DESIGNATION: Level I elective
GOALS: To use and apply derivatives and integration, to develop the ability to communicate mathematics clearly, both verbally and in writing, to develop problem solving techniques, and to develop an understanding of how calculus can be applied to a wide variety of real life problems. The ability to work in collaboration with others is essential to success in this course. A TI-Nspire graphing calculator is required.
MATERIAL COVERED: The first trimester begins with an overview of the four topics of Calculus: limits, derivatives, integrals, and definite integrals. This is followed by a detailed study of limits: left hand limits and right hand limits. Limits are then used to define the derivative. The term concludes with an in depth study of derivatives, the power rule, the chain rule, the product rule, the quotient rule, implicit differentiation, and applications of the derivative. The second term begins with applications of the derivative including extrema and related rates. This is followed by a study of the integral, the definite integral, and applications of integrals, such as the area between curves, volumes of rotation through plane slicing, and cylindrical shells. The third term begins with differential equations, slope fields, and exponentials, followed by a review of the entire year in preparation of the AP exam. Also, interwoven throughout each term is the study of graphs and interpreting and analyzing derivatives and anti derivatives from the graphs.
TEXT: Calculus: Early Transcendentals/Single Variable Text, 10th edition, Wiley
PREREQUISITE: Successful completion of Honors Precalculus and departmental approval.