Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FBÖ1432013334	GENERAL MATHEMATICS-I	Compulsory	1	1	5

Level of Course Unit

First Cycle

Objectives of the Course

Acknowledging the numerical systems and induction principle. Examining uni variable and real valued functions, interpreting their graphics, reinforcing limit, continuity and absolute value concepts and making applications and interpretations, transferring the knowledge in this course to others, building an infrastructure for mathematics course.

Name of Lecturer(s)

Yrd. Doç. Dr. Meral CANSIZ AKTAŞ

Learning Outcomes

1	Concepts and properties of proposition can be defined. The principle of induction and the concepts of range and absolute value are learnt.
2	Set concept is known and operations related with it can be done. Systems of numbers and their properties are learnt. The base arithmetic is known.
3	Relation concept and its properties are known. Equivalence and ordered relation can be described
4	The definition of the concept of function, its types and features are known.
5	The concept of limit and its characteristics are known
6	Limit calculations can be done
7	The concept of continuity and its features are known.
8	The concept of continuity and types of discontinuity are known
9	The concept of derivative can be defined.
10	The rules of derivation are known

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

Numbers, numerical systems and their properties, induction principle, range and absolute value, relation, paired relations, Cartesian product, Definition of relation, Properties of relation, Inverse Relation, equivalence relation, Order relation, Functions: Definition and properties of function, Types of functions, Inverse function, Compound function, Trigonometric functions, Exponential functions, Logarithmic functions, Inverse trigonometric functions, Special functions, Limit: Limit of a variable, Limit of functions, Limit of trigonometric functions, Continuity: Definition of continuity, Limit from the left and Limit from the right, Properties of continuity functions, Types of continuity, Derivative: Definition of derivative, Geometrical interpretation of derivative, Rules of Derivation, Higher order derivatives.

Course Contents

1 Propositional logic. General concepts and processes. Main characteristics of the operations. Proving methods. Exercises. 2 The concept of sets. Operations related with sets. Exercises.. 3 System of numbers. Definitions. The base of arithmetic. Exponential, root and logarithmic numbers. Exercises. 4 Absolute value. Complex numbers. Exercises. Polar notation of complex numbers. Equations of nth roots. Exercises. 5 Relation: Ordered pairs, cartesian product, the definition of correlation, properties of relation, inverse relation. Equivalence Relation and Order Relation. 6 Definition of function, function types, inverse function, composite functions. Some special functions (linear, quadratic functions) 7 Some special functions (absolute value, notation, the exact value, polynomial, rational, closed, partial, parametric). 8 Trigonometric functions, inverse-trigonometric functions and their graphs. 9 Exponential functions, logarithmic functions. Practice related with Functions. Exercises. 10 The concept of limit. A variable approach, the limit of functions. One-way limits. Formulas of limit calculation and calculation techniques. 11 The concept of continuity, right and left continuity, features of continuous functions, discontinuity types. Exercises. 12 Derivative concept, geometric and physical interpretation of the derivative. Derivation rules, high-ordered derivatives. Exercises. 13 Derivation rules, derivative of inverse and compound functions. High-ordered derivatives. Exercises. 14 Derivative of the parametric and closed functions. Exercises.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Numbers, numerical systems and their properties, induction principle, range and absolute value, relation, paired relations
2	Cartesian product, Definition of relation, Properties of relation, Inverse Relation, equivalence relation, Order relation
3	Functions: Definition and properties of function, Types of functions, Inverse function, Compound function
4	Trigonometric functions and Inverse trigonometric functions
5	Exponential functions and Logarithmic functions
6	Special functions.
7	Limit: Limit of a variable, Limit of functions.
8	Limit of trigonometric functions.
9	Limit of the uncertainty condition
10	Continuity: Definition of continuity, Limit from the left and Limit from the right, Properties of continuity functions, Types of continuity.
11	Derivative: Definition of derivative, Geometrical interpretation of derivative.
12	Rules of Derivation.
13	Rules of Derivation.
14	Higher order derivatives