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