A comprehensive treatment of the advanced methods of applied mathematics. Designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Review of elementary methods in complex analysis, ordinary differential equations, and partial differential equations. Expansions around regular and irregular singular points; asymptotic evaluation of integrals, regular perturbations; WKB method; multiple scale method; boundary-layer techniques.
This video segment adapted from NOVA explains the difference between weather and climate and features groundbreaking analysis revealing that Earth's climate has changed much faster than previously believed.
Human DNA profiling has applications in paternity testing and forensics. This exercise provides students the opportunity to gain first-hand experience with procedures that are currently used to extract DNA from their own cells, quantify the DNA in the extract, perform a multiplex PCR amplification of several loci used in forensic analysis, and determine their own genotype at those loci. In addition, methods for analyzing results relative to existing population databases will be presented. The exercise is normally presented in the context of a laboratory course in Forensic DNA Analysis that presents students with a variety of techniques that have been and/or continue to be employed in forensic laboratories.
Samples of soil were recovered from an Indiana murder victim's car and shoes. This experiment isolates DNA from plants grown from seeds that were found on the shoes. Two different ecotypes of a weed grow in different areas of Indiana. This difference can be detected using the polymerase chain reaction (PCR). DNA is extracted from the seedlings using the REDExtract-N-Amp Plant PCR Kit. Specific regions of the isolated DNA are then amplified by PCR. The PCR products are analyzed by gel electrophoresis and the results used to determine which suspect was in the same area as the victim. With data from previous exercises the students can determine who committed the murder. An alternate CTAB DNA isolation procedure is also included.
This experiment uses polymerase chain reaction to demonstrate the polymorphic nature of human DNA. Students obtain samples of their own DNA using a simple mouthwash procedure. PCR is used to amplify a noncoding region of chromosome 1 that contains a repeated DNA sequence. The number of times the sequence repeats can vary from person to person, resulting in a polymorphism. Following amplification, student samples are electrophoresed, stained, and photographed. Each student will see one or two bands in their gel lane, indicating whether they are homozygous or heterozygous for that region of chromosome 1. This experiment is adapted from Advanced DNA Science: An Introduction to Methods of Genome Analysis by Mark V. Bloom, Greg A. Freyer, and David A. Micklos (copyright 1993 Cold Spring Harbor Laboratory and Carolina Biological Supply Company); polymerase chain reaction is covered by patents owned by Hoffman La Roche.
Students use DNA profiling to determine who robbed a bank. After they learn how the FBI's Combined DNA Index System (CODIS) is used to match crime scene DNA with tissue sample DNA, students use CODIS principles and sample DNA fragments to determine which of three suspects matches evidence obtain at a crime location. They communicate their results as if they were biomedical engineers reporting to a police crime scene investigation.
Subject:
Mathematics and Statistics, Science and Technology
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