Course

Objective:

Learning Outcomes:

• calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and L'Hopital's Rule
• state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval, and justify the answer
• calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically
• calculate derivatives of polynomial, rational, and common transcendental functions, compositions thereof, and implicitly defined functions
• apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for functions given as parametric equations
• find extreme values of modeling functions given by formulas or graphs
• predict, construct, and interpret the shapes of graphs
• solve equations using Newton's method
• find linear approximations to functions using differentials
• restate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer
• state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions
• find antiderivatives by changing variables and using tables
• calculate definite integrals

General Topics: