복소수함수론 1

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강의학기

2021년 1학기

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강의계획서

This is the first part of the two-semester series of Complex Analysis which sets basis funderstanding

the structure of complex numbers and the applications of those, especially of analytic functions which will

be treated mainly in the second semester. This class covers definition of complex numbers, elementary functions

and series in complex numbers.

차시별 강의

1.	Video: Week 1-Part 1	This video contains explanantions about Syllabus, Definition of complex numbers, and Complex field.
2.	Video: Week1-Part2	This video talks about Ordered field and the geometry of complex numbers.
3.	Video: Week2-Part1	This video exaplains conjugate, properties of conjugate, and identities involving modulus.
4.	Video: Week2-Part2	This video explains polar representation, arg z, Arg z, and product in polar.
5.	Video: Week3-Part1	This video explains z^n, DeMoivre's Theorem, Euler's formula, exponential form, and the nth roots of a complex number.
	Video: Week14-Part2	We examine derivative of inverse trig function, complex integral on an interval in R, and the Jordan curve.
6.	Video: Week3-Part2	This talks about nth roots of unity, neighborhood of a complex number, bounded set, and interior point of a set. It also includes some explanations on Quiz#1.
7.	Video: Week4-Part1	This talks about an open set, limit point of a set, a closed set, and the closure of a set.
8.	Video: Week4-Part2	We talk about z^(-1/n), boundary point of a set, boundary of a set, and a connected set.
9.	Video: Week5-Part1	This video explains domain, region, (single-valued) function, preimage, image, onto, one-to-one, and inverse function.
10.	Video: Week5-Part2	This video explains translation, rotation, dilation, linear mapping, and inversion.
11.	Video: Week6-Part1	We talk about sequence of complex numbers, limit of a complex sequence, limit of a complex-valued function, and limit point in terms of a sequence.
12.	Video: Week6-Part2	We talk about Bolzano-Weierstrass Theorem on a complex plane.
13.	Video: Week7-Part1	This contains Inversion and exponential function.
14.	Video: Week7-Part2	We examine the continuity of a complex-valued function.
15.	Video: Week8-Part1	We talk about differentiability at a point, analytic on an open set, entire, and what it means by analytic at a point.
	Video: Week8-Part2	We examine Cauchy-Riemann equations as a consequence of the differentiability.
	Video: Week9	This video talks about C-R as nondifferentiability test, stereographic projection, the point at infinity, and the extended complex plane.
	Video: Week10-Part1	We talk about the limit at the point at infinity.
	Video: Week10-Part2	We see a relation between an analytic function and an open set, then talk about the Mean Value Theorem for a two-variable function.
	Video: Week11-Part1	We characterize an analytic function on a domain D in the Complex Plane.
	Video: Week11-Part2	We derive C-R in polar form, and talk about harmonic functions.
	Video: Week12-Part1	We talk about harmonic conjugate, a symmetric domain, and the Reflection Principle.
	Video: Week12-Part2	We look at Logarithmic function and see the branches of log z.
	Video: Week13-Part1	This video talks about the Principal Log, continuity of log, differentiability of log, and the analyticity in polar.
	Video: Week13-Part2	We see the definition of Complex exponents.
	Video: Week14-Part1	We look at sin z, cos z, sinh z, cosh z, and inverse trig functions.