Lecture Notes

Lecture Notes

  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

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Importing, parsing, processing and exporting datasets