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numerical-methods's Introduction

Contains all of the assignments of the course Numerical Methods Course during M1-Paris Physics Master

Kindly note when I did these Assignments, my programming skills were not very good. My programming skills have advanced a lot since then. Kindly see my latest projects: General Machine Learning Capabilities or Computer Vision

1 Numbers, Approximations, Errors & Linear Regression

  • Smallest Number
  • Biggest Number
  • Machine Precision
  • Subtractive Cancellation
  • Linear Regression - Solar Wind Data

2 Root Finding

  • Bisection Method
  • False Position Method
  • Newton-Raphson Method
  • Secant Method
  • Modified Secant Method

3 Numerical Integration

  • Left Rule
  • Right Rule
  • Midpoint Rule
  • Composite Simpson Rule
  • Trapezoidal Rule
  • Improper Integrals
  • Monte carlo

4 Ordinary Differential Equations

  • Euler Method
  • Modified Euler Method
  • Orbit of Moon (Using Modified Euler Method)
  • Orbit of Moon (Using RK4 Method)
  • Implicit Euler Method (Free Fall in a Viscous Fluid)

5 Gravity problem with RK5 Method

  • Orbit of EARTH (RK5 Method)
  • Adaptive step-size RK5 Solver
  • Orbit of Earth

6 Partial Differential Equations

  • 1D Linear Convection Equation

7 Partial Differential Equations 2

  • 1D Heat Diffusion Equation
  • Conductive Heat Transfer: Case of a window, with and without an air layer

8 Minimization

  • Simple Bisection Method
  • Parabolic Bisection Method
  • Fitting a mathematical model to data
  • 2D Minimization

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