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

Course Description Course Name : Advanced Calculus II Course Code : MT 242 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Spring (16 Weeks) ECTS : 7 Name of Lecturer(s) : Learning Outcomes of the Course : Knows limit theorems for functions, continuity, and proper continuity. Uses monotone and inverse functions to solve the problems faced by using fundamental theorems. Knows derivatives and differential calculus. Knows the Mean value theorem and its applications. Knows Taylor series expansion of the functions and how it is used for numerical computations. Learns to use sequences and series of functions to define new functions. Learns the Weirstrass M-test and the advantages of uniform convergence. Learns the analytical definitions of geometrically defined functions, using power series. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To comprehend fully the structure of and prove the properties of the real numbers analytically which were used in MT131 and MT 132 . Thus, equipped with the basic infrastructure of real-analysis, the student is able to comprehend advamced abstract concepts of analysis. Course Contents : Limit, continuity, derivatives in functions. Sequences and series of functions. Language of Instruction : Turkish Work Place : Faculty of Science Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Limits of functions and properties. Review of the relevant pages from sources Lecture and discussion 2 Limit theorems Review of the relevant pages from sources Lecture and discussion 3 Continuous functions and properties. Review of the relevant pages from sources Lecture and discussion 4 Continuous functions on intervals. Review of the relevant pages from sources Lecture and discussion 5 Uniform continuity Review of the relevant pages from sources Lecture and discussion 6 Continuity of Monotone and inverse functions Review of the relevant pages from sources Lecture and discussion 7 Derivative, differential. Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review topics discussed in the lecture notes and sources Written Exam 9 The mean value theorem and its applications Review of the relevant pages from sources Lecture and discussion 10 Taylor´s theorem and its applications Review of the relevant pages from sources Lecture and discussion 11 Sequences and series of functions Review of the relevant pages from sources Lecture and discussion 12 Pointwise and uniform convergence, and applications Weirstarass M-test Review of the relevant pages from sources Lecture and discussion 13 Change the order of the limit in function sequence Review of the relevant pages from sources Lecture and discussion 14 Relationship between the derivative of the limit and the limit of the derivatives in sequences of functions Review of the relevant pages from sources Lecture and discussion 15 Power series Review of the relevant pages from sources Lecture and discussion 16/17 Final exam Review of topics discussed in the lecture notes and sources Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert Required Course Material(s)  Principles of Mathematical Analysis, Walter Rudin   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 5 20 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. 2 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. 1 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 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 5 5 25     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 172 Total Workload / 25 (h): 6.88 ECTS Credit: 7