THE CALCULUS OF VARIATIONS
PAUL SIEGEL
1. Introduction
It is well-known that the shortest path between two points in the plane is a straight line. This statement
seems so obvious that it is tempting not to give it a second thought, but understanding why i
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CALCULUS IV - PROBLEMS AND SOLUTIONS
1. Calculus of Variations
Problem 1.1. Solve the differential equation x0 (t) = 4x2 t3 with initial condition x(1) = 1.
0
Solution. Rewriting the equation as xx2 = 4t3 and integrating, we get x1 = t4 + C where C is a c