FIZ228_LectureNotes.md

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Lecture Notes

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1. Importing, parsing, processing and exporting datasets
   • Usage of the Pandas library to import data from CSV files
   • Working with Pandas dataframe
   • Case Study: Processing a Meteorological Dataset
2. Visualization of datasets
   • Showcase of the Seaborn plotting library
3. Least Squares Method & Error Estimations
   • Case Study: Free Fall
   • Types of Error Estimations
   • Fitting through minimization of least squares error
   • Coefficient of Determination ($r^2$)
   • scipy.optimize.minimize, numpy.linalg.lstsq, scipy.linalg.lstsq, scipy.optimize.least_squares,
4. Regression
   • Case Study: Drag Force
   • Least-squares Method
   • Adaptation of the Least-squares to non-linear models
   • Case Study: FTIR data of Silica
   • np.polyfit, scipy.optimize.curve_fit
5. Interpolation
   • Polynomial Interpolation
   • Newton Interpolating Polynomials
   • Lagrange Interpolating Polynomials
   • Inverse Interpolation
   • Bonus: Finite Difference Method
   • Example: Heat distribution of a rod with boundary conditions
   • Polyfit, poly1d, polyval and poly + roots
6. Minimization & Optimization
   • Single variable function
   • Multi-variate function
   • Minimization with constraints
   • Example: Heron's Formula for Triangle's Area
   • Gradient Descent Algorithm
   • Case Study: 2 Springs, 1 Mass, 1 Side
7. Clustering and Classification
   • Advantages of Clustering
   • k-means Clustering
8. Ordinary Differential Equations
   • Finite Difference Method
   • Euler's Method
   • Runge-Kutta Method (4th order: RK4)
   • ODEs with initial conditions
   • ODEs with boundary conditions