Notice: This page requires JavaScript to function properly.
Please enable JavaScript in your browser settings or update your browser.Challenge: Solving the Optimisation Problem | Mathematical Analysis
Mathematics for Data Analysis and Modeling
course content

Contenido del Curso

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

Tarea

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.

Tarea

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.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 3. Capítulo 5
toggle bottom row

Challenge: Solving the Optimisation Problem

Tarea

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.

Tarea

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.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 3. Capítulo 5
toggle bottom row

Challenge: Solving the Optimisation Problem

Tarea

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.

Tarea

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.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Tarea

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.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
Sección 3. Capítulo 5
Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
We're sorry to hear that something went wrong. What happened?
some-alt