MATH 1920 Lecture Notes - Lecture 1: Standard Basis, Unit Vector, Linear Combination

• School: Cornell University
• Department: Mathematics
• Course: MATH 1920
• Professor: Andrew Sale

Document Summary

In calculus i and ii: f: d -> (function takes a value x from its domain and outputs a value in the real numbers) In multivariable calculus: f: -> n (functions are mapped onto any dimensional space) f: n -> m (functions are generalized to another dimension) 13. 1/13. 2 vectors in 2 (two dimensions) and 3 (three dimensions) 2 vectors: (a, b) a, b . 3 vectors: (a, b, c) a, b, c . A vector v has both magnitude/length/norm and direction. Length: ||pq|| = (32 + 32) = 3 2. Definition: a position vector is a vector with a specified base point at the origin. We can think of n as the space of an n-dimensional position vector. Commutative law: u + v = v + u u v u = v = u + v =