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

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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…
39:14

Week 12: Systems of Differential Equations

Week 12: Systems of Differential Equations

From Jesper Kampmann Larsen on November 25th, 2020

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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

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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

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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

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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…
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…
00:00

Week 10 Long Day: Eigenvalues and Eigenvectors -…

Week 10 Long Day: Eigenvalues and Eigenvectors - part 1

From Jesper Kampmann Larsen on November 11th, 2020

0 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

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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…
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

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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…
58:18

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.…
35:09

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

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

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.…
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

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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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