Türkçe | English SÜRMENE FACULTY of MARINE SCIENCES / DEPARTMENT of FISHERIES TECHNOLOGY ENGINEERING Course Catalog http://www.ktu.edu.tr/baltekmuh Phone: +90 0462 7522805 SDBF
SÜRMENE FACULTY of MARINE SCIENCES / DEPARTMENT of FISHERIES TECHNOLOGY ENGINEERING /    MAT1011 Mathematics - I 4+0+0 ECTS:5 Year / Semester Fall Semester Level of Course First Cycle Status Compulsory Department DEPARTMENT of FISHERIES TECHNOLOGY ENGINEERING Prerequisites and co-requisites None Mode of Delivery Contact Hours 14 weeks - 4 hours of lectures per week Lecturer Dr. Öğr. Üyesi Devran YAZIR Co-Lecturer Asst. Prof. Dr. Devran YAZIR Language of instruction Turkish Professional practise ( internship ) None The aim of the course: The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences.
 Learning Outcomes CTPO TOA Upon successful completion of the course, the students will be able to : LO - 1 : clasify numbers and understand functions and their properties 1,3 1 LO - 2 : know the concepts of limit and continuity of functions 1,3 1 LO - 3 : know the concepts of derivatives of functions 1,3 1 LO - 4 : apply of the derivative to some engineering problems 1,3 1 LO - 5 : know the concepts of integral of functions 1,3 1 LO - 6 : apply the integration to some engineering problems and to some applications 1,3 1 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 Midterm exam. 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 Final exam
 Textbook / Material
 1 Thomas, G.B., Weir, M.D., Hass, J., Thomas' Calculus, 12th Edition, 2009, Pearson, USA.