Basic Maths Assignment

Divergence:

• The term divergence is used to indicate the variation of flow field (i.e. Flow field like Velocity field) at a point in a system. It is a vector quantity.
• The Divergence of a flow field may be positive or negative (i.e. the divergence is positive if the vector direction of flow field is outwards, divergence is negative if the vector direction of flow field is inwards.

Gradient:

• Gradient of a line is also called as slope of a line. It tells us how steep the line is. The higher the gradient of a line, higher is its steep.
• Gradient of a line is typically found by, (change in Y-coordinates) / (Change in X-coordinates).
• While it is easy to find the gradient of a line by picking two points on the line in the graph, there needs some additional step in order to find the gradient of a curve. Thus, to find the gradient of a curve at a point, one has to draw a tangent from that point, and then the curve’s gradient is calculated with the coordinates of that point on the curve and the coordinates of a point on the tangent.

Curl:

• Curl describes the rotation of a vector field in a three dimensional space.
• It has direction of rotation and magnitude of rotation.
• When a vector field has zero rotation then it is called as irrotational in Fluid dynamics.

Rank of a Matrix:

• Rank of a matrix is the maximum number of linearly independent column vectors or linearly independent row vectors in a matrix
• Consider a m x n matrix,
  if m is less than n, then the maximum rank of the matrix is n
  if n is less than m, then the maximum rank of the matrix is m
• Here, linearly independent vector denotes a column or row vector which is not a scalar multiple of another column or row vector.
  
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