I am not sure if I understand your question correctly, but if you only ask how to calculate the deflection, shear force and bending moment along the rod/beam, you should find many resources online. If you would like to understand the theory behind it, you should read more about the "Euler-Bernoulli beam theory". Also check resources explaining how to draw shear force and bending moment diagrams for beams. For the case of cantilever beam, the attached document gives you an idea how to calculate the deflection and slope as function of the geometrical parameters "I and L", material properties "E" and the applied load "P". I hope you find this useful.