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The book of nature is written in the language of mathematics

The book of nature is written in the language of mathematics. Galileo Galilei. Our program. In this lecture we will apply basic mathematics and statistics to solve ecological problems. The lecture is therefore application centred.

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The book of nature is written in the language of mathematics

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  1. Thebook of natureiswritteninthelanguage of mathematics Galileo Galilei

  2. Our program In this lecture we will apply basic mathematics and statistics to solve ecological problems. The lecture is therefore application centred. Students have to prepare the theoretical background by their own!!! For each lecture I’ll give the concepts and key phrases to get acquainted with together with the appropriate literature!!! This literature will be part of the final exam!!! 1. Introduction 2. Basic operations and functions 3. Matrix algebra 4. Handling a changing world 5. First stepsin statistics 6. Moments and distributions 7. Parametric hypothesis testing 8. Correlation and linear regression  

  3. Matheonline http://www.mathe-online.at/

  4. http://tutorial.math.lamar.edu/

  5. Additionalsources

  6. Logarithms and logarithmicfunctions John Napier (1550-1617) A logarithmisthatnumberwithwhich we have to takeanothernumber (thebase) to thepower to get a third number. The logarithmic function Root Log 1 = 0 Asymptote Thelogarithmicfunctionis not defined for negativevalues

  7. Logarithms and logarithmicfunctions A general logarithmicfunction Curvature Shift aty-axis Increase Shift atx-axis Root

  8. Leonhard Paul Euler (1707-1783) Thenumber e Thefamous Euler equation y=ex e • e = 2.71828183….

  9. Thecommonlyusedbases Logarithms to base 2 Logarithms to base 10 Logarithms to base e Log10 x ≡ lg x Logex ≡ ln x Log2 x ≡ lb x Digital logarithm Natural logarithm Binarylogarithm The scientific standard Standard of software Publications Statistics Classicalmetrics pH DeziBel 1 byte = 32 bit =25 bit 232 = 4294967296 1 byte = lb( number of possibleelements)

  10. Weber Fechner law Humanbrightlessperception Sensoricalperception of bright, loudness, taste, feeling, and othersincreaseproportional to thelogarithm of themagnitude of thestimulus. Logarithmicfunction Stevens’ power law Thepowerfunction law of Stevens approachesthe Weber-Fechner law at k = 0.33 Power functions and logarithmicfunctionsaresometimesverysimilar.

  11. Loudnessindezibel Themagnitude of a soundisproportional to thesquare of soundpressure Therule of 20. Linearscale +40 Dezibelis a ratio and thereforedimensionless P: soundpressure x100 Logarithmicscale The threshold of hearing is at 2x10-5 Pascal. This is by definition 0 dB. What is the sound pressure at normal talking (40 dB)? Thesoundpressureis 100 timesthethresholdpressure.

  12. How much louder do we hear a machine that increases its sound pressure by a factor of 1000? The machine appears to be 60 dB louder To what level should the sound pressure increase to hear a sound 2 times louder? The multiplication factor k is linearly (directly) proportional to the sound pressure P.

  13. A first model Magicicadaseptendecim Photo by USA National Arboretum

  14. Magicicadaseptendecim Photo by USA National Arboretum

  15. Home work and literature • Refresh: • Greek alphabet • Logarithms, powers and roots: http://en.wikipedia.org/wiki/Logarithm • Logarithmictransformations and scales • Euler number (value, series and limes expression) • Radioactivedecay • Prepare to thenextlecture: • Logarithmicfunctions • Power functions • Linear and algebraicfunctions • Exponentialfunctions • Monodfunctions • Hyperbola

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