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Course Description Course Name : Mathematics I Course Code : TMZ102 Course Type : Compulsory Level of Course : First Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Assoc.Prof.Dr. AHMET TEMİZYÜREK Learning Outcomes of the Course : Defines the reversible function. describes the relationship between the definition of the inverse function and main function. Illustrates the inverse functions of special type Defines the coordinate systems with coordinate systems, and explains the relationship between the polar coordinate system and vertical coordinate system . Knows how to take the integral and makes integral applications Defines a function of multivariate. Understands a surfacescan be expressed by a functions of several variables Calculates the partial derivatives of a multivariate functions. Finds the critical points of functions of several variables. Solves conditional maximum-minimum problems using the method of Lagrange multipliers Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : The aim of this course is to teach the basic mathematical theory knowledge required of the engineering profession, gain the ability to use the knowledge acquired in the required fields correctly Course Contents : The inverse function theorem, exponential and logarithmic functions, trigonometric and inverse trigonometric functions, indefinite forms and Taylor polynomial, Polar coordinates, Idefinite integral, definite integral, integral applications, functions of several variables, maximum - minimum problems of functions of sevral variables , the method of Lagrange multipliers Language of Instruction : Turkish Work Place : Faculty of Engineering Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Exponential and logarithmic functions Review of the relevant pages from sources Lecture and discussion 2 Trigonometric and inverse trigonometric functions Review of the relevant pages from sources Lecture and discussion 3 Indeterminate forms Review of the relevant pages from sources Lecture and discussion 4 Taylaor polynomial Review of the relevant pages from sources Lecture and discussion 5 The polar coordinate system Review of the relevant pages from sources Lecture and discussion 6 Methods of integration Review of the relevant pages from sources Lecture and discussion 7 Integrals of trigonometric and inverse trigonometric functions Review of the relevant pages from sources Lecture and discussion 8 Mid-Term exam Review of the topics discussed in the lecture notes and sources again Written exam 9 Integration of rational functions using simple fractions Review of the relevant pages from sources Lecture and discussion 10 Definite integral Review of the relevant pages from sources Lecture and discussion 11 Applications of definite integral Review of the relevant pages from sources Lecture and discussion 12 Applications of definite integral Review of the relevant pages from sources Lecture and discussion 13 Limits and continuity of functions of several variables Review of the relevant pages from sources Lecture and discussion 14 Minimum - maximum and derivative of functions of several variables Review of the relevant pages from sources Lecture and discussion 15 Lagrange multipliers method Review of the relevant pages from sources Lecture and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources again Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  AKDENİZ,F, ÜNLÜ,Y., DÖNMEZ,D., . Analize Giriş Cilt 2, 3.Edition,Nobel publishing house, Adana, 2006.  SEWARD, J., Kalkülüs, Second Edition, TUBA, ISBN: 975-8593-94-3, Ankara, 2007.   STEIN, S. K. , BAREELLOS, A. Calculus ve Analitik Geometri, 1. Cilt. Literatür publishing, İstanbul, 1977. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Uses information and communication technologies and softwares at a required level 0 2 Has the professional and ethical responsibility. 1 3 Uses the knowledge obtained from the basic sciences and engineering in the field of textile engineering 4 4 Does process analysis, Identifies problems, interprets and evaluates data in the field of textile engineering 2 5 Selects and uses modern techniques and tools for engineering applications 2 6 Has the skills of designing experiments, data collection, cognitive analysis and interpretation of the results 0 7 Works effectively both individually and as a team member and takes responsibility 1 8 Searches literature, has access to information, uses databases and other sources of information 2 9 Recognizes the need of lifelong learning; follows developments in science and technology and renews self continuosly 2 10 Has effective oral and written communication skills. 1 11 Follows developments in the field in a foreign language, has good communication skills with colleagues. 0 12 Has the necessary awareness on the fields of occupational health and safety, legal side of engineering applications and environmental health. 0 13 Has required competence in project management, entrepreneurship and innovation. 1 14 Has sufficient background in the fields of Mathematics, Science and Textile Engineering 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 5 70 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 6 6     Final Exam 1 10 10 Total Workload: 128 Total Workload / 25 (h): 5.12 ECTS Credit: 5