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Course Code: 
MATH 111
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
9
Course Language: 
English
Course Objectives: 
To give the concepts of vectors and most fundamental analytic geometry (in two and three dimensions) together with some of their properties.
Course Content: 

Vectors, linear operations with vectors. Products of vectors. Definition of Euclidean space. Lines and planes. Circle and sphere. Parametrizations of curves and surfaces. Conics and quadrics, their symmetries and classifications. Translations, orthogonal transformations, similarities and inversions.

Course Methodology: 
1: Lecture, 2: Problem Solving 5: Quiz
Course Evaluation Methods: 
A: Written examination, B: Homework, C: Quiz

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) calculate vectors and matrices

1,2,5

A,B,C

2) solve the problems about lines and planes

1,2,5

A,B,C

3) define conics and obtain canonic equations

1,2,5

A,B,C

4) find the tangent planes of quadratic planes

1,2,5

A,B,C

5) describe quadratic planes with canonic equations

1,2,5

A,B,C

6) reduce the general quadratic equations to canonic form

1,2,5

A,B,C

Course Flow

Week

Topics

Study Materials

1

points, oriented segments, parallel translation, vectors, collinear and coplanar vectors,

Textbooks

2

linear operations with vectors, linear dependence, coordinates of vectors and points.

Textbooks

3

scalar(dot) product of vectors, projection, direction cosines, cosine theorem. Vector product, orientation of plane,

Textbooks

4

Lagrange identity, area, collinear points, triple (mixed) product,

Textbooks

5

volume, double vector product. A definition of affine and Euclidean spaces.

Textbooks

6

curves and surfaces, parametric, explicit and implicit equations, geometric locus. Equations of straight lines and planes, normal vectors.

Textbooks

7

geometric problems with lines and planes. Menelaos and Ceva theorems. Intersections, angles, skew lines, distances, pencils.

Textbooks

8

review and midterm exam,
Textbooks

9

circles and spheres, parametric equations, polar, cylindrical and spherical coordinates,

Textbooks

10

intersection with a line, secant and tangent, normal, polar line and plane.

Textbooks

11

conics: canonical equation of ellipse and hyperbola, focuses and vertices, asymptotes. Directrix, eccentricity, parabola. Parametric equations.

Textbooks

12

quadrics: ellipsoid of revolution, hyperboloids, asymptotic cone, elliptic and hyperbolic paraboloids,

Textbooks

13

conics and quadrics: affine classification theorem of Gauss.

Textbooks

14

review and midterm exam

Textbooks

Recommended Sources

Textbook

I. Vaisman, “Analytical Geometry”

H. İ. Karakaş, “Analytic Geometry”

Additional Resources

V. Gutenmacher and N. B. Vasilyev, Lines and Curves, Birkhauser 2004, QA 459.G983 2004.

    C. B. Boyer, History of Analytic Geometry, Dover 1956, QA 551.B813 2004.

    There are chapters on several books named "calculus and analytical geometry".

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

3

87

Quizzes

10

13

Assignments

   

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

30

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

70

Total

 

100

 

COURSE CATEGORY

Core Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

X

       

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

 

X

     

3

Ability form and interpret the relations between research topics in mathematics

       

X

4

Ability to define, formulate and solve mathematical problems

     

X

 

5

Consciousness of professional ethics and responsibilty

   

X

   

6

Ability to communicate actively

   

X

   

7

Ability of self-development in fields of interest

     

X

 

8

Ability to learn, choose and use necessary information technologies

X

       

9

Lifelong education

   

X

   

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

5

70

Hours for off-the-classroom study (Pre-study, practice)

14

7

98

Mid-terms (Including self study)

2

15

30

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

20

20

Total Work Load

 

 

218

Total Work Load / 25 (h)

 

 

8.72

ECTS Credit of the Course

 

 

9