Mathematical Modelling
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Mathematical Modelling.


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Mathematical Modelling.
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Slide 1

Scientific Modeling 24. April-24. July 2006: Monday 11-13, Room S3032 Literature: The nature of numerical displaying, N. Gershenfeld, Cambridge University Press, Cambridge, 2003, 344 pp. Connected Mathematical Modeling: A Multidisciplinary Approach; von D. R. Shier, K. T. Wallenius, pp. 443, CRC PrILlc, ISBN    1584880481 Script for some piece of the course Mathematical displaying, G. Lohmann, 2006 http://www.awi-bremerhaven.de/Modeling/Paleo/lessons/VL_SS2006/SS2006.html How to get the Credit Points/Schein? Ventures with matlab and R/minutes (5-10 pages including figures) Practical work inside of the lessons Help of Thomas Laepple (tlaepple@awi-bremerhaven.de)

Slide 2

Mathematical Modeling It is the address' point to grant the capacity to - investigate genuine natural frameworks and depict them as satisfactorily as could be expected under the circumstances by method for straightforward scientific models concerning fascinating inquiries; - talk about and sometimes logically resolve the subsequent numerical comparisons (particularly differential comparison frameworks); - look at convoluted models by method for PC projects and in this way comprehend the cutoff points of reenactment and the event of conceivable scientific antiques.

Slide 3

System: Example (1)

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System: Example (2)

Slide 5

Models are utilized to express the qualities of reality which are viewed as critical and to disregard those which appear to be auxiliary. By these disentanglements, great models permit us to acquire an effortlessly justifiable, numerically measurable picture of this present reality If a model is defined with the guide of scientific relations, we talk about scientific models. This address manages development and utilization of scientific models in regular sciences.

Slide 6

Models are utilized to express the attributes of reality which are viewed as imperative and to disregard those which appear to be auxiliary. By these disentanglements, great models permit us to acquire an effectively justifiable, scientifically measurable picture of this present reality If a model is detailed with the guide of numerical relations, we talk about numerical models. This address manages development and utilization of scientific models in common sciences.

Slide 7

Models are utilized to express the attributes of reality which are viewed as essential and to disregard those which appear to be optional. By these disentanglements, great models permit us to get an effectively justifiable, scientifically measurable picture of this present reality If a model is figured with the guide of numerical relations, we discuss numerical models. This address manages development and utilization of numerical models in regular sciences.

Slide 8

Examples of Models Architectural Chemical particles Feedbacks Kepler‘s Law

Slide 9

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the rule of order in the gathered information: Johannes Kepler (1571 - 1630) arranges Brahe's planetary circles, three laws 3. Comprehension: scan for a better guideline with which than comprehend the observationally discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are legitimate past space science. 4. Summing up: Can the laws be exchanged to different circumstances? Taking into account the comparability of latent and overwhelming mass, Albert Einstein (1879-1955) builds up his general hypothesis of relativity. 5. Guess: Can the (maybe summed up) regularities be utilized to foresee wonders? galactic wonders anticipated by Einstein were watched. At long last, gathering information just bodes well if further learning creates out of them, either as a summed up articulation, guess or to figure new inquiries, i. e. plan new investigations. Models are required for the use of perceptions.

Slide 10

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the standard of order in the gathered information: Johannes Kepler (1571 - 1630) groups Brahe's planetary circles, three laws 3. Comprehension: scan for a better rule with which than comprehend the observationally discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are substantial past space science. 4. Summing up: Can the laws be exchanged to different circumstances? In view of the identicalness of inactive and overwhelming mass, Albert Einstein (1879-1955) adds to his general hypothesis of relativity. 5. Anticipation: Can the (maybe summed up) regularities be utilized to foresee wonders? cosmic marvels anticipated by Einstein were watched. At long last, gathering information just bodes well if further learning creates out of them, either as a summed up proclamation, visualization or to figure new inquiries, i. e. plan new trials. Models are required for the utilization of perceptions.

Slide 11

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the rule of characterization in the gathered information: Johannes Kepler (1571 - 1630) groups Brahe's planetary circles, three laws 3. Comprehension: hunt down a better guideline with which than comprehend the experimentally discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are substantial past space science. 4. Summing up: Can the laws be exchanged to different circumstances? In view of the comparability of inactive and overwhelming mass, Albert Einstein (1879-1955) adds to his general hypothesis of relativity. 5. Anticipation: Can the (maybe summed up) regularities be utilized to foresee wonders? galactic marvels anticipated by Einstein were watched. At long last, gathering information just bodes well if further learning creates out of them, either as a summed up explanation, visualization or to define new inquiries, i. e. plan new analyses. Models are required for the utilization of perceptions.

Slide 12

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the standard of arrangement in the gathered information: Johannes Kepler (1571 - 1630) groups Brahe's planetary circles, three laws 3. Comprehension: hunt down a better rule with which than comprehend the exactly discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are substantial past space science. 4. Summing up: Can the laws be exchanged to different circumstances? Taking into account the comparability of latent and overwhelming mass, Albert Einstein (1879-1955) builds up his general hypothesis of relativity. 5. Visualization: Can the (maybe summed up) regularities be utilized to foresee wonders? cosmic wonders anticipated by Einstein were watched. At long last, gathering information just bodes well if further learning creates out of them, either as a summed up proclamation, guess or to figure new inquiries, i. e. plan new tests. Models are required for the utilization of perceptions.

Slide 13

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the rule of arrangement in the gathered information: Johannes Kepler (1571 - 1630) orders Brahe's planetary circles, three laws 3. Comprehension: look for a better rule with which than comprehend the exactly discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are legitimate past stargazing. 4. Summing up: Can the laws be exchanged to different circumstances? In light of the proportionality of dormant and overwhelming mass, Albert Einstein (1879-1955) builds up his general hypothesis of relativity. 5. Visualization: Can the (maybe summed up) regularities be utilized to anticipate marvels? cosmic marvels anticipated by Einstein were watched. At last, gathering information just bodes well if further learning creates out of them, either as a summed up explanation, forecast or to define new inquiries, i. e. plan new analyses. Models are required for the use of perceptions.

Slide 14

Role of models in science In building any hypothesis you see the accompanying stages: 1. Gathering: perceptions, estimations: In his ideally prepared observatory Uranienborg close Copenhagen Tycho Brahe (1546 - 1601) gathers information on planetary developments. 2. Sorting: quest for the guideline of grouping in the gathered information: Johannes Kepler (1571 - 1630) characterizes Brahe's planetary circles, three laws 3. Comprehension: hunt down a better standard with which than comprehend the exactly discovered request Isaac Newton (1643 - 1727) demonstrates that Kepler's laws can be clarified by physical standards which are substantial past cosmology. 4. Summing up: Can the laws be exchanged to different circumstances? In light of the proportionality of latent and substantial mass, Albert Einstein (1879-1955) adds to his general hypothesis of relativity. 5. Visualization: Can the (maybe summed up) regularities be u