course content

Course Content

Mathematics for Data Analysis and Modeling

1. Basic Mathematical Concepts and Definitions

What Is Function?What Are Number Series?Sum Of Elements Of The SeriesChallenge: Calculating Sum Of Geometric ProgressionVectors And Matrices

2. Linear Algebra

Numerical Operations On Vectors and MatricesChallenge: Calculate The Matrix Multiplication ResultMatrix DeterminantScaling Factor Of The Linear TransformationChallenge: Figures' Linear TransformationsInversed And Transposed MatricesSystem of Linear EquationsChallenge: Solving The Task Using SLEEigenvalues and Eigenvectors

3. Mathematical Analysis

Derivative of the FunctionPartial Derivative of the FunctionChallenge: Solving Task Using DerivativeOptimization ProblemChallenge: Solving the Optimisation ProblemGradient Descent MethodChallenge: Optimising Function Of Multiple Variables

Mathematics for Data Analysis and Modeling

Challenge: Figures' Linear TransformationsChallenge: Figures' Linear Transformations

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Everything was clear?

Section 2. Chapter 5
toggle bottom row