What mathematics does a mechanical engineer need? How can we compress the teaching of the information needed by graduate engineers into less time? How can we find place for modern subjects in the engineering curriculum? These questions are asked for both practical reasons to improve the effectiveness of engineering computation and to compress the time required for teaching mathematical techniques in mechanical engineering curriculum. A possible proposal for answering these questions can be formulated as follows: reduce the time spent on rigid and sterile mathematical proofs (without vulgarization); mobilize computer-aided techniques for obtaining engineering results; create combined numerical-analytical techniques, which permit evaluation of engineering problems and estimations on a level that is satisfactory in practice. Some such numeralytical techniques are explained and illustrated in this work.