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Coordinate Systems in 3 Dimensions: A Basic Introduction, Lecture notes of Mathematical Analysis

A basic introduction to coordinate systems in three dimensions. It covers the concept of coordinate axes, coordinate planes, and the distance formula in 3d space. The document also includes examples of how to represent surfaces in 3d space using equations. It is suitable for students who are new to the concept of 3d coordinate systems and need a basic understanding of the topic.

Typology: Lecture notes

2023/2024

Uploaded on 12/25/2024

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bg1
WEEK 4LECTURE 1
AY word
EEm
yfarad
Rage
el
a
coordinate axes
y
3dim coordinate system
axes Xaxis
nZ
I1
Htt
FE t.az WEaa
CT
xfloor
coordinate planes Xy plane
xy IEe
Pca bIz cord
xlaoid.ly cooed
pf3
pf4
pf5

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WEEK (^4) LECTURE (^1)

AY

word EEm y farad Rage el a coordinate (^) axes y

3 dim coordinate

system

axes X^ axis nZ I 1 Htt FE t.az WEaa CT x floor coordinate planes Xy^ plane xy I^ Ee Pca b Iz (^) cord xlaoid.ly (^) cooed

y Distance between^ two^ points in^3 dim^ coord^ system 379 PCq bi g (^) PzCaz (^) ez notation 11PaPall a^ distance^ between^ Pa and (^) Pz tee Remember in^2 dimensions Pecane^ Blazeee q f^ e HP^ Pak (^) VCaz 95 t^ s^95 Example What^ surfaces in^ 1123 are represented (^) by the following equations e z^5 2 x y 3 Z^ e^ X Z 4 x't^ ya g

5 Hi

y E (^16)

g

Tyg

2 a^ XZ AZ (^) in (^2) dimensions

x4y2 g^ Play z satisfying the constraint x2ty 9 2 n (^) in 2 dimensions

ny

Answer cylinder I

q

i

n

Cx 05 4 05 (^2 0 )

npcxiyihyq.gg

zoj

I PK

y

E and^ 06, T Answer sphere of^

radius 4

centered at 0

Next time^ what^ surface in^ 1123 is (^) represented by

the

equation (^2) Ft y