Analytic Geometry and Linear Algebra

Structure Type: Course
Code: IKTP0203
Type: Compulsory
Level: Bachelor
Credits: 3.0 points
Responsible Teacher: Mäkelä, Jarmo
Language of Instruction: Finnish

Course Implementations, Planned Year of Study and Semester

Curriculum  Semester  Credits  Start of Semester  End of Semester
I-KT-2010   1 spring   3.0   2011-01-05   2011-06-17  
I-KT-2010V   1 spring   3.0   2011-01-05   2011-06-17  
I-KT-2011   1 spring   3.0   2012-01-09   2012-06-18  
I-KT-2011V   1 spring   3.0   2012-01-09   2012-06-18  
I-KT-2012   2 autumn   3.0        
I-KT-2012V   1 spring   3.0   2013-01-05   2013-06-18  
I-KT-2013   2 autumn   3.0        
EY-2014   1 spring   3.0        
KT-2014   1 spring   3.0        
EY-2015   1 spring   3.0        
KT-2015   1 spring   3.0        

Learning Outcomes

The student becomes familiarized with matrices, vectors and complex numbers. At the end of the course the student knows the rules of calculation of determinants and matrices, and she is able to apply them, for instance, in the solution of linear systems of equations. The student is able to apply vectors for the solution of simple geometrical problems. The trigonometric functions are re-defined by means of the concept of unit circle. The student knows the most central properties of the trigonometric functions, and she is able to solve trigonometric equations. In addition, the student learns the basics of complex numbers.

Student's Workload

The total amount of student's work is 81 h, which contains 42 h of contact studies.

Prerequisites / Recommended Optional Courses

Introduction to Technical Mathematics.


Determinants and matrices, together with their rules of calculation. Application of determinants and matrices in the solution of linear systems of equations. Vectors, their addition and multiplication by a number. Component representation of vectors. The dot- and the cross products of vectors. The use of dot product in the calculation of angle and the cross product in the calculation of area. Trigonometric functions defined by means of the unit circle. The concept of radian. The basic properties of the trigonometric functions. Sine and cosine of the sum and the difference of two angles. Sine and cosines of double angles.

Recommended or Required Reading

Majaniemi: "Algebra I ja II" and "Geometria", Tietokotka Oy; the material prepared by the teacher.

Mode of Delivery / Planned Learning Activities and Teaching Methods

See the description of "Johdatus tekniikan matematiikkaan".

Assessment Criteria

Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.
Grade 3: The student is well-abled to utilize the course contents.
Grade 5: The student is able to apply creatively the contents of the course.

Assessment Methods

An exam, homework exercises and tutored exercise sessions. The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. At least 25 % of the given homework exercises must be solved in order to pass the course.