Penn State University - University Park MATH 140A, Calculus, Analytic Geometry, Algebra & Trigonometry Spring 2009 CATALOG DESCRIPTION: MATH 140A (GQ) Calculus, Analytic Geometry, Algebra, and Trigonometry (6) Review of algebra and trigonometry; analytic geometry; functions; limits; derivatives, differentials, applications; integrals, applications. Students may only take one course for credit from MATH 110, 140, 140A, 140B, 140E, 140G, and 140H. PREREQUISITE: 3-4 years of HS math including trigonometry with satisfactory performance on the FTCAP exam, or satisfactory performance on the algebra and trigonometry math proficiency examination. TEXT: Calculus (Single Variable) , Sixth Edition, (OR) Calculus, Sixth Edition, by James Stewart, published by Thomson (Brooks/Cole). An electronic version of the text (e-text) is available chapter by chapter through http://pennstate.ichapterssites.com COURSE FORMAT: There are three 50-minute lectures (MWF) and two 75-minutes lectures (TR) each week. The sections covered in lectures are listed at the end of this syllabus. MATH 140A LEARNING OBJECTIVES : Upon successful completion of Math 140A, the student should be able to: 1. Use algebra concepts and techniques required in calculus topics. 2. Use trigonometry concepts and techniques required in calculus topics 3. Calculate or estimate limits of functions given by formulas, graphs, or tables. 4. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval or on its domain. 5. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval. 6. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically. 7. Determine derivatives of some functions using the limit definition of the derivative. 8. Calculate derivatives of polynomial, rational, and common transcendental functions, and combinations of these functions. 9. Calculate derivatives of composite functions. 10. Calculate derivatives of implicitly defined functions. 11. Give examples to illustrate important theorems. (Intermediate Value Thm, Rolle’s Thm, Mean Value Thm, Extreme Value Thm, Squeeze Thm) 12. Apply the ideas and techniques of derivatives to related rate problems. 13. Apply the ideas and techniques of derivatives to finding local and absolute extrema. 14. Apply the ideas and techniques of derivatives to graphing functions. 15. Apply the ideas and techniques of derivatives to optimization problems. 16. Find linear approximations of functions (differentials). 17. Calculate the Riemann sum for a given function and partition. 18. Describe a definite integral as the limit of a Riemann sum. 19. Determine antiderivatives of some algebraic functions and some trigonometric functions. 20. Calculate values of definite integrals using antiderivatives and areas. 21. Use the Fundamental Theorem of Calculus to determine the derivative of an integral. 22. Use the Fundamental Theorem of Calculus to evaluate definite integrals. 23. Apply substitution techniques to integrate functions. 24. Apply the ideas of definite integrals to calculate the area of a region between curves. 25. Apply the ideas of definite integrals to calculate the volume of a solid of revolution rotated about a coordinate axis. 26. Apply the ideas of definite integrals to calculate the volume of a solid of revolution rotated about a line parallel to a coordinate axis. CALCULATORS: A graphics calculator is useful as a study and learning tool when used appropriately, but it is not essential. Calculus is a collection of ideas that is not mastered through calculator skills. No calculators are allowed on quizzes, midterms, or on the final examination.TUTORS AND MATH CENTER: Free mathematics tutoring is available at the Math Center located in 220 Boucke Building. For more information, go to the Math Center webpage. If you need extra help, a (paid) tutors list maintained by the Mathematics Department Undergraduate Office is available on-line at http://www.math.psu.edu/ug/PrivateTutorList.htm. EXAMINATIONS: Three 75-minute evening examinations will be given during the semester and a comprehensive final examination will be given during the final examination period. NO books, notes, or calculators may be used on the examinations. You must bring your University ID card to all exams. The examinations will be given from 6:30 to 7:45 PM on the following dates: Midterm Examination I Wednesday, February 4 Midterm Examination II Wednesday, March 4 Midterm Examination III Thursday, April 2 Rooms for the examinations will be announced by your instructor at a later date and may also be found on the bulletin board outside 104 McAllister. CONFLICT EXAMINATIONS: For the two mid-semester examinations, there is a conflict examination from 5:05 PM to 6:20 PM on the same night as the regular examination. Who may take the Conflict Exam? If you have a valid conflict with the regular examination time, such as a class or other scheduled activity, you may sign up for the conflict exam. How and when to sign up for the Conflict Exam. Students must sign up for the Conflict Exam in class, with your instructor, on a pink form. The student is responsible for knowing the room and time of the conflict examination. This information is on top of the pink form. Your instructor must turn in the pink form 2 class days prior to the examination date. If you have not signed up with your instructor, you will not be allowed to take the conflict exam. Instructions for Conflict Exam night. The student is responsible for knowing the room and time of the conflict examination. Students must bring their University ID to the conflict examination. The ID will be checked by the proctor. Although the conflict examination will end at 6:20 PM, no student will be permitted to leave the examination room before 6:25 PM. Any student who leaves before 6:25 PM will receive a grade of zero on the examination and will not be allowed to retake it. MAKEUP EXAMINATIONS: There will be no makeup examinations for students in Math 140A. If a student must miss the regularly scheduled examination and the conflict examination with a valid excuse, the score will be taken as the average percents of the exams surrounding that exam. For example, if a student must miss Exam 2, the average of Exam 1 and Exam 3 will be the score for