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# Files

Files with extension .nb require Mathematica to read and evaluate (or the free Mathematica Player just to read as is). Most of the Mathematica notebooks also require David Park’s Presentations add-on for Mathematica; Math 421 students will receive a free copy of Presentations for their personal use from the professor.

• Intro1.nb— first part of an interactive introduction to Mathematica
• Intro2.nb— second part of an interactive introduction to Mathematica
• Intro3.nb— third and last part of an interactive introduction to Mathematica
• UsingPresentationsPalette.mp4— video about how to use the palette for Presentations
• FactorTheorem.nb — roots and linear factors of complex polynomials
• FactorTheoremEvaluated.pdf— for reading: evaluated form of preceding notebook
• CardanoBombelli.nb — the origin of complex numbers
• CardanoBombelliEvaluated.pdf — for reading: evaluated form of preceding notebook
• nthRoots.nb — finding and drawing nth roots of unity and other complex numbers (revised 14 September 2010)
• CartesianPolarForms.nb — Cartesian and polar forms of complex numbers, and how to convert between them (some use of Presentations here) (revised 14 September 2010)
• DrawingComplexObjects.nb — using Presentations to draw geometric objects in the complex plane (newly revised 25 September 2010)
• DrawComplexPointAndArrow.nb —using Presentations to draw a point and vector in the complex plane; class demo 9/22/10
• VisualizingFunctions.nb — using Presentations to visualize how a complex function maps the complex plane in Cartesian and polar coordinates (renamed and revised 26 September 2010)
• CalculatingImages.nb — using complex algebra, with and without Mathematica, to determine images of geometric objects in the complex plane under a complex function
• AffineTransformationExample.nb — example from Sept. 29 class: image of half-plane Im(z)>1 under a particular affine function
• SquaringExample.nb —annotated examples from Oct 6–8 classes: images of a polar region and a rectangular region under the squaring function
• RiemannSphere.nb — stereographic projection and lifting complex functions to the Riemann sphere (updated 10/17/10)
• CauchyRiemannNotEnough.nb —examples of functions that are not differentiable yet satisfy the Cauchy-Riemann equations at a point
• ExponentialLogFunctions.nb — visualizing exp and Log (updated 11/7/10)
• Sine.nb — properties of complex sin (updated 11/7/10)
• ContourIntegrals.nb — calculating a contour integral as a limit of sums and as the definite integral of a complex-valued function on a real interval; cycloid as a contour