Türkçe | English FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES Course Catalog http://www.ktu.edu.tr/isbb Phone: +90 0462 +90 (462) 3773112 FENF
FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /    MAT1009 Mathematics-I 4+2+0 ECTS:6 Year / Semester Fall Semester Level of Course First Cycle Status Compulsory Department DEPARTMENT of STATISTICS and COMPUTER SCIENCES Prerequisites and co-requisites None Mode of Delivery Contact Hours 14 weeks - 4 hours of lectures and 2 hours of practicals per week Lecturer Doç. Dr. Pembe İPEK AL Co-Lecturer Assist. Prof. Hüsnü Anıl ÇOBAN Language of instruction Turkish Professional practise ( internship ) None The aim of the course: This course aims to teach the basic mathematical techniques, introducing mathematical skills to analyzes problems. With many examples of math emphasis is on the practical usability.
 Learning Outcomes CTPO TOA Upon successful completion of the course, the students will be able to : LO - 1 : learn the concepts of limit and continuity of functions LO - 2 : learn the concepts of derivatives of functions LO - 3 : learn the concepts of integral of functions CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome
 Contents of the Course
 Functions (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques
 Course Syllabus Week Subject Related Notes / Files Week 1 Definition of function, Introduction to function types, Summation, subtraction etc. properties of functions, Week 2 Graphs of basic functions and shifting graphs, Inverse functions Week 3 Trigonometric functions, Inverse trigonometric functions Week 4 Logarithmic, exponential and hyperbolic functions Week 5 Limit, limit computation rules. Formal definition of limit One-sided limits Week 6 Continuity, properties of continuous functions, Intermediate Value Theorem Limits at infinity and infinite limits, asymptotes of graphs Week 7 Derivative of a function, geometrical meaning of derivative, Differentiation rules, Derivatives of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions Week 8 Chain rule, Implicit differentiation Higher order derivatives L?hospital?s rule Week 9 Mid-term Week 10 Applications of differentiation (maximum-minimum and Mean Value Theorem) First and second derivative tests Week 11 Sketching the graph of a function by analyzing changes. Week 12 Optimization problems Week 13 Indefinite integrals (Anti-derivatives) Methods of integration (change of variables, integration by parts) Week 14 Partial fractions, Integrals of trigonometric (rational) functions. Week 15 Elimination of incomplete parts, general assessment Week 16 End-of-term exam
 Textbook / Material
 1 Thomas, G.B., Finney, R.L. 2001; Calculus ve Analitik Geometri (çeviri), Cilt 1, Beta Yayınları. 2 Thomas, G.B., Finney, R.L. 2001; Calculus ve Analitik Geometri (çeviri), Cilt 1, Beta Yayınları.