These are the more important topics (I'm excluding the very basic
stuff like functions, domain and range, limits and continuity, which I
assume you know well):
Derivative of a function, differentiation rules (including the
Chain Rule), table of elementary derivatives
Implicit differentiation
Related rates
Finding local/global max/min of a given function on a given
interval, increase/decrease, concavity of a graph, critical and
inflection points
Optimization
Linear approximation
Anti-derivatives (aka indefinite integrals)
The relation between the position, velocity, and acceleration of a
moving object
Definite integral as area, properties
Fundamental Theorem of Calculus I and II
Average value of a function over an interval
Application of integral in finding areas between two curves
Application of integral in finding volumes
Inverse functions and derivatives
Natural log, its properties, its derivative
The exponential function, its properties, its derivative
Exponential growth and decay
L'Hospital's Rule
Inverse trigonometric functions and their derivatives
Basic integration formulas (Table 7.1)
Integration by substitution
Integration by Parts
Partial fractions (simple cases, e.g. when you have two linear
factors in the denominator)
Trigonometric substitution (simple cases, e.g. when you have
a2-x2 or a2+x2 in your
integral)
Improper integrals (very simple cases as we briefly discussed in class,
no ``comparison tests'')