Functions:
how to graph them;
estimating when you have only the graph;
dervative as an operator;
solution to a differential equation is a function;
Exponential behavior:
exponential growth, decay and approach;
relating infinitesimal behavior to long-term behavior;
knowing which real life models behave in these ways'
Limits and continuity:
intuitive understanding;
ability to use the definition in tricky cases;
Estimating:
linear estimates with first derivative;
higher order estimates with Taylor series;
integrating something near gives something near;
computational tricks and knowing approximate constants;
Bounding:
what it means to bound a quantity in an interval;
bounding partial sums of series;
bounding series by integrals and vice versa;
convexity makes a linear estimate into a bound;
Units:
exponential and logarithm takes unitless quantities;
units of df/dx are units of f divided by units of x;
units of \int f dx are units of f times units of x;
Free and bound variables:
in integrals ("dummy variables");
in sums;
in max-min problems;
Orders of growth:
powers, exponentials, logs and their relations at 0 and infinity;
O(.) notation;
nth order approximation at a point;
Problem-solving heuristics:
check whether you understand what is being asked;
look at some data;
try to solve a special case;
try to solve a simpler problem;
Verbal skills:
use of proper grammar and precise terms;
recognizing counterexamples to hypotheses;
recognizing counterexamples to arguments;