The book presents advanced methods of integral calculus and
optimization, the classical theory of ordinary and partial
differential equations and systems of dynamical equations. It
provides explicit solutions of linear and nonlinear differential
equations, and implicit solutions with discrete approximations.The
main changes of this second edition are: the addition of
theoretical sections proving the existence and the unicity of the
solutions for linear differential equations on real and complex
spaces and for nonlinear differential equations defined by locally
Lipschitz functions of the derivatives, as well as the
approximations of nonlinear parabolic, elliptic, and hyperbolic
equations with locally differentiable operators which allow to
prove the existence of their solutions; furthermore, the behavior
of the solutions of differential equations under small
perturbations of the initial condition or of the differential
operators is studied.
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