MATH& 151

Calculus I

LEARNING OUTCOMES

 

Upon successful completion of Math& 151, the student should be able to:

 

  1. Calculate or estimate limits of functions given by formulas, graphs, or tables; also using properties of limits and LÕhopitalÕs Rule.

 

  1. Determine whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval.

 

  1. Distinguish between average and instantaneous rate of change, and interpret the definition of the derivative graphically.

 

  1. Calculate derivatives of polynomial, rational, common transcendental functions, combinations of these functions, and implicitly defined functions.

 

  1. Apply the ideas and techniques of derivatives to:

                                                                      i.       related rate problems,

                                                                   ii.       parametric equation models (optional).

 

  1. finding extreme values of modeling functions given by formulas or graphs:

                                                                      i.       predict, construct and interpret the shapes of graphs,

                                                                   ii.       solving equations (i.e. NewtonÕs Method),

                                                                 iii.       find linear approximations of functions (differentials).

 

  1. Estimate a slope, a rate of change and the reasonableness of a result.

 

  1. Interpret solutions to applied problems, attaching the appropriate units to an answer.

 

  1. Distinguish assumptions and conclusions in mathematical statements.