01006 Advanced Engineering Mathematics 1

01006 is the English version of the corresponding Danish course 01005 and is an obligatory two-semester course for all Civil Engineering students.

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38:34

Week 13, Long Day: Second-Order Differential…

Week 13, Long Day: Second-Order Differential Equations Part 2

From DTU Media Lab on December 3rd, 2020

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Today we investigate linear differential equations that contains both the first and second derivative of the unknown function. The coefficients to the unknown function…
51:16

Week 13, Long Day: Second-Order Differential…

Week 13, Long Day: Second-Order Differential Equations Part 1

From DTU Media Lab on December 3rd, 2020

36 plays 0
Today we investigate linear differential equations that contains both the first and second derivative of the unknown function. The coefficients to the unknown function…
39:14

Week 12: Systems of Differential Equations

Week 12: Systems of Differential Equations

From Jesper Kampmann Larsen on November 25th, 2020

34 plays 112
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…
01:00:10

Week 12: Systems of Differential Equations part 1

Week 12: Systems of Differential Equations part 1

From Jesper Kampmann Larsen on November 25th, 2020

53 plays 112
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…
56:08

Week 11, Short Day: Diagonalization by Orthogonal…

Week 11, Short Day: Diagonalization by Orthogonal Substitution

From Jesper Kampmann Larsen on November 20th, 2020

28 plays 112
We continue by investigating particular properties of symmetric matrices and their diagonalization. More precisely, what does it mean that the diagonalizing matrix is…
51:02

Week 11: Symmetric Matrices part 2

Week 11: Symmetric Matrices part 2

From Jesper Kampmann Larsen on November 18th, 2020

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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…
43:03

Week 11: Symmetric Matrices part 1

Week 11: Symmetric Matrices part 1

From Jesper Kampmann Larsen on November 18th, 2020

24 plays 0
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…
01:01:14

Week 10 Short Day: Diagonalization by Similarity…

Week 10 Short Day: Diagonalization by Similarity Transform

From Jesper Kampmann Larsen on November 13th, 2020

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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.…
45:57

Week 10 Long Day: Eigenvalues and Eigenvectors -…

Week 10 Long Day: Eigenvalues and Eigenvectors - part 2

From Jesper Kampmann Larsen on November 11th, 2020

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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…
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Week 10 Long Day: Eigenvalues and Eigenvectors -…

Week 10 Long Day: Eigenvalues and Eigenvectors - part 1

From Jesper Kampmann Larsen on November 11th, 2020

24 plays 109
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…
57:56

Week 9 Long Day: Linear First-Order Differential…

Week 9 Long Day: Linear First-Order Differential Equations (part 1)

From Jesper Kampmann Larsen on November 4th, 2020

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One of the most important mathematical tools available to engineers are differential equations and their solutions. Today we look at first order linear differential…
37:50

Week 9 Long Day: Linear First-Order Differential…

Week 9 Long Day: Linear First-Order Differential Equations (part 2)

From DTU Media Lab on November 4th, 2020

28 plays 0
One of the most important mathematical tools available to engineers are differential equations and their solutions. Today we look at first order linear differential…
52:18

Week 8 Short Day: Mapping Matrices and Change of…

Week 8 Short Day: Mapping Matrices and Change of Base

From Jesper Kampmann Larsen on October 30th, 2020

16 plays 107
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…
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Week 8, Long Day: Linear Maps (Part 1)

Week 8, Long Day: Linear Maps (Part 1)

From Jesper Kampmann Larsen on October 28th, 2020

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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.…
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Week 8, Long Day: Linear Maps (Part 2)

Week 8, Long Day: Linear Maps (Part 2)

From Jesper Kampmann Larsen on October 28th, 2020

9 plays 0
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.…
42:14

Week 7, Long Day: Vector Spaces part 2

Week 7, Long Day: Vector Spaces part 2

From Jesper Kampmann Larsen on October 21st, 2020

4 plays 0
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…

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