COURSE OBJECTIVES:

At the end of the semester, students will have an understanding of the concepts and techniques listed below.  This understanding will be enhanced, when appropriate, through directed group and individual computer exercises and group and individual projects.

COURSE CONTENT:

At the end of the semester, the student will be able to:

• perform calculus operations, graph functions and solve equations using Derive

• manipulate and graph numerical data using Excel

• define a function and find domain and range

•  manipulate and develop mathematical models using the following functions:  linear, exponential, power, inverse, logarithmic, trigonometric, polynomial and rational

• transform functions and generate composite functions

• explain the concept of and evaluate limits

• find intervals of continuity for a function

• ‘construct’ the definition of the derivative

•  explain how the secant and tangent line relate to the derivative, average and instantaneous rates of change, velocity and acceleration

•  find approximations for the derivatives at a point

• use local linearity to estimate functional values

• apply appropriate techniques of differentiation (product, quotient, chain, exponential, logarithmic)

• differentiate trigonometric functions

• perform implicit differentiation

• solve related rates applications

• determine increasing and decreasing intervals of a function

• determine concavity of a function and points of inflection

• sketch curves using appropriate techniques

• solve optimization problems

•  apply Newton 's method when finding roots

• recognize an antiderivative

• setup and evaluate Riemann Sums

• evaluate definite integrals