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Math 4200-001
4200-1 home page
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It is my goal to have lecture note outlines for each day posted by noon the day before. I will bring hard copies to class. In case you have to miss class I will also post filled in versions after class.
Week 1: August 19-23 Sections 1.1-1.3
aug19.pdf 1.1 introduction to algebra and geometry in the complex plane. aug19post.pdf after-class version.
aug21.pdf 1.1-1.2 algebra and geometry of complex arithmetic, continued. aug21post.pdf after-class version.
aug23.pdf 1.2-1.3 geometry of complex arithmetic and complex transformations aug23post.pdf after-class version.
Week 2: August 26-30 Sections 1.3-1.4
aug26.pdf 1.3 basic complex transformations aug26post.pdf after-class version.
aug28.pdf 1.3 general power functions; 1.4 3220-type analysis in C. aug28post.pdf after-class version.
aug30.pdf 1.4 part 2: adding functions and continuity to the mix. aug30post.pdf after-class version.
Week 3: September 4-6 Sections 1.4-1.5
sept4.pdf 1.4 slightly modified notes from last Friday sept4post.pdf after-class version.
sept6.pdf 1.5 complex differentiability sept6post.pdf after-class version.
Week 4: September 9-13 Sections 1.5-1.6
sept9.pdf 1.5: The Cauchy-Riemann equations, the differential map, chain rules. sept9post.pdf after-class version.
sept11.pdf 1.5: conformal maps, the inverse function theorem, examples. sept11post.pdf after-class version.
sept13.pdf 1.5-1.6: harmonic functions and conjugates; introduction to branch domains for inverse functions. sept13post.pdf after-class version.
Week 5: September 16-20 Sections 1.6, 2.1-2.2
sept16.pdf 1.6: branch domains for analytic functions. sept16post.pdf after-class version.
sept18.pdf 2.1: complex line integrals - "contour integrals". sept18post.pdf after-class version.
sept20.pdf 2.1-2.2 Contour integral tricks with Green's Theorem and antidifferentiation. sept20post.pdf after-class version.
Week 6: September 23-27 Sections 2.2-2.3
sept23.pdf 2.1-2.2 Cauchy's theorem and anti-derivatives on simply connected domains. sept23post.pdf after-class version.
sept25.pdf 2.3 Refinements of 2.2 sept25post.pdf after-class version.
sept27.pdf 2.3: rigorous "simply connected", antidifferentiation theorem, deformation theorem. sept27post.pdf after-class version.
Week 7: September 30 - Oct 4 Sections 2.3-2.4; exam
sept30.pdf 1-2.3 review notes sept30post.pdf after-class version.
oct4.pdf 2.4 index of a curve with respect to a point and the Cauchy integral formula. oct4post.pdf after-class version.
Week 8: October 14-18 Sections 2.4-2.5
oct14.pdf Cauchy integral formula for derivatives; Liouville's Theorem and the Fundamental Theorem of Algebra. oct14post.pdf after-class version.
oct16.pdf Morera's Theorem, and uniform limits of analytic functions; The Riemann Zeta function. oct16post.pdf after-class version.
oct18.pdf Maximum principles for analytic functions and harmonic functions oct18post.pdf after-class version.
Week 9: October 21-25 Sections 2.5, 3.1-3.2
oct21.pdf 2.5: conformal diffeomorphisms of the unit disk, and Poisson's formula. oct21post.pdf after-class version.
oct23.pdf 3.1: sequences and series of analytic functions oct23post.pdf after-class version.
oct25.pdf 3.2: power series and Taylor series oct25post.pdf after-class version.
Week 10: October 28 - November 1 Sections 3.2-3.3
oct28.pdf Taylor series and power series oct28post.pdf after-class version.
oct30.pdf Isolated zeroes for analytic functions; 3.3 Laurent series oct30post.pdf after-class version.
nov1.pdf 3.3 Laurent series nov1post.pdf after-class version.
Week 11: November 4-8 Sections 3.3-4.2
nov4.pdf classification of isolated singularities, Laurent series manipulations and residues nov4post.pdf after-class version.
nov6.pdf 4.1-4.2 residue theorem and calculation of residues nov6post.pdf after-class version.
nov8.pdf 4.2 residue theorem for exterior domains, and more residue table entries. nov8post.pdf after-class version.
Week 12: November 11-15 Section 4.3 and exam
nov11.pdf 4.3 intro to applications of contour integration; exam 2 review nov11post.pdf after-class version.
nov15.pdf 4.3 definite integral examples, via the Residue Theorem. nov15post.pdf after-class version.
Week 13: November 18-22 Sections 4.4, 5.1
nov18.pdf 4.3 examples, introduction to 4.4: infinite series expansions nov18post.pdf after-class version.
nov20.pdf 4.4 infinite series magic, and infinite partial fractions for meromorphic functions nov20post.pdf after-class version.
nov22.pdf 5.1 conformal transformations and the Riemann mapping theorem nov22post.pdf after-class version.
Week 14: November 25-27 Sections 5.1-5.2
nov25.pdf 5.1-5.2 Riemann mapping theorem and fractional linear transformations. nov25post.pdf after-class version.
nov27.pdf 5.2 conformal transformations nov27post.pdf after-class version.