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MULTIVARIATE ANALYSIS (21-256) SPRING 2017 Instructor: Dr. Dana Mihai, 8128 Wean Hall [email protected]Lecture: Lecture 1: MWF, Wean 7500, 1:30-2:20 pm Lecture 2: MWF, BH A53, 3:30-4:20 pm Course website: Office hours: Posted on Blackboard LEARNING OBJECTIVES These objectives should help you understand the level of preparation you should achieve in this class. After completing this course, you should be able to: •Solve mathematical models accurately (either given or that you have to determine from a word/applied problem) by using multivariate analysis techniques. •Solve multistep problems, be familiar with all formulas, definitions, theorems, and have a thorough understanding of how they have been derived •Interpret and analyze the results in the context of the problem (for example, the significance of the value of the Lagrange multiplier, the value and sign of a derivative). •Explore a given problem by using analytical and graphical methods. •Apply the concepts and techniques learned to new situations and problems. •Recognize situations in which multivariate analysis concepts can be applied to mathematics, economics, statistics, biology (or other fields), and identify which concepts and techniques are necessary to solve a specific problem. COURSE DESCRIPTION Multivariate Analysis is a course designed to help students acquire the mathematical concepts and analytical skills needed for other courses in mathematics, economics, and statistics. Students will be exposed to a variety of topics (see below) that typically occur in these areas, and will be expected to present their work in a concise, complete and logical manner. This course is NOT equivalent to a typical multidimensional course (Calculus in three dimensions, for example) due to the linear algebra module and some of the optimization topics. Topics: Vectors, dot product, cross product; Elements of Linear algebra: span, linear dependence and independence; matrices, determinants, inverses, systems of equations. Lines and planes. Functions of several variables, differentiation, linear and quadratic approximation, directional derivatives, optimization (unconstrained and constrained), Hessian and positive definite matrices, Lagrange multipliers. Multiple integration: iterated integrals; applications.
PREREQUISITES: 21-112 or 21-120 (You are expected to be familiar with differentiation and integration techniques, solving systems of linear and nonlinear equations in several variables, and, in general Calculus of functions of one variable. Lack of familiarity with these topics can have a significant impact on your performance in this course ) . The prerequisites cannot be void. TEXTS: Calculus-Early Transcendentals, by James Stewart, 8th Edition (with Enhanced Webassign).