Completed
- Newton's method is not good if your starting value is too far from the root
Class Central Classrooms beta
YouTube playlists curated by Class Central.
Classroom Contents
Inverses and Newton's Method in Computational Thinking - Lecture 5
Automatically move to the next video in the Classroom when playback concludes
- 1 - Introduction/Announcements
- 2 - Non-linear maps continued
- 3 - Invite to interact on Discord
- 4 - Another example of perspective projection
- 5 - Definition of a linear transformation
- 6 - Linearity relation is simply matrix times vector
- 7 - What is a matrix multiplication?
- 8 - Visual representation of how it works
- 9 - Coordinate transformations vs object transformations
- 10 - Julia: Images are arrays
- 11 - Julia: Probing a pixel
- 12 - Linking image coordinates (i,j) to spatial coordinates (x,y)
- 13 - Transforming image of a Corgi
- 14 - Function to transform xy to ij
- 15 - Creating reusable functions
- 16 - Inverse functions
- 17 - Trying different scaling
- 18 - What does inverse really do?
- 19 - Inverting non-linear transformations
- 20 - Bringing it all together
- 21 - Collisions
- 22 - Why are we doing this backwards?
- 23 - David takes over for the next part - Motivation
- 24 - What does it mean by calculating an inverse?
- 25 - Newton's method in 1D
- 26 - How does it work? - Interactive visualization using Plots.jl
- 27 - Trying the same with a new function
- 28 - What happens if we start from a different initial value?
- 29 - Newton's method is not good if your starting value is too far from the root
- 30 - Julia: Using Symbolics.jl
- 31 - Julia: Using ForwardDiff
- 32 - Perturbation to a non-linear function
- 33 - Looking back at the interactive visualization for Newton's method
- 34 - Writing the mathematical expressions behind the visualization
- 35 - Expanding via the definition of a derivative
- 36 - Obtaining a generic expression for the solution
- 37 - Julia: Implementing Newton's method in 1D
- 38 - Julia: For loop, x -= a is the same as x = x - a
- 39 - Derivatives in 2D
- 40 - Newton's method in 2D
- 41 - Changing to non-linear transformation
- 42 - Julia: Implementing Newton's method in 2D
- 43 - Julia: Use of the "\" operator
- 44 - Concluding remarks
