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39:14 Week 12: Systems of Differential Equations Week 12: Systems of Differential Equations	Week 12: Systems of Differential Equations 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 individually? Today we shall… From Jesper Kampmann Larsen on November 25th, 2020 0 plays 112
01:00:10 Week 12: Systems of Differential Equations part 1 Week 12: Systems of Differential Equations part 1	Week 12: Systems of Differential Equations part 1 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 individually? Today we shall… From Jesper Kampmann Larsen on November 25th, 2020 0 plays 112
56:08 Week 11, Short Day: Diagonalization by Orthogonal… Week 11, Short Day: Diagonalization by Orthogonal Substitution	Week 11, Short Day: Diagonalization by Orthogonal Substitution We continue by investigating particular properties of symmetric matrices and their diagonalization. More precisely, what does it mean that the diagonalizing matrix is positive orthogonal. At the end… From Jesper Kampmann Larsen on November 20th, 2020 0 plays 112
51:02 Week 11: Symmetric Matrices part 2 Week 11: Symmetric Matrices part 2	Week 11: Symmetric Matrices part 2 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 us the opportunity to… From Jesper Kampmann Larsen on November 18th, 2020 0 plays 0
43:03 Week 11: Symmetric Matrices part 1 Week 11: Symmetric Matrices part 1	Week 11: Symmetric Matrices part 1 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 us the opportunity to… From Jesper Kampmann Larsen on November 18th, 2020 0 plays 0
01:01:14 Week 10 Short Day: Diagonalization by Similarity… Week 10 Short Day: Diagonalization by Similarity Transform	Week 10 Short Day: Diagonalization by Similarity Transform 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. Today we investigate the… From Jesper Kampmann Larsen on November 13th, 2020 0 plays 109
45:57 Week 10 Long Day: Eigenvalues and Eigenvectors -… Week 10 Long Day: Eigenvalues and Eigenvectors - part 2	Week 10 Long Day: Eigenvalues and Eigenvectors - part 2 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 zero-vector), whose image vector is… From Jesper Kampmann Larsen on November 11th, 2020 0 plays 0
00:00 Week 10 Long Day: Eigenvalues and Eigenvectors -… Week 10 Long Day: Eigenvalues and Eigenvectors - part 1	Week 10 Long Day: Eigenvalues and Eigenvectors - part 1 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 zero-vector), whose image vector is… From Jesper Kampmann Larsen on November 11th, 2020 0 plays 109
52:18 Week 8 Short Day: Mapping Matrices and Change of… Week 8 Short Day: Mapping Matrices and Change of Base	Week 8 Short Day: Mapping Matrices and Change of Base 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 basis is changed in the domain… From Jesper Kampmann Larsen on October 30th, 2020 0 plays 107
58:18 Week 8, Long Day: Linear Maps (Part 1) Week 8, Long Day: Linear Maps (Part 1)	Week 8, Long Day: Linear Maps (Part 1) 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. We shall investigate how known… From Jesper Kampmann Larsen on October 28th, 2020 0 plays 0
35:09 Week 8, Long Day: Linear Maps (Part 2) Week 8, Long Day: Linear Maps (Part 2)	Week 8, Long Day: Linear Maps (Part 2) 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. We shall investigate how known… From Jesper Kampmann Larsen on October 28th, 2020 0 plays 0
42:14 Week 7, Long Day: Vector Spaces part 2 Week 7, Long Day: Vector Spaces part 2	Week 7, Long Day: Vector Spaces part 2 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 likely experience that… From Jesper Kampmann Larsen on October 21st, 2020 4 plays 0
54:51 Week 7, Long Day: Vector Spaces part 1 Week 7, Long Day: Vector Spaces part 1	Week 7, Long Day: Vector Spaces part 1 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 likely experience that… From Jesper Kampmann Larsen on October 21st, 2020 9 plays 0
01:29:14 Week 6, Short Day: Geometry in the Plane and in… Week 6, Short Day: Geometry in the Plane and in Space	Week 6, Short Day: Geometry in the Plane and in Space Today we continue to manage concepts such as linear combinations, linear independence, basis and coordinates. The day will also cause a repetition of knowledge from highschool about vectors in… From Jesper Kampmann Larsen on October 9th, 2020 26 plays 76
56:21 Week 6, Long Day: Determinants and Vector… Week 6, Long Day: Determinants and Vector Geometry (Part 1)	Week 6, Long Day: Determinants and Vector Geometry (Part 1) To every square matrix a special number - called the determinant - is attached. How do you compute this number, and what does the number say about the matrix? Today we start with these questions and… From Jesper Kampmann Larsen on October 7th, 2020 25 plays 0
49:04 Week 6, Long Day: Determinants and Vector… Week 6, Long Day: Determinants and Vector Geometry (Part 2)	Week 6, Long Day: Determinants and Vector Geometry (Part 2) To every square matrix a special number - called the determinant - is attached. How do you compute this number, and what does the number say about the matrix? Today we start with these questions and… From Jesper Kampmann Larsen on October 7th, 2020 32 plays 74