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