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From DTU Media Lab on December 3rd, 2020
Today we investigate linear differential equations that contains both the first and second derivative of the unknown function. The coefficients to the unknown function… -
From DTU Media Lab on December 3rd, 2020
Today we investigate linear differential equations that contains both the first and second derivative of the unknown function. The coefficients to the unknown function… -
From Jesper Kampmann Larsen on November 25th, 2020
We have already worked with first-order linear differential equations. But what if there are more differential equations, and they are coupled, so they cannot be solved… -
From Jesper Kampmann Larsen on November 25th, 2020
We have already worked with first-order linear differential equations. But what if there are more differential equations, and they are coupled, so they cannot be solved… -
From Jesper Kampmann Larsen on November 20th, 2020
We continue by investigating particular properties of symmetric matrices and their diagonalization. More precisely, what does it mean that the diagonalizing matrix is… -
From Jesper Kampmann Larsen on November 18th, 2020
The starting point for talking about orthogonal vectors in Rn and orthogonal matrices in Rn×n is the scalar product, popularly known as the dot product. This gives… -
From Jesper Kampmann Larsen on November 18th, 2020
The starting point for talking about orthogonal vectors in Rn and orthogonal matrices in Rn×n is the scalar product, popularly known as the dot product. This gives… -
From Jesper Kampmann Larsen on November 13th, 2020
If a square matrix is similar to a diagonal matrix, it is said to be diagonalizable by a similarity transformation. This is closely connected to the eigenvalue problem.… -
From Jesper Kampmann Larsen on November 11th, 2020
When you investigate a linear map f:V→V of a vector space into itself a special question arises: Is there proper vectors (i.e. vectors different from the… -
From Jesper Kampmann Larsen on November 11th, 2020
When you investigate a linear map f:V→V of a vector space into itself a special question arises: Is there proper vectors (i.e. vectors different from the… -
From Jesper Kampmann Larsen on November 4th, 2020
One of the most important mathematical tools available to engineers are differential equations and their solutions. Today we look at first order linear differential… -
From DTU Media Lab on November 4th, 2020
One of the most important mathematical tools available to engineers are differential equations and their solutions. Today we look at first order linear differential… -
From Jesper Kampmann Larsen on October 30th, 2020
We continue to work with linear maps and their mapping matrices and we shall study typical examples on how you can determine their kernel an images. Important: When the… -
From Jesper Kampmann Larsen on October 28th, 2020
You know elementary functions y=f(x) that to every real number x attaches a real number y. Todays subject is linear maps y=f(x) that to a vector x attaches a vector y.… -
From Jesper Kampmann Larsen on October 28th, 2020
You know elementary functions y=f(x) that to every real number x attaches a real number y. Todays subject is linear maps y=f(x) that to a vector x attaches a vector y.… -
From Jesper Kampmann Larsen on October 21st, 2020
Today we shall work with general vector spaces. Vector spaces are sets of widely different mathematical objects, that have some decisive properties in common. You should…