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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 0 plays 0  

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 0 plays 0  

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 5 plays 76  

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 19 plays 0  

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 22 plays 74  

Week 5, Short Day: Matrix Algebra

Today we continue with systems of linear equations and matrix algebra. Part of the work is about a special type of matrices, the square matrices, that give rise to concepts like regular, singular and…

From  Jesper Kampmann Larsen on October 2nd, 2020 19 plays 0  

Week 5: Long Day: Systems of Linear Equations (Part 2)

Today we shall work with systems of equations. The subject is new to most new students. All can follow as long as you know the four elementary arithmetic operations! Along the way we show how we by…

From  Jesper Kampmann Larsen on September 30th, 2020 10 plays 0  

Week 5: Long Day: Systems of Linear Equations (Part 1)

Today we shall work with systems of equations. The subject is new to most new students. All can follow as long as you know the four elementary arithmetic operations! Along the way we show how we by…

From  Jesper Kampmann Larsen on September 30th, 2020 16 plays 0  

Week 4, Long Day: Taylor’s Formulas - Maple Demo

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 23rd, 2020 8 plays 69  

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 23rd, 2020 5 plays 69  

Week 4, Long Day: Taylor’s Formulas part 1

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 23rd, 2020 8 plays 69  

Week 3, Short Day: Differentiability

In highschool you have probably seen a differentialquotient introduced as the limit of a difference quotient: f′(xo)=f(x)−f(xo)x−xo for x→xo. Today we introduce alternatively…

From  Jesper Kampmann Larsen on September 18th, 2020 1 plays 0  

Week 3, Long Day: Polynomials - Part 2

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 roots different polynomials have?…

From  Jesper Kampmann Larsen on September 16th, 2020 2 plays 0  

Week 3, Long Day: Polynomials - Part 1

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 roots different polynomials have?…

From  Jesper Kampmann Larsen on September 16th, 2020 4 plays 0  

Week 2, Short Day: Polar Coordinates and the Exponential Function

From highschool you know that the natural exponential function and the natural logarithmic function are inverse to each other. But what are the inverse functions to cosine and sine, and are you aware…

From  Jesper Kampmann Larsen on September 11th, 2020 1 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 9th, 2020 0 plays 44