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:
.. interpret the definite integral
.. perform integration using u-substitution, integration by parts, partial fractions, trigonometric substitution, power reduction of integrals involving trig functions and table look-up
.. approximate the definite integral using Riemann Sums, Trapezoidal Rule (with error) and Simpson's Rule with error
.. apply L'Hopital's Rule when evaluating limits
.. evaluate improper integrals
.. apply the definite integral (position-velocity-acceleration, growth and decay, work, force-pressure, economics, probability distributions, volumes by slicing, arc length and surface area), using rectangular and polar functions
.. solve separable differential equations using tables, slope fields, numerical techniques including Euler's Method and algebraic techniques
.. solve logistic and preditor/prey population models
.. Determine convergence/divergence of infinite sequences
.. Determine convergence/divergence of geometric series
.. Apply integral, comparison, alternating series, absolute convergence, and ratio tests to determine series convergence/divergence
.. determine radius of convergence of power series
.. find Taylor and MacLaurin polynomials and Taylor and MacLaurin series with error term