-Sequences 

-Limits: neighborhoods and tails, epsilon definition

-Working with specific sequences: finding limits from definition, estimates, limit laws

-Properties of convergent sequences: uniqueness of limit, convergent sequence is bounded, etc

-Infinite limits, properties of sequences diverging to infinity

-Limit Laws (and their versions for infinite limits, when applicable

-Bounded sets and sequences, upper/lower bounds, supremum and infimum, completeness axiom

-Theorem: monotone bounded sequence converges

-subsequences: definition, finding subsequences with certain properties. 
 Theorem: if a sequence converges, all its subsequences converge to the same limit.

-integers, rationals, algebraic and order axioms for rationals and reals. 
 (This topic will not be emphasized. You need not memorize the axioms, 
  but you should be able to derive simple statements from the axioms by using logic)

- Bolzano-Weierstrass theorem: every bounded sequence has a convergent subsequence. 
   (know the statement, understand what it means. what happens if the sequence is not bounded?)

-Continuous functions. Two definitions: via sequences and epsilon-delta. 
 (be able to check whether simple functions are continuous or not, construct basic examples of continuous
and discontinuous functions.  Understand why two definitions are equivalent)

-Operations (sums, products, etc) with continuous functions. Continuity of polynomials and rational 
functions (know proofs). Other examples of continuous functions (not much required here, just know that 
the basic functions from calculus, sin x, cos x, exp x, etc are continuous. You can use this without proof.)

- Properties of continuous functions on closed, bounded intervals: bounded, attains max/min, intermediate 
 value theorem. (know the statements and an outline of proofs. understand where proofs fail if
 interval not closed/not bounded or function not cont., give counterexamples.)

- Limits of functions (two-sided, one-sided, limits at infinity). Sequential and epsilon-delta definition. 
  Theorem: two-sided limit exists <=> both one-sided lims exist and are equal. (understand proof; be able 
  to use the theorem.) Relation between existence of limit and continuity at the point. Various additional 
  properties whose proofs are very similar to those for continuous functions/sequences: limit laws for lim f(x), 
  uniqueness of limit, etc.

-Derivatives (know the definition, be able to prove existence/non-existence of derivative, compute derivative
 from definition for simple functions)

-Differentiation rules: sum rule, product rule, etc (understand proofs, be able to use them & to prove similar statements 
from definition). Chain rule (stetement only; you DO NOT need to remember a complete proof).

- Derivatives and maxima/minima of a function. Local max/min  => f ' =0. (Know the proof, be able to answer 
various related questions: is the converse true? is f ' = 0 for a global max on [a,b]? etc)

- The mean value theorem (know the statement, its interpretation, proof via Rolle's thm). Applications 
 of the mean value thm. (f ' =0 at all pts => f=const, etc.)

- Increasing and decreasing functions. Detect increasing/decreasing via derivatives (know proofs, be able 
  to prove related statements).

The differentiation part of the course covered sections 28, 29 (pp.205-217) of the textbook. Best practice
 questions can be found in past homeworks. Extra questions for differentiation: 28.2, 28.3, 28.4, 28.11,
 28.13, 29.1, 29.2, 29.3, 29.8, 29.10, 29.11.