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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Masters with Thesis
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Masters with Thesis
Katalog Ana Sayfa
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MATL5032Calculus on manifolds3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseSecond Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 3 hours of lectures per week
LecturerDr. Öğr. Üyesi Seda ÖZTÜRK
Co-LecturerNone
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The aim of the course is to examine n dimensional space functions. To learn how the concepts of derivative and integral work in n-dimensional Euclidean space.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : learning of functions on Euclidean space
PO - 2 : Calculate n-dimensional space derivative
PO - 3 : understanding integration and calculate of integration on chains
PO - 4 : learning of integration on manifolds
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

 
Contents of the Course
Functions on Euclidean Space, Differantition, Integration, Integration on Chains, Integration on Manfolds
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Norm and inner product
 Week 2Subsets of Euclidean space
 Week 3Functions on Euclidean space
 Week 4Limit and continuity
 Week 5Derivative on Euclidean space
 Week 6Theorems of differentiation
 Week 7Partial derivatives
 Week 8Inverse and implicit functions
 Week 9Mid-term exam
 Week 10Defination of integration on Euclidean space
 Week 11Integrable functions and Fubini's theorem
 Week 12Change of varible and integration on chains
 Week 13The fundamental theorem of calculus and its applications
 Week 14Stokes' theorem and its applications
 Week 15Integration on manifolds and Green's theorem
 Week 16End-of-term exam
 
Textbook / Material
1Calculus on manifolds, Michael Spivak, Newyork, 1965.
 
Recommended Reading
1 Calculus, Michael Spivak, Houston-Texas, 1994.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 11/04/2017 2 30
Quiz 11 25/04/2017 1 30
End-of-term exam 16 7/06/2017 2 40
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 5 14 70
Arasınav için hazırlık 4 8 32
Arasınav 2 1 2
Ödev 4 9 36
Kısa sınav 1 1 1
Dönem sonu sınavı için hazırlık 5 8 40
Dönem sonu sınavı 2 1 2
Total work load225