Summary

Summary Everything You Need To Pass MAM1000W.

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Course
MAM1000W (MAM100W)

Institution
University Of Cape Town (UCT)

This course covers all major topics in MAM1000W, such as derivatives and integration, the applications thereof, matrices, vectors and so forth. Provided are documents of "cheat sheets" with the introduction and in-depth derivation of a topic , as well as the outlines of the specific equations, when...

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Uploaded on November 4, 2022
Number of pages 10
Written in 2022/2023
Type Summary

derivatives
limits and continuity
proof b
functions and inverse functions

Institution
University of Cape Town (UCT)
Course
MAM1000W (MAM100W)

$17.02

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VECTORS
A vector is a quantity that hasboth magnitudeanddirection
Examples are force displacement and acceleration

GEOMETRIC DESCRIPTION OF VECTORS
Suppose a particle moves along a line segment from A to B thevector y has
an initial point A thetail andterminal point B the tip and we indicate thisby
writing I AB

7

He can also combine two vectors AB and BE to have the resultantvector
AT

É To get to point c from A we can movefrompoint A
g to B with vector AB and from point B to point Cwith
vector BE
A AB Bc Ad

We now define Yeater Addition and Scalar multiplication

VECTOR ADDITION

If i and I are vectors positioned so the initialpointoff is at the terminal
ut
thenthesum Itf is the vector from the initial point of it totheterminal
port
of f

Triangle Law
II Parallelogram Law

some represent
vector P and I
SCALARMULTIPLICATION
If c is a scalar and I vector then the scalarmultiple of is thevector
whose length is c times thelength of t andwhose direction is thesameas I
it c o and is opposite to 7 if Cao
vector
If c o or to cry on The zero

, I In E É
we can now define difference of 2 vectu

DIFFERENCE OF TWO VECTORS

É T at Cf Its basically vector Addition of it and opposite
directionof F

i Est
II n

our path

COMPONENTS OF A VECTOR

If the initialpoint of a vector at at the origin of a rectanglecoordia
we place
vector at has coordinates of the form
system then the point of a
terminal
9,9
or Ca 92,93 if 30
These coordinates are called
components of a and we conte

at ya ya or at 9,9293
ya Callan
Ca ar93
n

o z
at La y
an
y
a a 92,937

Given thepoints ACK y Z and B ka gu ta the vectra with respresentation
AB is a ka ki yo y Zz t

MAGNITUDE OF A VECTOR
If a a asas then the length of a at a taita
A unitvector is avectorwithmagnitude of 1 an a as as is a unitvector
aptaita

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