Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal.  They should understand the connections among these representations.

Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.

Students should understand the meaning of the definite integral both as a limit of Rieman sums and as the net accumulation of a rate of change and should be able to use integrals to solve a variety of problems.

Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

Students should be able to communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.

Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.

Students should be able to use technology to help solve problems, experiment, interpret results, and verify conclusions.

Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.