COURSE UNIT TITLE

: ANALYSIS II

DEGREE PROGRAMMES

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 (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR SEÇIL GERGÜN

Offered to

Mathematics (English)
Mathematics (Evening)

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 differentiability of functions of several variables.
3   will be able to understand the Inverse Function Theorem and Implicit Function Theorem.
4   will be able to define the concepts of integrability on generalized rectangles, 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.
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.
12 Iterated integrals. Fubinis 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 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

%40(midterm)+%60(final)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture
notes on the topics to be covered every week, coming to class by solving the given
problems, establishing the concepts by discussing the parts you do not understand
with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

e-mail: sedef.erim@deu.edu.tr

Office Hours

to be announced later

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Tutorials 14 2 28
Lectures 14 4 56
Preparations before/after weekly lectures 14 5 70
Preparation for midterm exam 1 26 26
Preparation for final exam 1 30 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 214

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.155333
LO.255333
LO.355333
LO.455333
LO.555333

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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