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Mathematics for Data Analysis and Modeling
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Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

1. Basic Mathematical Concepts and Definitions
What is a 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

Challenge: Solving the Optimisation Problem

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Все було зрозуміло?

Секція 3. Розділ 5
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Challenge: Solving the Optimisation Problem

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Все було зрозуміло?

Секція 3. Розділ 5
toggle bottom row

Challenge: Solving the Optimisation Problem

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Все було зрозуміло?

Завдання

Let's consider a physics-related optimization problem where we need to find the maximum height reached by an object thrown vertically upward with a given initial velocity.

We have the following equation:
h = v * t - 0.5 * g * t**2
that describes the motion of an object.

Our task is to find the time t when the object reaches its maximum height and then find the maximum height h_max.

  1. Calculate the derivatives of the first and second order for the h function.
  2. Find critical points of h function.
  3. Check if these critical points are points of the maximum of the function h.

Секція 3. Розділ 5
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