Calculus, sometimes called the "mathematics of change", is a branch of mathematics concerned with describing the precise way in which changes in one variable relate to changes in other. In almost every human activity we encounter two types of variables : those that we can control directly and those that we cannot. Fortunately, those variables that we cannot control directly often respond in some way to those that we can. For example, the acceleration of a car responds to the way in which we control the flow of gasoline to the engine, and the level of an antibiotic in a person's bloodstream responds to the dosage and timing of a doctor's prescription. By understanding quantitatively how the variable we cannot control directly respond to those that we can, we can hope to make predictions about the behavior of our environment and gain some mastery over it. Calculus, founded by Newton and Leibniz, is one of the fundamental mathematical tools used for this purpose.
MUSIC
Researchers at Yale University have investigated the application of wavelets to sound synthesis (music and voice). To approximate the sound of a musical instrument or voice, samples are taken and decomposed mathematically into numbers called wavelet packet coefficients. These coefficients can be stored on a computer and later sound can be reconstructed (synthesized) from the computer data. This area of research makes it possible to reproduce complex sounds from a small amount of data and to transmit those data electronically in a highly compressed form. This research may eventually speed up the transmission of sound over the Internet.
WEATHER PREDICTION
Modern meteorology is a marriage between mathematics and physics. Today's meteorologists are concerned with much more than predicting daily weather changes--their research delves into such areas as global warming, holes in the ozone layer and weather patterns on other planets. In 1904 the Norwegian meteorologist Vilhelm Bjerknes proposed that the state of the atmosphere at any future time can be determined by measuring appropriate variables at a single instant of time and then solving certain hydrodynamic equations. Although, it is difficult to apply this principle. However, new mathematical discoveries have dramatically improved meteorological predictions and spawned enormous
economic benefits.
MEDICAL IMAGING & DNA STRUCTURE
Advances in nuclear magnetic resonance (NMR) have made it possible to determine the structure of biological macromolecules, study DNA replication, and determine how proteins act as enzymes and antibodies. Related advances in Magnetic Resonance Imaging (MRI) have made it possible to view internal human tissue without invasive surgery and to provide real-time images during surgical procedures. High-quality NMR and MRI would not be possible without mathematical discoveries that have occurred within the last decade.
CONTROLLING CHAOTIC BEHAVIOR OF HUMAN-HEART
Chaos theory, which is one of the most exciting new branches of mathematics, is concerned with identifying regularities in phenomena that on the surface seem random and unpredictable. Today's research literature abounds with applications of chaos theory to almost every imaginable branch of science. Researchers at Georgia Tech University collaborated with physicist at the Emory University Medical Center in applying chaos theory to control the chaotic behaviour of heart tissue that is undergoing ventricular fibrillation (cardiac arrest). The research, though experimental, is already showing promising result.
DEEP SPACE EXPLORATION
Alexander Wolszczan of Penn State University may go down in history as the first scientist to identify a planetary system beyond our own. While searching the radio sky, he discovered a new pulsar, PSR1257+12, that seemed to wobble as it travelled through space. As a result of an extensive mathematical analysis, many scientists are now convinced that the wobble is caused by two or three planets orbiting the pulsar. Although scientists have been able to detect pulsars for some time by searching for faint periodic radio signals from outer space, it is only recently that the mathematical techniques have been developed to analyse the data in a way that stands up to scientific scrutiny.
Finally, we can see that today's life has an exciting applications of calculus but, it has roots that can be traced to the work of the Greek mathematician Archimedes, but the actual discovery of the fundamental principles of calculus was made independently by Isaac Newton (English) and Gottfried Leibniz (German) in the late seventeenth century.
Calculus drives our lives today, and further advances will help us achieve even greater heights!!
Isaac Newton Gottfried Leibniz
Calculus has enormous, but often unnoticed, impact on our daily lives. Here are a few areas of research where calculus is used extensively. All of these applications involve other branches of science and mathematics, but they all use calculus in some essential way.
FBI FINGERPRINT COMPRESSION
The U.S. Federal Bureau of Investigation began collecting fingerprints and handprints in 1924 and now has 30 million such prints in its files, all of which are being digitized for storage on computer. It take about 0.6 megabyte of storage space to record a fingerprint and 6 megabytes to record a pair of handprints, so that digitizing the current FBI archive would result in about 200 x 10^12 bytes of data to be stored, which is the capacity of roughly 138 million floppy disks. All this would cost roughly 200 million dollars. To reduce the cost, FBI's began working with several other Institutes and groups to devise compression methods for reducing the storage space. These methods, which are based on wavelets, are proving to be highly successful. Thus, calculus paved the way!!
MUSIC
Researchers at Yale University have investigated the application of wavelets to sound synthesis (music and voice). To approximate the sound of a musical instrument or voice, samples are taken and decomposed mathematically into numbers called wavelet packet coefficients. These coefficients can be stored on a computer and later sound can be reconstructed (synthesized) from the computer data. This area of research makes it possible to reproduce complex sounds from a small amount of data and to transmit those data electronically in a highly compressed form. This research may eventually speed up the transmission of sound over the Internet.
WEATHER PREDICTION
Modern meteorology is a marriage between mathematics and physics. Today's meteorologists are concerned with much more than predicting daily weather changes--their research delves into such areas as global warming, holes in the ozone layer and weather patterns on other planets. In 1904 the Norwegian meteorologist Vilhelm Bjerknes proposed that the state of the atmosphere at any future time can be determined by measuring appropriate variables at a single instant of time and then solving certain hydrodynamic equations. Although, it is difficult to apply this principle. However, new mathematical discoveries have dramatically improved meteorological predictions and spawned enormous
economic benefits.
MEDICAL IMAGING & DNA STRUCTURE
Advances in nuclear magnetic resonance (NMR) have made it possible to determine the structure of biological macromolecules, study DNA replication, and determine how proteins act as enzymes and antibodies. Related advances in Magnetic Resonance Imaging (MRI) have made it possible to view internal human tissue without invasive surgery and to provide real-time images during surgical procedures. High-quality NMR and MRI would not be possible without mathematical discoveries that have occurred within the last decade.
CONTROLLING CHAOTIC BEHAVIOR OF HUMAN-HEART
Chaos theory, which is one of the most exciting new branches of mathematics, is concerned with identifying regularities in phenomena that on the surface seem random and unpredictable. Today's research literature abounds with applications of chaos theory to almost every imaginable branch of science. Researchers at Georgia Tech University collaborated with physicist at the Emory University Medical Center in applying chaos theory to control the chaotic behaviour of heart tissue that is undergoing ventricular fibrillation (cardiac arrest). The research, though experimental, is already showing promising result.
DEEP SPACE EXPLORATION
Alexander Wolszczan of Penn State University may go down in history as the first scientist to identify a planetary system beyond our own. While searching the radio sky, he discovered a new pulsar, PSR1257+12, that seemed to wobble as it travelled through space. As a result of an extensive mathematical analysis, many scientists are now convinced that the wobble is caused by two or three planets orbiting the pulsar. Although scientists have been able to detect pulsars for some time by searching for faint periodic radio signals from outer space, it is only recently that the mathematical techniques have been developed to analyse the data in a way that stands up to scientific scrutiny.
Finally, we can see that today's life has an exciting applications of calculus but, it has roots that can be traced to the work of the Greek mathematician Archimedes, but the actual discovery of the fundamental principles of calculus was made independently by Isaac Newton (English) and Gottfried Leibniz (German) in the late seventeenth century.
Calculus drives our lives today, and further advances will help us achieve even greater heights!!
No comments:
Post a Comment