Analytic Geometry and Linear Algebra
| Structure Type: | Study unit |
|---|---|
| Code: | IXP0402 |
| Type: | Compulsory / Basic Studies |
| Curriculum: | I-KT 2005 / 2005V / 2006 / 2007 / 2007V / 2008 / 2009 / 2009V I-RT 2005 / 2006 / 2006V / 2007 / 2008 / 2009 I-ST 2005 / 2006 / 2006V / 2007 / 2008 / 2008V / 2009 / 2010V / 2012V I-TT 2005 / 2006 / 2007 / 2008 / 2008V / 2009 / 2010V / 2011V I-YT 2005 / 2006 / 2007 / 2008 / 2009 / 2009V ST 2014V / 2016V / 2018V / 2020V TT 2020V |
| Level: | Bachelor of Engineering |
| Year of Study: | 1 (2005-2006 / 2006-2007 / 2007-2008 / 2008-2009 / 2009-2010 / 2010-2011 / 2011-2012 / 2012-2013 / 2014-2015 / 2016-2017 / 2018-2019 / 2020-2021) |
| Credits: | 2 cr |
| Responsible Teacher: | Ojanen, Jussi |
| Language of Instruction: | Finnish |
Courses
| Impl. | Group(s) | Study Time | Teacher(s) | Language | Enrolment |
|---|---|---|---|---|---|
| 1 | 2006-01-02 – 2006-02-25 | Jarmo Mäkelä | Finnish | 2005-12-05 – 2006-01-09 | |
| 2 | 2006-01-02 – 2006-02-25 | Jarmo Mäkelä | Finnish | 2005-12-05 – 2006-01-09 | |
| 3 | 2006-01-02 – 2006-02-25 | Paavo Leppänen | Finnish | 2005-12-05 – 2006-01-09 | |
| 4 | 2006-01-02 – 2006-02-25 | Mikko Hurme | Finnish | 2005-12-05 – 2006-01-09 | |
| 5 | I-ST-1 | 2006-01-02 – 2006-02-25 | Jarmo Mäkelä | Finnish | 2005-12-05 – 2006-01-09 |
| 6 | 2006-01-02 – 2006-02-25 | Mikko Hurme | Finnish | 2005-12-05 – 2006-01-09 | |
| 7 | 2006-01-02 – 2006-02-25 | Jarmo Mäkelä | Finnish | 2005-12-05 – 2006-01-09 | |
| 8 | 2006-08-28 – 2006-10-28 | Jarmo Mäkelä | Finnish | 2006-08-18 – 2006-09-10 | |
| 9 | 2007-01-08 – 2007-03-09 | Jarmo Mäkelä | Finnish | 2006-12-11 – 2007-01-14 | |
| 10 | 2007-01-08 – 2007-03-09 | Mikko Hurme | Finnish | 2006-12-11 – 2007-01-14 | |
| 11 | 2007-01-08 – 2007-03-09 | Jarmo Mäkelä | Finnish | 2006-12-11 – 2007-01-14 | |
| 12 | 2007-01-08 – 2007-03-09 | Olli Korosuo | Finnish | 2006-12-11 – 2007-01-14 | |
| 13 | 2007-01-08 – 2007-03-09 | Carl Källman | Finnish | 2006-12-11 – 2007-01-14 | |
| 14 | 2007-01-08 – 2007-03-09 | Henry Niemi | Finnish | 2006-12-11 – 2007-01-14 | |
| 15 | 2007-01-08 – 2007-03-09 | Paavo Leppänen | Finnish | 2006-12-11 – 2007-01-14 | |
| 16 | I-RT-1V, I-ST-1V | 2007-01-08 – 2007-03-09 | Mikko Hurme | Finnish | 2006-12-11 – 2007-01-14 |
| 17 | 2007-08-27 – 2007-10-26 | Mikko Hurme | Finnish | 2007-08-17 – 2007-09-12 | |
| 18 | 2008-01-07 – 2008-03-07 | Henry Niemi | Finnish | 2007-12-10 – 2008-01-11 | |
| 19 | 2008-01-07 – 2008-03-07 | Henry Niemi | Finnish | 2007-12-10 – 2008-01-11 | |
| 20 | 2008-01-07 – 2008-03-07 | Mikko Hurme | Finnish | 2007-12-10 – 2008-01-11 | |
| 21 | 2008-01-07 – 2008-03-07 | Jarmo Mäkelä | Finnish | 2007-12-10 – 2008-01-11 | |
| 22 | 2008-01-07 – 2008-03-07 | Virpi Elomaa | Finnish | 2007-12-10 – 2008-01-11 | |
| 23 | 2008-01-07 – 2008-03-07 | Virpi Elomaa | Finnish | 2007-12-10 – 2008-01-11 | |
| 24 | 2008-08-25 – 2008-10-25 | Henry Niemi | Finnish | 2008-08-15 – 2008-08-31 | |
| 25 | 2009-01-05 – 2009-03-07 | Henry Niemi | Finnish | 2008-12-08 – 2009-01-11 | |
| 26 | 2009-01-05 – 2009-03-07 | Jarmo Mäkelä | Finnish | 2008-12-08 – 2009-01-11 | |
| 27 | 2009-01-05 – 2009-03-07 | Mikko Hurme | Finnish | 2008-12-08 – 2009-01-11 | |
| 28 | 2009-01-05 – 2009-03-07 | Paavo Leppänen | Finnish | 2008-12-08 – 2009-01-11 | |
| 29 | 2009-01-05 – 2009-03-07 | Henry Niemi | Finnish | 2008-12-08 – 2009-01-11 | |
| 31 | I-ST-2V | 2009-08-24 – 2009-10-24 | Paavo Leppänen | Finnish | 2009-08-14 – 2009-09-06 |
| 32 | 2010-01-04 – 2010-03-06 | Virpi Elomaa | Finnish | 2009-12-07 – 2010-01-10 | |
| 33 | 2010-01-04 – 2010-03-06 | Jarmo Mäkelä | Finnish | 2009-12-07 – 2010-01-10 | |
| 34 | 2010-01-04 – 2010-03-06 | Henry Niemi | Finnish | 2009-12-07 – 2010-01-10 | |
| 35 | 2010-01-04 – 2010-03-06 | Mikko Hurme | Finnish | 2009-12-07 – 2010-01-10 | |
| 36 | 2010-01-04 – 2010-03-06 | Sanna Rintala | Finnish | 2009-12-07 – 2010-01-10 | |
| 37 | I-YT-1V | 2010-01-04 – 2010-03-06 | Paavo Leppänen | Finnish | 2009-12-07 – 2010-01-10 |
| 38 | 2010-01-04 – 2010-03-06 | Henry Niemi | Finnish | 2009-12-07 – 2010-01-10 | |
| 39 | 2010-01-04 – 2010-03-06 | Jarmo Mäkelä | Finnish | 2009-12-07 – 2010-01-10 | |
| 40 | H-VV | 2010-05-03 – 2010-06-18 | Ari Luukkonen | Finnish | 2010-04-16 – 2010-05-09 |
