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Unformatted text preview: f ‘integrating the area of each slice’ Determine the type of cross section (triangle, semi-circle, square, etc.) and its relationship to the given function or set of functions Create an expression for the area of each slice in terms of the function to be used as the integrand Set up and evaluate integrals to find volume Sketch a slope field given a derivative in terms of x, y or both Visualize the position functions that differ by a constant (change in vertical shift) Understand the process behind finding a solution to a differential equation given an initial condition; i.e. separating the variable, taking the antiderivative, etc. NJ CCCS Strands & Indicators 4.1 4.2 4.3 4.5 A,B,C A,B,C,D A,B,C,D A,B,C,D,E,F 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B,C,D A,B,C,D,E,F Suggested Timeframe (in blocks) 3 2 Course Objective(s) Review applications of differential equations Student Objectives • • • Recall finding solutions to differential equations Apply knowledge to problems involving compound interest, population growth, Newton’s Law of Cooling, Law of Exponential Change and half-life Apply Euler’s Method of Approximation NJ CCCS Strands & Indicators 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B,C,D A,B,C,D,E,F Suggested Timeframe (in blocks) 3 RESOURCES • Textbook: :Calculus: Graphical, Numerical, Algebraic Finney,Demana,Waits,Kennedy Addison Wesley, 1999 • Supplementary Materials Workbooks D & S Marketing Workbooks 8th Edition, Edited by David Lederman, 2004 Barron’s “How to Prepare for the AP Calculus Exam” 6th Edition, Edited by Shirley O. Hockett, 1998 Reference Hand-Outs TI-89 Titanium: Calculator Extraordinaire Trigonometry: Unit Circle with Exact Radian Values, Identities Derivative and Integral Identities Various Supplements from AP Central Websites www.collegeboard.com: provides information about AP exams http://archives.math.utk.edu/visual.calculus/: an extremely thorough site for pre-calculus through integral calculus with accompanying tutorials, practice problems, interactive quizzes and animations http://online.math.uh.edu/HoustonACT/: contains Powerpoint presentations for each section correlating to our text book www.calculus-help.com/funstuff/phobe.html: animated explanations of the first two chapters of calculus www.calculusabc.com: teacher and student resources containing multiple choice problems for each unit and well as a forum for teachers to exchange teaching ideas http://clem.mscd.edu/~talmanl/APCalculus.html: FRQ solutions, explanations, links to number of other sites and much more! www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calculus.html: calculus lesson plans & activities Technology (Software/Equipment) Geometer’s Sketchpad Winplot Various Online Tutorials/Animations Smartboard© Technology Calculators TI-83, TI-89 Titanium with associated software and programs Additional Teacher Resources All resources and files available through College Board’s AP Central as well as a large bank of websites, journal and magazine articles, and newsletters Barton, et. al. Preparing for the Calculus AP Exam with Calculus: Graphical, Numerical, Algebraic. (Finney/Demana/Waits/Kennedy), Pearson, 2006. Kennedy, Dan. Teacher’s Guide – AP Calculus. The College Board. Lifshitz, Maxine. Amsco’s AP Calculus AB/BC, Amsco School Publications, Inc. 2004 Lipp, Alan. Visualizing Differential Equations with Slope Fields. Little Book of Big Ideas, People’s Publishing Group. 2006. McMullin, Lin. Teaching AP Calculus, 2nd Edition; D&S Marketing Systems, Inc. 2005 Ralph, Bill. Journey Through Calculus. Brooks, Cole. 2000. Stewart, James. Calculus Concepts and Contexts, 3rd Edition. Thompson, Brooks/Cole. 2005. 2004 – 2005 Professional Development for AP Calculus—Special Topic: Differential Equations. Workshop Materials, College Board. 2005 Professional Development & Workshops Available for Teaches: “Teaching AP Calculus” Sponsored by the College Board. This program is offered through the College Board itself or through public and private institutions throughout the school year AP Calculus Roundtable, Summit, NJ (bi-annual meetings): Past readers share concerns and suggestions toward the FreeResponse Questions Discussion of common errors and discrepancies Breakdown of the test for scoring AP Calculus List-Serve through AP Central: open discussion on methods and specific problems Full AP Exams: Multiple-Choice and FRQ: 2003, 1998, 1997, 1993, 1988, 1985 Free-Response Questions: 1985 – 2007 (both forms, when applicable) with Scoring Guides The Princeton Review: Cracking the AP Calculus AB Exam Additional Practice Exams from Student and Teacher Resources ACTIVITIES • • • • • • • • • • • • Lecture Class discussions Student presentations Cooperative Learning structures Guided practice Technology infusion Learning Styles activities Brain-based activities Differentiated Instruction State and standardized test preparation Homework review AP Test Preparation: Exams and practice exercises ASSESSMENT • • • • • • • Tests Quizzes Homework In-Class assignments Presentations Class participation Midterm/final exams...
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This note was uploaded on 03/12/2010 for the course CALCULUS 1561234586 taught by Professor Zalla during the Spring '10 term at Air Force Institute of Technology, Ohio.

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