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

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