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