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.
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’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 | 5 | 70 |
| Mid-terms (Including self study) | 2 | 10 | 20 |
| Quizzes | - | - | - |
| Assignments | - | - | - |
| Final examination (Including self study) | 1 | 10 | 10 |
| Total Work Load | 170 | ||
| Total Work Load / 25 (h) | 6,8 | ||
| ECTS Credit of the Course | 7 |