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Dec 30, 2024
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MATH 409 - Introduction to Complex Variables(3 cr) The course begins with the arithmetic of complex numbers, including powers, roots, and polar representation, with special emphasis on the geometric view. Several function classes are studied in the setting of the complex plane, especially linear, linear fractional, exponential, logarithmic, and trigonometric. Includes basic notions from calculus, particularly limits, continuity, and the derivative, are reexamined in the complex setting. Special attention is given to the properties of analytic functions, harmonic functions, and the Cauchy-Riemann equations. Applications are considered in areas such as steady state temperature patterns and electrostatic potentials. The latter part of the course deals with contour integration techniques, power series representation, and the classic theorems on analytic functions of a complex variable. Prerequisites: MATH 309 or permission of instructor.
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