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).