DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Vector Analysis Course Code : MT 236 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Spring (16 Weeks) ECTS : 4 Name of Lecturer(s) : Asst.Prof.Dr. NAZAR ŞAHİN ÖĞÜŞLÜ Learning Outcomes of the Course : Is able to prove the properties of vector functions using their basic concepts. Uses basic properties of vector functions to solve some problems of physics. Calculates line integrals. Is able to prove the basic properties of Green´s theorem. Calculates surface integrals. Is able to prove the basic properties of divergence theorem. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Gain skills related to intangible and tangible aspects of vector analysis, to understand the basic concepts and physical applications of vector functions, line integrals, Green´s theorem and divergence theorem, teach understanding of abstract mathematical concept and abstract thinking. Course Contents : Vector functions, line integrals, Green´s theorem, surface integrals, divergence theorem Language of Instruction : Turkish Work Place : Halls at the Department of Mathematics   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Limit and derivative of vector functions. Review of the relevant pages from sources Lecture and discussion 2 Properties of the derivative of vector functions. Review of the relevant pages from sources Lecture and discussion 3 Motion along curve: speed, acceleration vector and uniform circular motion. Review of the relevant pages from sources Lecture and discussion 4 Tangential and normal compenents of the acceleration vector. Review of the relevant pages from sources Lecture and discussion 5 Newton and Kepler laws. Review of the relevant pages from sources Lecture and discussion 6 Vector and scalar fields and methods to obtain a new vector field from a vector field Review of the relevant pages from sources Lecture and discussion 7 Line integrals. Review of the relevant pages from sources Lecture and discussion 8 midterm exam Review of the topics discussed in the lecture notes and sources Written exam 9 Some physical applications of line integrals. (the work done along the curve, total flux) Review of the relevant pages from sources Lecture and discussion 10 Proof of Green´s theorem. Review of the relevant pages from sources Lecture and discussion 11 Green´s theorem for the regions bounded by two curves. Review of the relevant pages from sources Lecture and discussion 12 Conservative vector fields and fundemental theorem of line integrals. Review of the relevant pages from sources Lecture and discussion 13 Computation of surface integrals. Review of the relevant pages from sources Lecture and discussion 14 Proof of the Divergence theorem. Review of the relevant pages from sources Lecture and discussion 15 Some applications of divergence theorem 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 Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Calculus and Analytic Geometry, Authors: Shermann K. Stein, Anthony Barcellos. 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 Is able to prove Mathematical facts encountered in secondary school. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 4 6 Expresses clearly the relationship between objects while constructing a model 3 7 Draws mathematical models such as formulas, graphs and tables and explains them 5 8 Is able to mathematically reorganize, analyze and model problems encountered. 4 9 Knows at least one computer programming language 4 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 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 2 28     Out of Class Study (Preliminary Work, Practice) 14 2 28 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 91 Total Workload / 25 (h): 3.64 ECTS Credit: 4