We solve partial differential equations (PDE’s) using Fourier transformation methods using the heat and wave equation as examples.
In addition we explore using Matlab for data science on an example of predicting a cars fuel efficiency from features like its horsepower and weight.
This week we will pick up from previous lectures on differential equations and use the Fourier series to solve ordinary differential equations (ODEs).
We continue programming in Matlab considering classical computational algorithms for root finding and optimization.
Week 9 features programming in Matlab using loops, conditional statements and map-containers.
Lecture 8 featuring the discrete (and fast) Fourier transformation.
Feedback control systems (PID) using Laplace transformations.
Laplace transformation. Derivations and application to circuits.
This week we are looking at solving ordinary differential equations (ODE) and investigate a simple climate model
Last week we used PCA to make recommendations to users for artists. For our small data with many missing ratings (NaN) made it difficult to derive stable recommendations. One way to deal with this situation is to use PCA first to generate lower dimensional user and artist factors, but then use another model to make rating predictions based on the user specific factors. Below are two scripts that use the Matlab regression tree function to make predictions based on two PDA factors. One is keeping the unknown ratings as is, the other replaces those ratings with the average rating before generating PCA factors.