Directional Derivative — Gradient
And More: Double & Triple Derivative & Chain Rule in Python :) — #PySeries#Episode 26
Hi, This time, Double & Triple Derivative & Chain Rule & grads in Python!
Again, Geogebra will be our secret!
Let’s jump to a fresh Colab Notebook and please answer these 8 questions (or open this Colab notebook right away:)
01 PyEx — Python — Double Integration
Double integrate:
02 PyEx — Python — Double Integration
Double integrate:
03 PyEx — Python — Double Integration
Double integrate:
04 PyEx — Python —Triple Integration
Triple integrate:
05 PyEx — Python — Area Between Circumferences
Calculate the area between the circumferences (Use Double integral):
06 PyEx — Python — Differentiation By Chain Rule
Use Chain Rule to Differentiate this function by hand:)
07 PyEx — Python — Differentiation By Chain Rule
Use Chain Rule to Differentiate this function by hand:)
08 PyEx — Python — Gradient — Directional Derivative
Gradient — Curl (from https://docs.sympy.org/latest/modules/vector/fields.html)
A curl is a mathematical operator that describes an infinitesimal rotation of a vector in 3D space.
The direction is determined by the right-hand rule (along the axis of rotation), and the magnitude is given by the magnitude of rotation.
In the 3D Cartesian system, the curl (or Gradient of scalar field) of a 3D vector F , denoted by ∇×F is given by:
The Del, or ‘Nabla’ operator — written as ∇ is commonly known as the vector differential operator. Depending on its usage in a mathematical expression, it may denote the gradient of a scalar field, the divergence of a vector field, or the curl of a vector field.where Fx denotes the X component of vector F.
So
Calculate Gradient - Directional Derivative:
That’s All for this lecture!
See you in the next Python Episode!
See answer below!
Bye!!!!
Colab File link:)
Google Drive link:)
Geogebra Solution link:)
Video link:)
Credits & References
Directional derivative by en.wikipedia.org
https://www.geogebra.org/m/VKU7BrFK
Scalar and Vector Field Functionality by docs.sympy.org
introduction of the divergence of a vector field by auckland.figshare.com
A Guided Tour of Mathematical Physics by physics.bgu.ac.il
Directional derivative and gradient examples by mathinsight.org
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26Episode#PySeries — Directional Derivative — Gradient — And More: Double & Triple Derivative & Chain Rule in Python (this one)
