# Analytic Geometry I (MATH121) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Analytic Geometry I MATH121 2 1 0 2 4
Pre-requisite Course(s)
None
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Team/Group. This course is designed as a first year course for mathematics students. The goal of the course is to recover the sets, relations and functions and cartesian coordinates in the plane, to review line equations and some methods on graphing relations and functions and also graphs in polar coordinates, to have some basic ideas about vectors in the plane with some of their applications, to make some discussions on parabolas, ellipses, hyperbolas with graphs and their applications. The students who succeeded in this course; understand the sets, relations and functions understand Cartesian coordinates in the plane, lines and be able to sketch the of relations and graphs in polar coordinates understand vectors in the plane and their applications learn the parabola, ellipse and hyperbola and their applications Fundamental principles of analytic geometry, cartesian coordinates, lines in plane, trigonometry, polar coordinates, rotation and translation in plane, conics.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Fundamental Principles of Analytic Geometry. CARTESIAN COORDINATES: Cartesian Coordinates in the Plane, Lines in Plane, Graphs of Relations from R to R pp.2-33
2 Trigonometry pp.35-36
3 Trigonometric identities pp.36-38
4 Polar Coordinates pp.39-44
5 Change of Coordinates: Rotation and Translation pp.45-49
6 VECTORS IN THE PLANE: Directed Segments and Vectors, Algebra of Vectors, Scalar Products, Angle Between Two Vectors pp.54-70
7 Midterm
8 Lines, Half-Lines and Line Segments, More About Lines: Distance, Bisectors, Symmetry pp.71-79
9 Convex Sets, Half-Planes and Polygones pp.80-85
10 CONIC SECTIONS: Fundamental Definitions, The Parabola pp.87-95
11 Central Conics, The Ellipse pp.96-102
12 The Hyperbola, The Asymptotes of an Hyperbola pp.103-108
13 The General Quadratic Equation pp.109-116
14 Tangents and Polars pp.117-123
15 Review
16 Final Exam

### Sources

Course Book 1. Analytic Geometry, H. İ. Karakaş, M V (ODTÜ Matematik Vakfı)

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
Percentage of Semester Work 100 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 2 28
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10