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MA 166* ANALYTIC GEOMETRY AND CALCULUS II Course Outcomes 1. Learn the basic notions used in vector algebra which are needed in their early courses in engineering and science, and which are also needed later in the development of vector calculus. [A1, A2, A3] 2. Learn techniques of integration which are needed to compute basic integrals in engineering and science. [A1, A2, A3] 3. Apply integration to compute geometric and physical quantities of importance in science and engineering. [A1, A2, A3] 4. Learn the basic ideas in sequences and series which will be needed in later studies of Fourier analysis and signal processing. [A1, A2, A3] Vectors 1. 2. 3. 4. Cartesian Coordinates Vectors in Space Dot Product Cross Product Techniques of Integration 1. Integration by Parts 2. Trigonometric Integration 3. Trigonometric Substitutions 4. Partial Fractions 5. Improper Integrals 6. L’Hopital’s Rule * Equivalent Courses: MA 162 (includes a 2nd hr. recitation) MA 173 (Accelerated option – requiring testing out of MA 165) MA 181 (Honors option – requiring testing out of MA 165) Applications of the Integral 1. Volumes by Disks and Shells 2. Length of a Curve 3. Area of a Surface 4. Work 5. Moments and Center of Gravity Sequences and Series 1. Convergence 2. Integral, Comparison, Ratio and Root Tests 3. Alternating Series and Absolute Convergence 4. Power Series and Taylor Series Curves in the Plane 1. Parametrized Curves 2. Polar Coordinates COURSE NUMBER: MA 166 COURSE TITLE: Analytic Geometry and Calculus II REQUIRED COURSE OR ELECTIVE COURSE: Required TERMS OFFERED: Fall, Spring, and Summer TEXTBOOK/REQUIRED MATERIAL: J. Stewart, Calculus, Early Transcendentals, 5th ed., Brooks/Cole Publishing Company, 2002. PRE-REQUISITES: MA 165 Analytic Geometry and Calculus I COORDINATING FACULTY: S.K. Yeung, Chair, Calculus Committee COURSE OUTCOMES: 1. Learn the basic notions used in vector algebra which are needed in COURSE DESCRIPTION: Continuation of MA 165. Vectors in two and three their early courses in engineering and science, and which are also dimensions. Techniques in integration, infinite series, polar coordinates, surfaces needed later in the development of vector calculus. (A1, A2, A3] in three dimensions. Not open to students with credit in MA 162. 2. Learn techniques of integration which are needed to compute basic integrals in engineering and science. [A1, A2, A3] ASSESSMENTS TOOLS: 3. Apply integration to compute geometric and physical quantities of 1. Daily homework importance in science and engineering. [A1, A2, A3] 2. Quizzes 4. Learn the basic ideas in sequences and series which will be needed in 3. Three one-hour exams later studies of Fourier analysis and signal processing. [A1, A2, A3] 4. Comprehensive final exam. PROFESSIONAL COMPONENT: 1. Mathematics – 4 credits (100%) RELATED ME PROGRAM OUTCOMES: A1. Math and science A2. Engineering fundamentals A3. Analytical skills NATURE OF DESIGN CONTENT: N/A COMPUTER USAGE: None COURSE STRUCTURE/SCHEDULE: 1. Lecture – 3 days per week at 50 minutes. 2. Recitation – 1 day per week at 50 minutes. PREPARED BY: A. Weitsman REVISION UPDATE: June 14, 2007