Analytic Geometry and Linear Algebra
|Compulsory / Basic Studies
|Bachelor of Engineering
|Year of Study:
|Language of Instruction:
Courses During the Academic Year 2015-2016
|2016-01-04 – 2016-04-20
|2015-12-07 – 2016-01-10
|2016-01-04 – 2016-05-07
|2015-12-07 – 2016-01-10
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.
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 and Other Learning Resources/Tools
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".
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.
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.