Something about calculus and Sympy is lovable

I find it effective to use closed form solutions and to be able to develop/verify special cases using well-known (and well worn) formulas.

**I built a Jupyter notebook. Here is my summary of the contents.**

- Given a beam with fixed ends and a single concentrated load :

(a) Write the equation for the reactions, , , , and ,

(b) Plot the reaction for all possible locations of ,

(c) Build a function, using indefinite integration to determine and for a partial uniform moment, ,

(d) Build a function, using definite integration to determine and for a partial uniform moment, ,

(e) Consider the point load, , located at a distance, , from the left support. What location would result in the maximum moment at the left support?,

(f) Consider a partial uniform load, applied to the beam only over a distance L/2, what location of the uniform load would result in the maximum moment at the left support?,

(g) Determine the solution of for any arbitrary partial uniform loading, ,

(h) Determine the solution of for any arbitrary partial uniform loading, ,

(Bonus 1) Determine the solution of for various ‘checkered’ uniform loadings, ,

(Bonus 2) Determine the solution of for various ‘checkered’ uniform loadings, .

**My Jupyter Notebook**

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