Analytic Geometry and Linear Algebra
| Structure Type: | Study unit |
|---|---|
| Code: | ITTP0304 |
| Type: | Compulsory / Basic Studies |
| Curriculum: | I-TT 2010 |
| Level: | Bachelor of Engineering |
| Year of Study: | 1 (2010-2011) |
| Credits: | 2 cr |
| Responsible Teacher: | Mäkelä, Jarmo |
| Language of Instruction: | Finnish |
Courses During the Academic Year 2010-2011
| Impl. | Group(s) | Study Time | Teacher(s) | Language | Enrolment |
|---|---|---|---|---|---|
| 1 | I-TT-1N | 2011-01-03 – 2011-03-05 | Jarmo Mäkelä | Finnish | 2010-12-07 – 2011-01-09 |
Learning Outcomes
A 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 28 h of contact studies in the youth program and 20 h of contact studies in the adult program. The remaining time is used for individual 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
See the description of "Introduction to Technical Mathematics".
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
See the description of "Introduction to Technical Mathematics".