Math 4200-1
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Professor Korevaar
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Lectures are listed in reverse chronological order.
Week 16
finalreview.pdf review sheet, and a copy of my 2002 Math 4200 final exam questions
dec5.pdf 5.2 fractional linear transformations.
Week 15
dec2.pdf 5.1-5.2 Riemann mapping theorem, intro to FLT's.
nov30.pdf 5.1-5.2 conformal transformations and the Riemann Mapping Theorem.
nov28.pdf extra: Using Fourier transform and contour integration to solve the heat equation on the real line.
Week 14
nov23.pdf extra: two class exercises for harmonic functions in the disk, and exam 2 score distribution.
nov21.pdf 2.5 and extra: harmonic functions in the disk, with prescribed boundary values.
nov21maple.pdf extra: Maple pictures illustrating the class notes
Week 13
nov18.pdf extra: FTC and divergence theorem in R^m - key tools in derivation of PDE's.
Week 12
nov11.pdf 8.1-8.2 a Math 2280 example using Laplace transform
nov9.pdf 8.1-8.2 Laplace transform and its inverse
nov7.pdf 4.3-4.4 more favorite countour integrals
Week 11
nov4.pdf 4.3-4.4 favorite contour integrals
nov2.pdf 4.2 Residue theorem and residue theorem for exterior domains
oct31.pdf 4.1 calculating residues
Week 10
oct28.pdf 4.1 Residues and introduction to the residue theorem
oct26.pdf 3.3 Classification of isolated singularities
Week 9
oct21.pdf 3.3 Laurent series
oct19.pdf 3.2 uniqueness of continuation for analytic functions
oct17.pdf 3.2 power series are analytic inside their radius of convergence, and can be differentiated, integrated, or multiplied term by term
Week 8
oct14.pdf 3.1-3.2 power series for analytic functions
oct12.pdf 2.5 finishing maximum modulus principle and some application examples.
oct10.pdf 2.5 Mean value property and harmonic functions revisited
Week 7
oct5.pdf 2.4 Consequences of Cauchy: Liouville's Theorem and the Fundamental Theorem of Algebra
Week 6
sept30.pdf 1-2.3 review sheet for first exam
sept28.pdf 2.4 index and the Cauchy Integral formula
sept26.pdf 2.3 The antiderivative theorem for simply connected domains and fixed endpoints and closed loop deformation theorems.
Week 5
sept23.pdf 2.3 the local antiderivative theorem for analytic functions
sept21.pdf 2.2 simple connected domains have the path-independence and antiderivative property
sept19.pdf 2.1-2.2 path independence for complex line integrals is equivalent to having a complex antiderivative for the integrand.
Week 4
sept16.pdf 2.1-2.2 curve "addition" and line integrals; reparameterization of line integrals
sept14.pdf 2.1 review of real line integrals, introduction to complex line integrals.
sept12.pdf 1.6 branches of analytic functions
Week 3
sept9.pdf 1.5 continued
sept7.pdf 1.5 Calculus, for complex differentiable functions, continued
Week 2
sept2.pdf 1.5 Calculus for complex differentiable functions
aug31.pdf 1.3 "elementary" complex transformation functions
aug29.pdf 1.5 Complex differentiability means real differentiability with rotation dilation derivative matrix; CR equations.
Week 1
aug26.pdf 1.1-1.2 Euler's formula; complex conjugation; identities and estimates.
aug24.pdf 1.1 algebra and geometry of the complex plane