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Course Description Course Name : Complex Calculus Course Code : EEE203 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 4 Name of Lecturer(s) : Asst.Prof.Dr. SAMİ ARICA Learning Outcomes of the Course : Understand complex functions , analyticity; Cauchy-Riemann equations; harmonic functions. Learn exponential, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions. Compute complex integrals, apply Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences. Realize Residues, the Residue Theorem, evaluate improper real integrals using the Residue Theorem. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : In this course, functions of a complex variable, continuity, limits, derivative and contour integrals of the functions are discussed. In other words, the topic is an extension of calculus to the functions of a complex variable. Course Contents : Review of complex numbers. Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions. Elementary functions: exponential transformations, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions. Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences. Taylor and Laurent series, classification of singularities. Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem. Conformal mappings and applications. Language of Instruction : English Work Place : Department of Electrical and Electronics engineering building classrooms.   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Review of complex numbers. Textbook reading/Problem solving. Lecture. 2 Review of complex numbers (continued). Textbook reading/Problem solving. Lecture. 3 Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions . Textbook reading/Problem solving. Lecture. 4 Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions (continued). Textbook reading/Problem solving. Lecture. 5 Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions (continued). Textbook reading/Problem solving. Lecture. 6 Elementary functions: exponential transformations, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions. Textbook reading/Problem solving. Lecture. 7 Elementary functions: exponential transformations, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions (continued). Textbook reading/Problem solving. Lecture. 8 Midterm Exam I Textbook reading/Problem solving. Written exam. 9 Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences. Textbook reading/Problem solving. Lecture. 10 Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences (continued). Textbook reading/Problem solving. Lecture. 11 Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences (continued). Textbook reading/Problem solving. Lecture. 12 Midterm Exam II. Taylor and Laurent series, classification of singularities. Textbook reading/Problem solving. Written exam. Lecture. 13 Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem Textbook reading/Problem solving. Lecture. 14 Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem (continued). Textbook reading/Problem solving. Lecture. 15 Conformal mappings and applications. Textbook reading/Problem solving. Lecture. 16/17 Final Exam. Textbook reading/Problem solving. Lecture.   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Complex analysis: an introduction to the theory of analytic functions of one complex variable. Lars Valerian Ahlfors. 3 edition (January 1, 1979). McGraw-Hill.  Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics. Edward B. Saff Edward B. Saff, Arthur David Snider. 3 edition (January 10, 2003). Prentice Hall.  Complex Analysis. John M. Howie. (April 20, 2007). Springer. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 2 100     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 Has capability in those fields of mathematics and physics that form the foundations of engineering. 5 2 Grasps the main knowledge in the basic topics of electrical and electronic engineering. 5 3 Comprehends the functional integrity of the knowledge gathered in the fields of basic engineering and electrical-electronics engineering. 3 4 Identifies problems and analyzes the identified problems based on the gathered professional knowledge. 3 5 Formulates and solves a given theoretical problem using the knowledge of basic engineering. 3 6 Has aptitude for computer and information technologies 0 7 Knows English at a level adequate to comprehend the main points of a scientific text, either general or about his profession, written in English. 3 8 Has the ability to apply the knowledge of electrical-electronic engineering to profession-specific tools and devices. 0 9 Has the ability to write a computer code towards a specific purpose using a familiar programming language. 0 10 Has the ability to work either through a purpose oriented program or in union within a group where responsibilities are shared. 2 11 Has the aptitude to identify proper sources of information, reaches them and uses them efficiently. 3 12 Becomes able to communicate with other people with a proper style and uses an appropriate language. 0 13 Internalizes the ethical values prescribed by his profession in particular and by the professional life in general. 0 14 Has consciousness about the scientific, social, historical, economical and political facts of the society, world and age lived in. 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) 16 3 48 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 2 2 4     Final Exam 1 2 2 Total Workload: 96 Total Workload / 25 (h): 3.84 ECTS Credit: 4