In this appendix integral lists are presented that are used for the numerical solution of many aerospace problems. Computer algorithms have been developed, as those described in Appendix D, using first-order solutions for the differential equations of motion. These solutions can be generalized using an array of state parameters, y ₁, y ₂, y ₃, ..., y _n, and an array of their first derivatives, ₁, ₂, ₃, , _n. The numerical solution is characterized by the stepwise integral:

This integral is performed in ? t steps until the end boundary condition is reached, for example, until the state parameter achieves a desired value or until the stop time is reached. The following integral lists refer to the indicated solutions of Eq. (C.1).