Complex function and probability theory are instrumental and can be solved by engineering students.
Ordinary differential equations from first order to higher order are basically limited to linearity, and the core lies in the existence and uniqueness theorem of solutions. Qualitative theory and bifurcation problem are slightly involved, so it is not difficult to learn.
Real variables and functionals come down in one continuous line, and the key lies in the understanding of the two concepts of measure and function space. It should be said that it is difficult to change a person's mind.
Abstract algebra, differential geometry and topology can really be regarded as "gymnastics of thinking". Some people may find it difficult, but it's interesting. Their respective theoretical systems also have a clear context, and they have a great sense of accomplishment in learning. Although it is difficult, it is ok.
Well, the last thing left is the partial differential equation.
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