COURSE UNIT TITLE

: ANALYSIS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
OMT 1011 ANALYSIS I COMPULSORY 4 2 0 7

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ESRA BUKOVA GÜZEL

Offered to

Mathematics Teacher Education

Course Objective

Recognize the fundamental concepts of Calculus; natural, examine all the features of integers, rational, irrational and real number systems needed for the Calculus; recognize the real-valued functions of one real variable; real-valued functions of one real variable: to examine the concept of limits, continuity, and, uniform continuity; provide for students to understand the basic concepts of Calculus and the interrelationships among them and examples of real world; gain problem-solving skills by using the concepts in Calculus.

Learning Outcomes of the Course Unit

1   To be able to know natural numbers, integers, rational numbers, irrational numbers and the real number sets, and relate these sets of numbers; to express their differences.
2   To be able to recognize the only real variable real-valued functions and make applications with these functions.
3   To be able to learn the basic concepts such as limits, continuity, uniform continuity and discontinuity for real-valued functions of one real variable, to make applications related to these concepts, to prove the theorems with the use of the basic properties of these concepts and problem solving
4   To be able to define the concept of derivative fr real-valued functions of real variables, to learn differentiation rules, to make the relevant applications about them and problem-solving.
5   To be able to solve the real-life problems of a different discipline using basic understanding of the Calculus with the ability of mathematical modeling.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Natural numbers, integers, rational numbers the set of natural numbers, integers, rational numbers set, a set of real numbers and their properties.
2 A single real-valued functions of real variable; range and domain; algebraic and non-algebraic functions.
3 Unit function, constant function, one to one function, onto function, one to one and bijective functions
4 Components of Functions; inverse of a function
5 The limit for a single real variable and real-valued functions
6 Finding the limit of a function at a point; applications
7 The fundamental theorems on limits and applications
8 Midterm
9 Continuity and applications; the discontinuity and types of discontinuity
10 The concept of derivative of one variable functions
11 Derivation rules and practices
12 The geometrical interpretation
13 Non-algebraic and algebraic functions (polynomial, trigonometric, logarithmic, exponential functions, ...), derivatives and applications
14 Parametric and implicit differentiation, derivatives of the inverse of a function, Higher derivatives and applications
15 Final Exam

Recomended or Required Reading

Balcı, M. 2008; Matematik Analiz I, Balcı Yayınları, Ankara.
Çoker, D. & O. Özer & K. Taş (1994) Genel Matematik. Ankara: Adım Yayıncılık.
Süer, B. & H. Demir (1984)Freshman Calculus. Ankara: O.D.T.Ü. Yayınları

Planned Learning Activities and Teaching Methods

Lecture, discussion, question-answer, problem solving, active learning techniques, group work

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 STT TERM WORK (SEMESTER)
3 FINS FINAL EXAM
4 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + STT * 0.10 + FINS * 0.60
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

esra.bukova@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Practice (Reflection) 13 2 26
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 3 3
Preparation for final exam 1 5 5
Preparing assignments 13 2 26
Preparing presentations 1 15 15
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 170

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1543323
LO.2543323
LO.3543323
LO.4543323
LO.554523243

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2012 DEÜ. BİD

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