Complex Calculus (MATH 305)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Nihat Gökhan Göğüş nggogus@sabanciuniv.edu,
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English
Undergraduate
MATH102
Formal lecture
Interactive,Communicative
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CONTENT

Analytic functions, Cauchy's theorem and the Cauchy integral formula. Taylor series. Singularities of analytic functions, Laurent series and the calculus of residues. Infinite products. Conformal mappings.

OBJECTIVE

To give an introduction to main methods of Complex Analysis which are needed for successful activity in many fields (engineering, economics, etc.) and for developing of mathematical thinking, as well

LEARNING OUTCOME

Upon completion of this course, students should be able to:
Operate with complex numbers;

Differentiate and integrate complex valued functions;
Distinguish analyticity from differentiability by real variables (Cauchy-Riemann equation);
Understand how analytic and harmonic functions are connected;
Formulate Cauchy Theorem and Cauchy Formula and apply them consciously for integration;
Identify Taylor and Laurent expansions and distinguish isolated singularities;
Apply Cauchy Residue Theorem to calculations of definite integrals;

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Midterm 22.5
Exam 67.5
Participation 10

RECOMENDED or REQUIRED READINGS

Readings

E. B. Saff, A. D. Snider, Fundamental of Complex Analysis, Pearson Education International, New Jersey
J. E. Marsden, M. J. Hoffman, Basic Complex Analtsis, W. H. Freeman, New York