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Syllabus ( MATH 106 )


   Basic information
Course title: Analytical Geometry
Course code: MATH 106
Lecturer: Prof. Dr. Sibel ÖZKAN
ECTS credits: 5
GTU credits: 3 (3+0+0)
Year, Semester: 1, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: Teaching to relate mathematical expressions to geometrical objects and the applications of algebraic methods in geometry.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Relate mathematical expressions to geometrical objects and the applications of algebraic methods in geometry.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  2. Recognize solution methods for Scientific and Engineering problems

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Being fluent in English to review the literature, present technical projects, and write journal papers.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Find out methods to develop knowledge.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: The meaning of analytic geometry.
Systems of linear equations.
Matrices and operations on them.
Week 2: Determinants and their properties.
Applyıng determınants to the systems of linear equations solving.
Week 3: Plane coordinates.
Square,parallel and polar coordinates.
Square coordinated ın the space.
Week 4: Vectors. Introduction to the vector algebra.
Operations on vectors.
Week 5: Vectors on the plane and solutions of some problems.
Week 6: Coordinates transformations on the plane.
Translational and rotational transformations of coordinates.
Affıne transformations.
Quiz
Week 7: The curves definition and visualization.
Classification of curves.
Algebraic curves: examples and three related problems.
Week 8: Examples of trancendent curves.
Conics and their common definition.
Week 9: Second order curves on the plane.
Families of curves.
Week 10: Lines and planes in the space and related problems.
Symmetry in the space.
Week 11: Surfaces and their definitions.
The graphs of surfaces and their intersections.
Sphere and cylinder ( their definitions and equations).
Week 12: Conic surfaces. Plane and rotational surfaces.
Transformations of coordinates in the space.
Midterm exam.
Week 13: The second order surfaces: their types and classification.
Curves on the surfaces.
Spatial curves and their graphs.
Week 14: Other systems of coordinates in the space.
Cylindric and spheric coordinates. Homogen and polar coordinates.
Analytic geometry in the n-dimensional space.
Week 15*: -
Week 16*: Final exam
Textbooks and materials: Rüstem Kaya 'Analitik Geometri' 9-cu baskı
Recommended readings: Arif Sabuncuoğlu 'Analitik Geometri' 3*cu baskı
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 12 20
Other in-term studies: 0
Project: 0
Homework: 2,4,6,7,8,9,10,12 10
Quiz: 6 30
Final exam: 16 40
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 3 13
Practice, Recitation: 0 0
Homework: 2 8
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 15 1
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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