Differentiable Manifolds (MATH572) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Differentiable Manifolds MATH572 3 0 0 3 5
Pre-requisite Course(s)
Consent of the department
Course Language English
Course Type N/A
Course Level Ph.D.
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Discussion, Question and Answer.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives Differentiable manifolds which is used in many different areas of mathematics especially mathematical physics are essentially the generalizations of smooth surfaces in R^3 to higher dimensions. Aim of this course is to learn the fundamental notions, local and global theory about the subject such as, differentiable manifolds, tangent and cotangent bundles, vector fields, flows, Lie derivatives, tensors, differential forms, orientation and integration.
Course Learning Outcomes The students who succeeded in this course;
Course Content Topological manifolds, differentiable manifolds, tangent and cotangent bundles, differential of a map, vector fields, submanifolds, tensors, differential forms, orientations on manifolds, integration on manifolds, Stokes` theorem.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation


Course Book 1. L. Conlon, Differentiable Manifolds, 2.edition, Modertn Birkhauser Classics, 2001
2. J.M. Lee, Introduction to Smooth Manifolds, 2. edition, Springer, 2013
3. N. Hitchin, Differentiable Manifolds, Lecture Notes
4. Shigeyuki Morita, Geometry of Differential Forms, AMS, 2001

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 5 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Special Course Internship
Field Work
Study Hours Out of Class
Presentation/Seminar Prepration
Homework Assignments 3 5 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 35