I am a first-year graduate student in mathematics. My undergraduate mathematics curriculum did not emphasize "calculating"; it was a theoretical curriculum in which even a traditional course in multivariable calculus was not "required" (a course in differential geometry sufficed).
I am training to be a "hands-on analyst", if that term makes any sense. For example, I know how to existence and uniqueness of solutions to PDE, but I haven't yet the "nose" to compute, to perform certain critical integration by parts, etc. I am starting to realize that theories are built on calculations and certain very interesting techniques in PDE--such as viscosity methods for example--arose from refining one's intuition while performing calculations. This is very inspiring for me and I want to learn to calculate!
Calculating has been an acquired taste for me, and as a "hands-on analyst", I would like to work in PDE and variational problems where one is interested in producing sharp bounds, etc. (this is vague, I know).
I am wondering if anyone can suggest any references/ workbooks where I can refine my "computation" skills. For example, I heard that the physicist Lev Landau gave his prospective students a preliminary test in integration. I suspect I will not pass such a test at this moment, but I would like to try to get myself to a stage where I can. Is there perhaps (a Russian?) text that emphasizes computation and serves as a good workbook for refining one's computation/calculation abilities.
Much thanks in advance!