| 41 | I-ST-1V, I-TT-1V | 2011-03-07 – 2011-04-30 | Henry Niemi | Finnish | 2011-02-14 – 2011-03-13 |
| 42 | H-VV | 2011-05-02 – 2011-06-21 | Ari Luukkonen | Finnish | 2011-04-05 – 2011-04-27 |
| 43 | I-ST-1V, I-TT-1V | 2012-01-09 – 2012-03-02 | Jussi Ojanen | Finnish | 2011-12-07 – 2012-01-15 |
| 44 | H-VV | 2012-04-30 – 2012-06-10 | Ari Luukkonen | Finnish | 2012-03-26 – 2012-04-22 |
| 45 | I-ST-1V | 2013-01-07 – 2013-04-26 | Henry Niemi, Virpi Elomaa | Finnish | 2012-12-07 – 2013-03-04 |
| 46 | I-ST-1V, I-TT-1V | 2015-01-05 – 2015-03-16 | Jussi Ojanen | Finnish | 2014-12-08 – 2015-01-12 |
| 47 | I-ST-1V, I-TT-1V | 2017-01-09 – 2017-03-30 | Jarmo Mäkelä | Finnish | 2016-12-12 – 2017-01-16 |
| 48 | I-ST-1V, I-TT-1V | 2019-01-07 – 2019-04-01 | Jussi Ojanen | Finnish | 2018-12-10 – 2019-01-14 |
| 3001 | ST2020V-1, ST2020V-1A, ST2020V-1B, TT2020V-1A | 2021-01-04 – 2021-02-28 | Jussi Ojanen | Finnish | 2020-08-17 – 2021-01-10 |
The descriptions shown below are for the academic year: 2020-2021
Learning Outcomes
The student is made familiar with matrices, vectors, trigonometry, complex numbers and inequalities. She knows the rules of calculation of matrices, and she is able to calculate the determinant of a given square matrix. She learns to calculate the inverse of a square matrix, and to apply matrices and determinants for a solution of linear systems of equations. In trigonometry she is made familiar with the concept of radian, and she understands the connection between trigonometric functions and the coordinates of a point of a unit circle correponding to a given angle, together with the basic properties of trigonometric functions following from this connection. In vector calculus the sudent is made familiar with addition and substraction of vectors, together with a multiplication of a vector by a number and the component representation of a vector. In addition, the student learns the concepts of dot and cross products of vectors, and knows how to apply them in the solution of geometrical problems. The student is made familiar with complex numbers, and she can write a given complex number in a polar representation. Using the polar representation the student can multiply and divide complex numbers by each other, and to raise a complex number to a given power. The student learns to solve linear, quadratic and rational inequalities.
Student's Workload
The total amount of student's work is 54 h, which contains 22 h of scheduled contact studies. The assessment of student’s own learning 1 h is included in contact lessons.
Prerequisites / Recommended Optional Courses
Introduction to Technical Mathematics.
Contents
Matrices, determinats, and their appplications for the solution of linear systems of equations. Trigonometric functions defined by means of the coordinates of the points of a unit circle. The concept of radian. Basic properties of trogonometric functions, graphs of trigonometric functions, and trigonometric equations. Vectors, their component representation, and dot and cross products. Applications of vector calculus for a solution of simple geometric propblems. Complex numbers, their basic properties and the polar representation. Multiplication, division and powering of complx numbers in a polar representation. Linear, quadratic and rational inequatlities.
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
The basics of learning constitutes of lectures where the theory is explained and examples are given. An essential ingredient of learning, however, consists of exercises which are gone through during the lectures, and independent homework performed by the student. A mere attending the lectures and listening to the lecturer is not sufficient for proper learning. In practice, an independent pondering of the contents of the course becomes best realized when a student solves independently, at home, the problems given by the lecturer. Solutions to the problems are given during the lectures.
Assessment Criteria
Grade 5: The student is able to apply creatively the contents of the course.
Grade 3: The student is well-abled to utilize the course contents.
Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.
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 passt the course.