect. The user-defined function returns the derivatives at the requested time and state values.

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C. x = sp.Symbol('x')
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Correct.

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3. Analytic solutions are not exact.

A. True
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Incorrect. Numerical solutions are not exact. Analytic solutions are exact.

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B. False
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Correct. Numerical solutions are not exact. Analytic solutions are exact.

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4. Numerical solutions are typically an approximation of an exact solution.

A. True
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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.

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B. False
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Incorrect. The exact analytic solution is often not possible, but the numeric error can be approximated and reduced to a specified level.

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