• Turkish
  • English
Course Code: 
MATH 311
Course Type: 
Area Elective
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
6
Course Language: 
English
Course Objectives: 
To teach the theory of exterior differential forms and integration on smooth manifolds.
Course Content: 

Functions on Euclidean spaces. Differentiation. Inverse and implicit function theorems. Integration. Partitions of unity. Sard's theorem. Multilinear functions, tensors, fields and differential forms. Poincare lemma. Chains and integration over chains. Stokes' theorem. Differentiable manifolds. Fields and forms on manifolds. Orientation and volume. Applications.

Course Methodology: 
1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Program Learning Outcomes

Teaching Methods

Assessment Methods

1) Knows the properties of exterior algebra of a finite dimensional real vector space.

2,3

1,4

A,B

2) Knows Stokes’ theorem for a manifold with boundary.

2,3

1,4

A,B

Course Flow

Week

Topics

Study Materials

1

Point-set topology in R^n

Textbook

2

Point-set topology in R^n (continued)

Textbook

3

Differentiation

Textbook

4

Differentiation (continued)

Textbook

5

Integration

Textbook

6

Integration (continued)

Textbook

7

Integration (continued)

Textbook

8

Integration on chains

Textbook

9

Integration on chains (continued)

Textbook

10

Integration on chains (continued)

Textbook

11

Integration on chains (continued)

Textbook

12

Integration on manifolds

Textbook

13

Integration on manifolds (continued)

Textbook

14

Integration on manifolds (continued)

Textbook

Recommended Sources

Textbook

Calculus on Manifolds, by M. Spivak.

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

66

Quizzes

-

-

Assignments

5

34

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Expertise/Field 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

3

42

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

14

3

42

Mid-terms (Including self study)

2

15

30

Quizzes

-

-

-

Assignments

5

3

15

Final examination (Including self study)

1

21

21

Total Work Load

 

 

150

Total Work Load / 25 (h)

 

 

6

ECTS Credit of the Course

 

 

6