Here is an brief outline of the material we've covered that you should know for the exam. There is an extended review here that ties the material together and discusses some common mistakes. 

  • Limits and continuity. limits, algebra of limits (with proof), epsilon-delta proofs of limits; continuity, continuity theorems: intermediate value theorem, boundedness theorem, maximum value theorem.
  • Topology of R^n. Least upper bound property, supremum, infimum; open, closed, interior, exterior, boundary; open covers, compactness, Heine-Borel.
  • Differentiability in one variable. Derivative, algebra of derivatives, chain rule; Rolle's theorem, mean value theorem, Cauchy mean value theorem.
  • Differentiability in several variables. Derivative, directional derivatives, partial derivatives, continuous partials theorem, C^1 function, chain rule.

Tip: it's helpful to know examples that illustrate the concepts or hypotheses of various definitions/theorems. For the major theorems, you should be comfortable applying them and you should know the hypotheses and why they're necessary. 

Practice Midterm 1, Practice Midterm 2

Solutions 1, Solutions 2

There are additional practice problems in Spivak, Munkres, and Spivak. It's also suggested that you understand any mistakes you made on homework.