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.

### Complex Calculus (MATH 305)

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Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | |||

BA-Economics | |||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | |||

BS-Computer Science & Eng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Electronics Engineering | * | ||

BS-Electronics Engineering | * | ||

BS-Industrial Engineering | * | ||

BS-Manufacturing Systems Eng. | * | ||

BS-Materials Sci. & Nano Eng. | * | ||

BS-Materials Science & Eng. | * | ||

BS-Mechatronics | * | ||

BS-Mechatronics | * | ||

BS-Microelectronics | |||

BS-Molecular Bio.Gen.&Bioeng | |||

BS-Telecommunications | * | ||

Mathematics | |||

Physics |

### CONTENT

### 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;

### Update Date:

### 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 |