How best to prepare for preliminary exams (for phd)

[xaos]

the exams I'm looking at will be in analysis and applied math, the first covers: real analysis, advanced calculus, and complex variables; the second: a second course in differential equations, partial differential equations, and numerical methods. i may be able to take preparatory classes in the first and second semesters, but there's only enough room in my time to take two courses in each of the semesters, leaving holes in some areas. but if i can prepare strong in some areas, i can reduce the number of courses i may need to take.

one idea is to try to do this on my own, but i will be starting from scratch in all six areas, so I'm not sure how I'm going to put it all together in a finite amount of time and stepping through six books will take me a good year at the very least.

another idea is to focus all of my self study efforts on the first test in analysis, and then take some classes to prepare for the second over the two semesters.

 

[xaos]

the complication is that i have to choose between work and study. if i work, then i can save up for the high cost of education much faster. if i study, i can add an additional fifteen hours a week to my study time, so that i can complete this study project much sooner.