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MA 261 Lecture 1

by: Viktoryia Zhuleva

MA 261 Lecture 1 MA 26100

Viktoryia Zhuleva
GPA 3.0
Multivariable Calculus
Patricia E Bauman

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About this Document

The first lecture of calc III at Purdue, spring 2016.
Multivariable Calculus
Patricia E Bauman
Class Notes
Math, Calculus, AP Calculus BC, Purdue
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This 2 page Class Notes was uploaded by Viktoryia Zhuleva on Friday January 15, 2016. The Class Notes belongs to MA 26100 at Purdue University taught by Patricia E Bauman in Fall 2015. Since its upload, it has received 297 views. For similar materials see Multivariable Calculus in Applied Mathematics at Purdue University.

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Date Created: 01/15/16
Lecture 1 Review 1 Graphing A point P x0 yo 20 in space is graphed on the coordinate system 2 Finding distance between points Example P l 2 4 and Q l 2 3 PQ J1 122 224 32 V016 2W 3 Sphere equation x x02 y yo2 z 202 r2 1 Figure 1 Figure in space Vectors in Space They are determined by their magnitude and direction For example displacement vector pointing from point A l l 2 to point B 2 4 3 49 a ma Vectors in 3 dimentional Figure 2 Sphere space are 39 denoted as a lt a1 a2 a3 gt Vectors in plane 2D are denoted as a lt a1 all gt instead ofci lt a1 a1 0 gt x Vector operations Figure 3 Distance between points Let a lt a1a2a3 gt and lt b1b2b3 gt Sum a13 lt a1 b1a2 b2a3 b3 gt Diff ci 1 lt a1 b1a2 b2a3 b3 gt Figure 4 Vector sum Figure 5 Vector difference Multiplication by constant c d lt c al C a2 c a3 gt If C gt 0 then the resulting vector will have same direction and will be c times as long If C lt 0 then the resulting vector will have an opposite direction and will be c times as long Two vectors are parallel if the ratios of their vector components are equal Let a lt a1 a2 a3 gt and I lt 191192193 gt If an then b1 b2 b3 Unit vectors are vectors with length l and if a at O a unit vector in the direction of a is I d Dot pIOdUCt Let a lt 611612613 gt and lt 191192193 a 39 I 11191 12192 13193 Also a I a bcos6 If one vector is perpendicular orthogonal to another their dot product is zero because cosine of is zero 3i X B a bsin0 Cross product of the vectors is equal to the product of their magnitudes times the cosine of the angle between them Cross product calculation using matrix a lt x y z gt gt bltmlkgt 39 i y z x z x y x 3 Z ll k m k k m l lyk lz 1xk mzxl my 2 yk lz xk mz xl my Rule cross product of vectors is perpendicular to original vectors


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