Vectors and MatricesLaajuus (3 ECTS)

Objective

After completing this course, the student will be familiar with the fundamentals of the theory of vectors and matrices, as well as some of the most important applications. The student will be able to construct and solve linear models and interpret the solutions. The student will be able to distinguish between linear and nonlinear phenomena and understand the potential of vectors and matrices in real-world modeling. In particular, the student will be aware of the fact that, within information and communication technology, many problems can be solved using matrices.

Content

1) Vector quantities and vectors in a coordinate system.
2) Matrices and linear transformations.

Qualifications

Comprehensive school mathematics is a sufficient background for understanding the theory.

Assessment criteria, satisfactory (1)

1) Vector quantities and vectors in a coordinate system.
The student is familiar with vectors and fundamental concepts associated with them. The student has a command of vector operations (norm and scalar product included) provided that vectors are represented in the standard basis i, j and k.
2) Matrices and linear transformations.
The student is familiar with matrices, matrix operations and fundamental concepts associated with matrices. The student is able to transpose a matrix. The student is able to calculate the determinant of a square matrix and the inverse of an invertible matrix. The student is able to find out whether a matrix is invertible or not by computing the determinant.

Assessment criteria, good (3)

1) Vector quantities and vectors in a coordinate system.
The student is able to make vector calculations within and without a coordinate system. The student has a command of the scalar and vector product as well as their geometrical interpretations. The student is able to represent vectors in an arbitrary basis, in addition to the standard basis i, j and k. The student is able to project vectors perpendicularly. The student is able to solve geometrical and real-world problems by using vectors.
2) Matrices and linear transformations.
The student has a good command of indices, the sigma notation and matrix expressions. The student is able to solve a matrix equation and a group of linear equations by using an inverse matrix. The student is able to solve a linear group by Gauss elimination. The student understands the connection between spatial transformations and matrices. The student is able to solve real-world problems with the aid of matrices.

Assessment criteria, excellent (5)

1) Vector quantities and vectors in a coordinate system.
The student has an excellent talent in manipulating vectors. The student is able to derive formulas by using vectors (e.g. the law of sines or cosines).
2) Matrices and linear transformations.
The student has an excellent talent in matrix manipulations and linear modeling.

Further information

Computer exercises will be included.