Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
The first portion of this work is devoted to a consideration of the practical aspects of the proctoscopic examination and thus presents the indications for performing a proctologic evaluation, the information that may be obtained from the patient's medical history, an example of a preprinted data form for use in the recording of the physician's findings, the preparation and positioning of the patient, and the preliminary examination of the anus including the digital rectal examination. The instruments needed to perform proctoscopy are uncomplicated, and the basic tools are inexpensive. The instruments currently available do not really differ from each other except in minor details. In the text, therefore, we have only described the prototype instruments, and details about the pro posed advantages of any particular instrument can be obtained from its manufac turer. The concluding portion of the text describes how the proctoscopic and colonoscopic examinations are performed. The atlas itself is a topographical stratification of the various diseases that may involve the perianal region, the anus, and the adjacent portions of the large bowel as well as their classification according to morphologic criteria, for example, inflammatory bowel diseases and tumors. Since many pathologic findings in the rectum and sigmoid colon are comparable to those in the upper portions of the large bowel, a duplication of these proctoscopic and colonoscopic illustrations has been avoided.
The first portion of this work is devoted to a consideration of the practical aspects of the proctoscopic examination and thus presents the indications for performing a proctologic evaluation, the information that may be obtained from the patient's medical history, an example of a preprinted data form for use in the recording of the physician's findings, the preparation and positioning of the patient, and the preliminary examination of the anus including the digital rectal examination. The instruments needed to perform proctoscopy are uncomplicated, and the basic tools are inexpensive. The instruments currently available do not really differ from each other except in minor details. In the text, therefore, we have only described the prototype instruments, and details about the pro posed advantages of any particular instrument can be obtained from its manufac turer. The concluding portion of the text describes how the proctoscopic and colonoscopic examinations are performed. The atlas itself is a topographical stratification of the various diseases that may involve the perianal region, the anus, and the adjacent portions of the large bowel as well as their classification according to morphologic criteria, for example, inflammatory bowel diseases and tumors. Since many pathologic findings in the rectum and sigmoid colon are comparable to those in the upper portions of the large bowel, a duplication of these proctoscopic and colonoscopic illustrations has been avoided.
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