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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5029 CALCULUS ON MANIFOLDS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics Mathematics

Course Objective

This course gives a comprehensive and rigorous treatment on calculus of several variables, and a modern treatment of integration theory in the language of differential forms which is essential for more advanced studies in analysis and geometry

Learning Outcomes of the Course Unit

1   will be able to know what are the inverse function and the implicit function theorems 2   will be able to determine the differentiability and integrability of specific functions 3   will be able to manipulate differential forms 4   will be able to do integration of specific functions on chains 5   will be able to explain the Stokes theorem on manifolds

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Norm and inner Product, Subspaces of Euclidean space 2 Functions and continuity 3 Differentiation: Basic definitions and theorems 4 Partial derivatives, Derivatives 5 Inverse functions 6 Implicit functions 7 Integration: Basic definitions, Measure zero and Content zero 8 Midterm 9 Integrable functions, Fubini s theorem, Partitions of Unity, Change of Variable 10 Integration on Chains: Fields and Forms 11 The fundamental theorem of calculus 12 Integration on Manifolds 13 Stokes Theorem on Manifolds 14 The Classical Theorems on Manifolds

Recomended or Required Reading

Textbooks: 1. Michael Spivak, Calculus on Manifolds, Westview Press, 1971, ISBN-13: 978-0805390216 2. James R. Munkres, Analysis on Manifolds, Westview Press, 1997, ISBN-13: 978-0201315967

Planned Learning Activities and Teaching Methods

Lecture notes, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU E-mail: celalcem.sarioglu@deu.edu.tr Office phone: 0232 3018585

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 25 25 Preparation for final exam 1 30 30 Preparing assignments 3 10 30 Midterm 1 3 3 Final 1 3 3 Project Assignment 3 1 3 TOTAL WORKLOAD (hours) 172

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 3 4 4 4 3 LO.2 4 3 5 3 3 3 4 3 3 3 LO.3 3 4 4 4 3 4 4 3 LO.4 3 4 4 4 3 4 4 3 LO.5 3 3 4 4 4 3 3 3