MAT 211- Midterm Exam Guide - Comprehensive Notes for the exam ( 20 pages long!)
Document Summary
Math 211 table of contents: functions of several variables. Applications: best a ne approximations, optimization, lagrange multipliers, conservation of energy, functions of several variables. The cartesian product of s and t is the set of ordered pairs: S t := {(s, t) | s s, t t}. Notation: if (s, t) w , we write f (s) = t. the subset w , which is by de nition the function f , is also called the graph of f . Let f : s t and g: t u . The composition of f and g is the function g f : s u given by (g f )(s) := g(f (s)). Rn is the cartesian product of r with itself n times. We think of rn as the set of ordered n-tuples of real numbers: , an) | ai r, 1 i n}. The elements of rn are called points or vectors.
