Computer methods in engineering

About this repository

This repository contains materials for the course TPG4155 - Computer Methods in Engineering. All material is stored as jupyter notebook files. Please install jupyter notebook from the jupyter website if you want to run the Python codes on your own.

Content

Introduction

Differential equations

• Ordinary differential equations - Exercise (Solution)
• Partial differential equations - Exercise (Solution)
  • Elliptic equations (Laplace equation) - Exercise (Solution)
  • Parabolic equations (heat equation/diffusivity equation)
  • Hyperbolic equations (wave equation)
    • Wave equation 2D - Exercise (Solution)

Optimization

• Introduction
• Bracket search - Exercise (Solution)
• Gradient methods (local)
  • Gradient descent
  • Conjugate gradient method - Exercise (Solution)
  • LU decomposition
• Derivative-free optimization (global)
  • Pattern search
  • Nelder-Mead - Exercise (Solution)
  • Simulated Annealing
  • Evolutionary algorithms
    • Genetic algorithm
    • Particle swarm optimization
• Automatic differentiation

Machine learning

• Neural networks
• Clustering and Classification algorithms
  • K-means algorithm
  • Support vector machine
  • Decision Trees
• Dimensionality reduction

Exercises

• Exercise 1
  • Solution 1
• Exercise 2
  • Solution 2
• Exercise 3
  • Solution 3
• Exercise 4
  • Solution 4
  • wave1d
• Exercise 5
  • Solution 5
• Exercise 6
  • Solution 6
• Exercise 7
  • Solution 7
• Exercise 8
  • Solution 8
  • Solution-code
• Exercise 9
  • Solution 9