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Numerical Methods and Machine Learning for Differential Equations with Applications in Python

Ch01- Euler Method

Ch02- Taylor Methods

Ch03- Runge Kutta Methods

Ch04- Multistep Methods

Ch05- Consistency, Convergence and Stability

Initial Value Problems Review Questions

Ch06- Boundary Value Problems

Linear Shooting Method
Non-Linear Shooting Method
Finite Difference Method
Problem Sheet 6 - Systems of Equations and Boundary Value Problems
- Finite Difference Method

Ch07- Integrate and Fire Example

Ch08- Introduction to Artificial Neural Networks

Introduction to Newton Raphson
- Two Variable Newton Raphson
- Cost Function Newton-Raphson
McCulloch-Pitts Neuron
Gradient Descent
Problem Sheet 8

Ch09- Universal Approximation Theorem and Backpropagation

One Node Back Propagation ReLU
The Universal Approximation Theorem (UAT)
- Universal Approximation Theorem in Action
Vector Form of Back Propagation
- General Back Propagation for a Deep ANN
- Backpropagation Strengths, Weaknesses and Pitfalls
Problem Sheet 9

Ch10 - ANNs and Differential Equations

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By John S Butler