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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 2044 ANALYSIS II COMPULSORY 4 2 0 9

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR SEDEF KARAKILIÇ

Offered to

Mathematics (Evening) Mathematics

Course Objective

The aim of the course is to develop rigorously the following concepts and their properties: Topology of R^n, Differentiability on R^n, Inverse and Implicit Function Theorems, Line and Surface Integrals, Green s and Stoke s Theorems.

Learning Outcomes of the Course Unit

1   will be able use the basic topological properties of R^n. 2   will be able to understand the Inverse Function Theorem and Implicit Function Theorem. 3   will be able to define the concepts of integrability on generalized rectangles and on bounded subsets of R^n. 4   will be able to define the concepts of line and surface integrals. 5   will be able to write complete and formal proofs for the problems related with the above topics.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 The Euclidean Space R^n. Algebraic structure and the scalar product. Sequences in R^n. 2 Topology of R^n. Open and Closed sets. The Boundary and Exterior of a set. 3 Continuity and Compactness . Continuous Functions and Mappings. Sequential Compactness, Extreme Values and Uniform Continuity. 4 Continuity and Connectedness. Pathwise Connectedness, Connectedness and Intemediate Value Theorem. 5 Limits. Partial Derivatives. 6 The Mean Value Theorem and Directional Derivatives. 7 Continuity and Differentiability of Transformations. MIDTERM 1 8 The Inverse Function Theorem. 9 The Implicit Function Theorem. 10 Integrating Functions on Generalized Rectangles. Copntinuity and integrability. 11 Integrating Functions on Jordon Domains. MIDTERM 2 12 Iterated integrals. Fubini s Theorem. 13 Line and Surface integrals. 14 Green and Stokes Theorems.

Recomended or Required Reading

Textbook(s): Fitzpatrick, P.M., Advanced Calculus, 2. edition, AMS, 2009 Supplementary Book(s): Wade, William R., Introduction to Analysis, 4. edition, Pearson, 2010 William F. T., Introduction to Real Analysis, Pearson, 2003

Planned Learning Activities and Teaching Methods

Lecture Notes Text Book(s) Solving Problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 0.60 *** 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

To be announced.

Contact Details for the Lecturer(s)

e-mail: didem.coskan@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Tutorials 13 2 26 Lectures 13 4 52 Preparations before/after weekly lectures 12 6 72 Preparation for midterm exam 1 28 28 Preparation for final exam 1 32 32 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 214

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 PO.12 PO.13 LO.1 5 5 3 3 3 LO.2 5 5 3 3 3 LO.3 5 5 3 3 3 LO.4 5 5 3 3 3 LO.5 5 5 3 3 3