41. As a generalised function, the second derivative may be taken as two times the Dirac delta function. 42. The second derivative of Ritz's equation is 43. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. 44. This generates so much hash ( noise ) that the second derivative ( acceleration ) was uselessly inaccurate. 45. Then the convexity would be the second derivative of the price function with respect to the interest rate. 46. Note that for linearly parameterized Hamiltonian, there is no second derivative 0 } } on the operator level. 47. We have carefully written all expressions in a form such that these first and second derivatives appear explicitly. 48. The limit above just gives a possibility for calculating the second derivative but does not provide a definition. 49. This will work since the second derivative can be written in a form involving a power of x '. 50. For many combinations of boundary conditions explicit formulas for eigenvalues and eigenvectors of the second derivative can be obtained.
