the (mostly) quintessential aengineer's grimoire {now with included beastiary!}

O

it is assumed that you have spent roughly your first year as a mage becoming familiar with the art of incantation- mathemagicks most important, up to linear algebra & elementary differential equations. you'll take a primer spellcasting course on applied differential equations in this study, and learn more through exploration (as any good caster). it is also necessary to understand the fundamentals of chemistry.
a dedicated aegineer will study the ways of differential forms throughout their whole mathemagick career, which requires linear algebra to be understood first, then the differentials in higher dimensions can be approached. literature on this is sparce- only the most brazen aegineer can sail through the choppy waters currently.

I

I.A - statics (includes fluid statics + allusions of dynamics)
I.B - materials
I.C - drafting, GDT, graphical communication
I.D - creation / manufacturing

II

II.A - dynamics (includes rotational dynamics)
II.B - solid mechanics
II.C - CAD
II.D - electricity & magnetism (sans circuitry, all physics. at multivar level)

III

III.A - fluid dynamics (sister class with thermo)
III.B - wielding solid mechanics
III.C - thermodynamics
III.D - mathematical modeling and analysis

IV

IV.A - system dynamics
IV.B - vibration + system affects
IV.C - heat transfer
IV.D - circuitry

we hold slots V and VI free for the current time, as to cover your specification.