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Over the past few decades, there has been a considerable increase in the use of mathematical analysis, both for solving everyday problems and for theoretical developments of many disciplines. For example, economics, biology, geography and medicine have all seen a considerable increase in the use of quantitative techniques. Twenty years ago applied mathematics meant the application of mathematics to problems in mechanics and little else--now, applied mathematics, or as many people prefer to call it, applicable mathematics, could refer to the use of mathematics in many varied areas. The one unifying theme that these applications have is that of mathematical modeling, by which we mean the construction of a mathematical model to describe the situation under study. This process of changing a real life problem into a mathematical one is not at all easy, we hasten to add, although one of the overall aims of this book is to improve your ability as a mathematical mod
A. to become a good mathematical modeler
B. to tackle as many mathematical problems as possible
C. to do the problems given in the book on one's own
D. to have confidence in constructing mathematical models
Today many people who live in large metropolitan areas such as Paris and New York leave the city m summer. They go to the mountains or to the seashores to escape the city noise and heat. Over 2.000 years ago, many rich Romans spent their summers in the city of Pompeii. Pompeii was a beautiful city. It was located on the ocean, on the Bay of Naples. In the year 79 A. D., a young Roman boy who later became a very famous Roman historian was visiting his uncle in Pompeii. The boy’s name was Pliny. One day Pliny was looking at the sky. He saw a frightening sight. It was a very large dark cloud, this black cloud rose high into the Sky. Rock and ash flew through the air. What Pliny saw was the eruption—the explosion—of the volcano. The city of Pompeii was at the foot of Mt. Vesuvius.
When the volcano first erupted, many people were able to flee the city and to escape death. In fact, 18,000 people escaped the terrible disaster. Unfortunately, there was not enoug
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