MA 261* MULTIVARIATE CALCULUS Course Outcomes 1. Students develop the concepts of vector calculus which are needed in the studies of many areas of engineering and science such as dynamics and electromagnetic field theory. These include properties of the gradient of a scalar field, line and surface integration, and Green’s Theorem. [A1, A2, A3] 2. Students learn how to apply calculus techniques in elementary problems of optimization in several variables. [A1, A2, A3] 3-D Analytic Geometry 1. Angle Between Two Vectors 2. Scalar Plot 3. Cross Product 4. Planes, Lines, Surfaces 5. Curves in 3-D Space Partial Differentiation 1. Functions of Several Variables 2. Partial Derivatives 3. Differential of a Function of Several Variables 4. Partial Derivatives of a Higher Order 5. Chain Rule 6. Extreme Value Problems 7. Directional Derivatives 8. Gradient 9. Implicit Functions and LaGrange Multipliers Multiple Integrals 1. Double Integrals 2. Iterated Integrals - rectangular coordinates - polar coordinates 3. Surface Integrals 4. Triple Integrals - rectangular coordinates - cylindrical coordinates - spherical coordinates Integration of Vector Fields 1. Vector Fields 2. Line and Surface Integrals 3. Independence of Path and Potential Functions 4. Green’s Theorem 5. Divergence Theorem * Equivalent to: MA 174 (Accelerated option) MA 182 (Honors option – requires MA 181)COURSE NUMBER: MA 261 COURSE TITLE: Multivariate Calculus 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 162 Plane Analytic Geometry and Calculus II, or MA 166 Analytic Geometry and Calculus II COORDINATING FACULTY: S,K Yeung, Chair, Calculus Committee COURSE DESCRIPTION: Planes, lines, and curves in three dimensions. Differential calculus of several variables; multiple integrals. Introduction to vector calculus. Not open to students with credit in MA 174 or MA 271. ASSESSMENTS TOOLS: 1. Daily homework 2. Quizzes 3. Three one-hour exams 4. Comprehensive final exam. COURSE OUTCOMES: 1. Students develop the concepts of vector calculus which are needed in the studies of many areas of engineering and science such as dynamics and electromagnetic field theory. These include properties of the gradient of a scalar field, line and surface integration, and Green’s Theorem. [A1, A2, A3] 2. Students learn how to apply calculus techniques in elementary problems of optimization in several variables. [A1, A2, A3] PROFESSIONAL COMPONENT: 1. Mathematics – 4 credits (100%) 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. RELATED ME PROGRAM OUTCOMES: A1. Math and science A2. Engineering fundamentals A3. Analytical skills PREPARED BY: A. Weitsman REVISION UPDATE: June 14,