Undergraduate calculus, analysis, linear algebra, and abstract algebra.
Problem types
| Problem type | Page |
|---|---|
| Evaluate an integral, a series, or a limit | Which technique? |
| Decide whether a statement is true | Counterexamples |
Pages
Which technique? – integration techniques by the form of the integrand, convergence tests for series, and methods for limits and multivariable integrals.
Useful tricks – tabular integration by parts, the Maclaurin series of \(1/(1-x)\), \(e^x\), \(\cos x\), \(\sin x\), \(\ln(1+x)\), and \(\arctan x\) with their intervals of validity, and the sums \(\sum_n n^kx^n\).
Counterexamples – counterexamples to false statements in analysis and algebra.
Worked exams – UGA prelims, one page per exam.
Problems – the Berkeley and UCLA exam archives and an integral practice sheet.