# Assignments

## Take-Home Exam-II

Please download the Take-Home Exam-II here, and carefully read the explanations/instructions given in Introduction before you start to work on it. Please, follow the given instructions; remark that "work on your own" part is emphasized, and please solve every problems on a single A4 sheet. Good Luck and Happy New Year!

## Exercise Sheet 9

In this exercise sheet, we will focus on the solution of coupled ODEs with forming and solving fundamental systems. We will discuss Exercise-Sheet 9 first in the New Year. I strongly recommend you to work on the exercises during the new-year break.

## Exercise Sheet 8

In this exercise sheet, we will focus on type of ODEs, and the solution of first and second order ODEs. Moreover, constructing the fundamental system is also concerned. We will discuss Exercise-Sheet 8 first in the New Year. I strongly recommend you to work on the exercises during the new-year break.

## Exercise Sheet 6-7

In this exercise sheet, we will focus on SVD, The Jordan Form, QR decomposition, Norms of Linear Maps, and Best-fit Functions and Errors.

## Exercise Sheet 5

In this exercise sheet, we will focus on the singular value decomposition and the Jordan form.

## Exercise Sheet 4

In this exercise sheet, we will focus on the eigenvalues, eigenvectors and the characteristic polynomial.

## Exercise Sheet 3

In this exercise sheet, we will focus on the matrix decompositions, LU and PLU decomposition.

## Take-Home Exam-I

Please download the Take-Home Exam-I here, and carefully read the explanations given in Introduction before you start to work on it. Good Luck!

## Exercise Sheet 2

In this exercise sheet, we will focus on the topics that we covered in the fourth lecture:

• Inverse of matrices;
• Block matrices;
• Linear Mapping and projection;
• General solution of system of linear equations;
• Homogeneous coordinate system.