Mathematica (Trademark) and the Method of Steepest Descents. Part 1

Abstract

Mathematica is a symbolic manipulator with graphical capabilities. During the fall 1990 semester, I used Mathematica on my NeXT workstation to create graphics for teaching the method of steepest descents. This required level curve plots and surface plots for the real or imaginary part of functions of a complex variable. By the end of this topic in the course, I was doing near- research-level analysis of complex valued functions. The response of my class was also very positive. In this paper, I describe some of the more elementary examples discussed in the class. In Part II, I will describe the steepest descent analysis for the Lamb problem as a representative of research level application and utility of Mathematica for this type of analysis. This is the easiest example demonstrating how refracted and evanescent waves in a layered medium are treated by the method of steepest descents with the additional enhancement of Mathematica.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1992
Accession Number
ADA252779

Entities

People

  • Norman Bleistein

Organizations

  • Colorado School of Mines

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bessel Functions
  • Cartography
  • Complex Variables
  • Computer Graphics
  • Computer Science
  • Computers
  • Conformal Mapping
  • Graphics
  • Integrals
  • Laser-Induced Breakdown Spectroscopy
  • Lip
  • Mathematics
  • Numbers
  • Students
  • Wave Phenomena
  • Wave Propagation
  • Waves

Readers

  • Computational Modeling and Simulation
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Research Science/Academic Research