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Lecture Notes - Dynamics MAM1044H (2021) - Notes
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  • Course
  • MAM1044H (MAM1044H)
  • Institution
  • University Of Cape Town (UCT)

Syllabus Notes for First-Year, Dynamics MAM1044H Course! All Summaries and Important Parts, Detailed and In-Depth. Excludes Dynamics Section, but includes all Vector Manipulation, Eigenvalue Problems, Matrices, etc.

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Document information

  • December 1, 2021
  • 61
  • 2021/2022
  • Class notes
  • Daniel burger
  • Excluding dynamics

Subjects

  • 2021
  • mam1044h
  • applied mathematics
  • dynamics
  • uct
  • university of cape town

Written for

  • University of Cape Town (UCT)
  • MAM1044H (MAM1044H)
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, Definitions
Vector
Quantity that is characterised by both magnitude and
direction, and any object lives in a vector space.


Scalar
Quantity that is only characterised by magnitude, and does
not depend on the orientation of the coordinate axes.


Translation Invariance
Geometric property to be unaffected by a shift of the origin
of a coordinate system.


Vector Field
A vector that does depend on where in space it is, and has
components that are functions of position, such as electric
field at a point.


Isotropic
Looks the same in any direction we look.


Vector Space

, Vectors
Vector Representation
Geometrically, as an arrow in space.

Algebraically, in terms of its components. (𝐴𝐴𝑥𝑥 , 𝐴𝐴𝑦𝑦 ) are the
projections of 𝐴𝐴 onto the 𝑥𝑥- and 𝑦𝑦-axes.




�����⃗
A vector connecting two points: 𝐴𝐴𝐴𝐴
Length equal to the length of the line segment [𝐴𝐴𝐴𝐴].


- Vector Equality
�⃗ = 𝑊𝑊
Vectors with the same length and direction: 𝑉𝑉 ���⃗ .



- Vector Operations
Scalar Multiplication (shrinks/extends)

Vector Addition
The Triangle Rule

, Vector Addition is commutative:




Translation Invariance
Geometric property to be unaffected by a shift of the origin
of a coordinate system.

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