As Wolfgang Keller has already written, it depends on the concoke engineering science. Today, they are divided into almost a hundred different variants, and with increasing specialisation, retraining and shortening of the courses of study, there will surely soon be many more.
Let us take the three “classic” main directions of mechanical engineering, civil engineering and electrical engineering as orientation and see what one “needs” beyond the upper secondary school mathematics (LK level).
In civil engineering, this certainly includes statistics, also some what is deepened integral calculus, a little knowledge about differential equations (DGl.en), otherwise not much more.However, there are disciplines such as the statics of surface structures, where considerably more knowledge about differential calculation, also multidimensional, is needed. Triple integrals are still quite normal, but not the end of the flagpole. For the mechanics of finite elements (which also occurs in mechanical engineering) tensor calculation is also necessary; a discipline that is hardly pre-occurring in mathematics.
In mechanical engineering, it will normally be sufficient to be able to deal with certain main types of DGl.en (see above).But more differential calculation is needed for fluid mechanics or thermodynamics. For certain problems of static or dynamic stability “complicated” (i.e. usually curved, often quite irregular) body is also necessary here, among other things tensor calculation.
In these two main directions of engineering, however, extremely high safety factors are often “built in” with such high safety factors that even the rather roughly calculating physical practitioners quickly move from wondering to shaking their heads.
Electrical engineering requires significantly more.In this main direction, mathematics is the most common reason for early drop-out. This is not only related to differential and integral calculus, which far exceeds the necessities of the other two main directions, but above all to the larger field of (multidimensional) complex analysis. Many are already failing in the basics of calculating with complex numbers. Sham impedances are just one of many peaks of the iceberg.
Recently, certain orientations of practical informatics are also included in engineering sciences.It doesn’t really seem to make sense, but somehow no one asked me before…
In computer science, you need quite different mathematics than in the other three directions.Thus, proofs of existence are more important (the others often simply presuppose them) and “oblique” detailed knowledge is rather desirable. They can be very helpful in locating algorithms. That is why it is not predictable here what is really canonically necessary. Proximity methods (numerical mathematics), statistics and heuristics, estimates (including control of the error width) are more important here than in the other directions.
Physicists, who themselves often drop “small stuff”, are still usually not satisfied with all these procedures.If one then knows that mathematicians often find the mathematical approaches of physics highly questionable, then it is easier to see what “real” mathematicians think of the mathematical methods and aids of the engineers: