MTH 252 Lecture Notes - Lecture 1: Multivariable Calculus, Euclidean Vector, Scalar Multiplication
30 Aug 2016
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What you need from calc i & ii: Basic integration: power rule in reverse, u substitution, simple integration by parts. Note: free 3-d program mathematica is available for lecture note downloads. {(a,b) | a and b are real numbers} this means on a 2-d plane. Vector addition is such that (a,b) + (c,d) = (a+c, b+d) In example, (3,1) + (1,1) = (3+1,1+1) = (4,2) Similarly, if is defined as {(a,b,c) | a,b,c are real numbers} this is 3-d, but vector addition remains the same. Geometry of vector addition: vector a is drawn from the origin. Vector b is drawn from the end of vector a . The resultant vector (the vector from the previous example (4,2)) is drawn from the origin to the end of vector b , forming a triangle. Vector subtraction is such that (a,b,c) (d,e,f) = (a-d,b-e,c-f) (this works in 2-d as well) Scalar multiplication in 3-space: let r represent a real number, represents (,,)
