## Files

May 16th, 2010 by math421-murrayThis page will have links to *Mathematica *notebooks and other files for your use.

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*

- AboutPresentations.nb — installing, loading, getting help about
*Presentations*(*updated*18 Sept 2010) - 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
*n*th 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