COURSE UNIT TITLE

: CALCULUS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
LMÖ 1001 CALCULUS I COMPULSORY 4 2 0 6

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR ESRA BUKOVA GÜZEL

Offered to

Mathematics Teacher Education

Course Objective

Recognize the fundamental concepts of Calculus; examine the properties of natural numbers, integers, rational, irrational, and real number systems necessary for understanding Calculus; identify real-valued functions of a single real variable; explore key concepts such as limits, continuity, and uniform continuity; help students grasp the basic concepts of Calculus and understand their interrelationships through real-world examples; develop problem-solving skills by applying Calculus concepts.

Learning Outcomes of the Course Unit

1   Know natural numbers, integers, rational numbers, irrational numbers and the real number sets, and relate these sets of numbers; to express their differences.
2   Recognize the only real variable real-valued functions and make applications with these functions.
3   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   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   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, 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

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

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 VZ Midterm
2 FN Semester final exam
3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60
4 BUT Make-up note
5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Assessment of students is measured by midterm and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

esra.bukova@deu.edu.tr

Office Hours

It will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Tutorials 13 2 26
Preparations before/after weekly lectures 13 1 13
Preparation for midterm exam 1 21 21
Preparation for final exam 1 30 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 146

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.1543131111112311111
LO.2543131111112311111
LO.3543131111112311111
LO.4543131111112311111
LO.5545231111124311111

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

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