Search for media from: "Jesper Kampmann Larsen"

Determinants and Vectors - Week 6 Short Day

From  Jesper Kampmann Larsen on October 11th, 2019 72 plays 0  

Week 5 Long Day - Plane Integrals Part 1

You have most likely in highschool seen that integrals can be used for the computations of areas and volumes; but these are only a few of the many interpretations and applications of integration.…

From  Jesper Kampmann Larsen on March 2nd, 2020 48 plays 0  

Week 2, Long Day: Polar coordinates and Exponential Form Part 2

Just as we were getting familiar with the rectangular form of complex numbers, we are now on the road to a new way of describing and calculating with the numbers, viz. with their polar coordinates…

From  Jesper Kampmann Larsen on September 11th, 2019 47 plays 0  

Week 4, Long Day: Taylor’s Formulas part 2

In Highschool you have worked with approximating polynomials of first degree (whose graph is the tangent in the development point), but today we introduce approximating polynomials of higher degree.…

From  Jesper Kampmann Larsen on September 25th, 2019 41 plays 0  

Week 2, Long Day: Polar coordinates and Exponential Form part 1

Just as we were getting familiar with the rectangular form of complex numbers, we are now on the road to a new way of describing and calculating with the numbers, viz. with their polar coordinates…

From  Jesper Kampmann Larsen on September 11th, 2019 35 plays 0  

Week 5 Long Day - Plane Integrals Part 2

You have most likely in highschool seen that integrals can be used for the computations of areas and volumes; but these are only a few of the many interpretations and applications of integration.…

From  Jesper Kampmann Larsen on March 2nd, 2020 35 plays 0  

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 27th, 2019 34 plays 0  

Week 6, Long Day: Spatial Fields and Space Integrals part 1

We have integrated along curves (1d), over plane regions and surfaces (2d) and end today by integration of spatial regions, also called ”solids” (3d). Again we shall look at…

From  Jesper Kampmann Larsen on March 9th, 2020 34 plays 0  

Week 1, Short Day: More about Functions of Two Variables

We continue with the study of functions of two variables with their level curves, partial derivatives, gradients , directional derivatives, etc. From the differentiable functions of one variable we…

From  Jesper Kampmann Larsen on February 7th, 2020 32 plays 0  

Week 12: Systems of Differential Equations part 2

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 27th, 2019 28 plays 0  

Week 3, Long Day: Maxima and Minima Part 1

Today must be considered as a preliminary clou in the spring curriculum! We shall find minimum og maximum for functions of more variables, both local and global. In short we shall optimize. There is…

From  Jesper Kampmann Larsen on February 17th, 2020 28 plays 0  

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 20th, 2019 23 plays 0  

Week 6, Long Day: Spatial Fields and Space Integrals part 2

We have integrated along curves (1d), over plane regions and surfaces (2d) and end today by integration of spatial regions, also called ”solids” (3d). Again we shall look at…

From  Jesper Kampmann Larsen on March 9th, 2020 22 plays 0  

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 20th, 2019 20 plays 0  

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 13th, 2019 18 plays 0  

Week 3, Long Day: Maxima and Minima part 2

Today must be considered as a preliminary clou in the spring curriculum! We shall find minimum og maximum for functions of more variables, both local and global. In short we shall optimize. There is…

From  Jesper Kampmann Larsen on February 17th, 2020 18 plays 0