-
So far we have only considered first-order differential equations. This week we will step it up to second-order differential equations where both first and second…
-
In a previous week we worked with first-order linear differential equations. It is very common to have not just one but several of such differential equations. If they…
-
From DTU Media Lab
We will continue the topic from Wednesday by investigating particular properties of symmetric matrices and their possibility of diagonalization. More precisely, what… -
The concept of scalar product, popularly known as the dot product, gives us the opportunity to generalize concepts from 2D and 3D geometry such as length and angle. With…
-
From Georgi Yankov
If a square matrix is similar to a diagonal matrix, it is said to be diagonalizable via a similarity transformation. This is closely connected to the eigenvalue problem.… -
When a linear map f:V→V maps a vector space into itself, then it could happen that some (proper) vectors (i.e. non-zero vectors) have images that are identical to…
-
One of the most important mathematical tools available to engineers are differential equations and their solutions. Many phenomena from the real world can be described…
-
From DTU Media Lab
We will today continue our work with linear maps and their mapping matrices and we will study typical examples of how to determine their kernels and images. An important… -
A function y=f(x) attaches to every real number x a real number y. This is called a map! Today’s topic is linear maps where this idea is expanded to vector inputs…
-
Today we will work with vector spaces in more general forms. Vector spaces are sets of widely different mathematical objects that have some decisive properties in…
-
From Georgi Yankov
Today we continue with concepts such as linear combinations, linear independence, basis and coordinates. Our subjects will also involve some repetition of knowledge from… -
To every square matrix we define a special number called the determinant. How do you compute this number, and what does the number say about the matrix? Today we will…
-
From DTU Media Lab
Today we will continue with systems of linear equations and in particular matrix algebra. Parts of today’s work concerns a special case of a matrix called a square… -
Today we will be working with systems of equations. We are already more than capable of solving single linear equations, but systems of them can quickly be a time…
-
In highschool you have - maybe without realising it - worked with the approximating polynomial of the first degree. Its graph is a straight line which is the tangent to…
-
From Georgi Yankov
Polynomials are central to complex numbers. It all started with polynomials. Why do certain polynomials have roots, and which rules apply to the question of how many…