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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02:02:28

Week 13 - Long Day: Second-Order Differential…

Week 13 - Long Day: Second-Order Differential Equations

From Steeven Hegelund Spangsdorf

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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…
02:02:52

Week 12 - Long Day: Systems of Differential…

Week 12 - Long Day: Systems of Differential Equations

From Steeven Hegelund Spangsdorf

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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…
01:01:58

Week 11 - Short Day: Diagonalization by…

Week 11 - Short Day: Diagonalization by Orthogonal Substitution

From DTU Media Lab

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We will continue the topic from Wednesday by investigating particular properties of symmetric matrices and their possibility of diagonalization. More precisely, what…
02:01:30

Week 11 - Long Day: Symmetric Matrices

Week 11 - Long Day: Symmetric Matrices

From Steeven Hegelund Spangsdorf

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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…
01:00:55

Week 10 - Short Day: Diagonalization by…

Week 10 - Short Day: Diagonalization by Similarity Transformation

From Georgi Yankov

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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.…
02:04:14

Week 10 - Long Day: Eigenvalues and Eigenvectors

Week 10 - Long Day: Eigenvalues and Eigenvectors

From Steeven Hegelund Spangsdorf

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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…
02:00:44

Week 9 - Long Day: Linear First-Order…

Week 9 - Long Day: Linear First-Order Differential Equations

From Steeven Hegelund Spangsdorf

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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…
01:01:04

Week 8 - Short Day: Mapping Matrices and Change…

Week 8 - Short Day: Mapping Matrices and Change of Basis

From DTU Media Lab

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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…
02:01:02

Week 8 - Long Day: Linear Maps

Week 8 - Long Day: Linear Maps

From Steeven Hegelund Spangsdorf

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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…
02:02:14

Week 7 - Long Day: Vector Spaces

Week 7 - Long Day: Vector Spaces

From Steeven Hegelund Spangsdorf

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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…
01:03:30

Week 6 - Short Day: Geometry in the Plane and in…

Week 6 - Short Day: Geometry in the Plane and in 3D Space

From Georgi Yankov

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Today we continue with concepts such as linear combinations, linear independence, basis and coordinates. Our subjects will also involve some repetition of knowledge from…
02:03:08

Week 6 - Long Day: Determinants and Vector…

Week 6 - Long Day: Determinants and Vector Geometry

From Steeven Hegelund Spangsdorf

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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…
01:04:30

Week 5 - Short Day: Matrices

Week 5 - Short Day: Matrices

From DTU Media Lab

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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…
02:02:52

Week 5 - Long Day: Systems of Linear Equations

Week 5 - Long Day: Systems of Linear Equations

From Steeven Hegelund Spangsdorf

144 plays 198
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…
02:03:26

Week 4 - Long Day: Taylor’s Formulas

Week 4 - Long Day: Taylor’s Formulas

From Steeven Hegelund Spangsdorf

138 plays 198
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…
01:02:40

Week 3 - Short Day: Polynomials

Week 3 - Short Day: Polynomials

From Georgi Yankov

137 plays 0
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…

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