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• Title:Modelling nature : an introduction to mathematical modelling of natural systems / Edward Gillman, School of Physics and Astronomy, University of Nottingham, Michael Gillman, School of Life Sciences, University of Lincoln.
  
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• Author/Creator:Gillman, Edward, author.
  
• Other Contributors/Collections:Gillman, Michael, author.
  
• Published/Created:Oxfordshire, OX ; Boston, MA : CABI, [2019]
  

• Holdings

  Holdings Record Display

  • Location: c.1  Temporarily shelved at WOODWARD LIBRARY Great ReadsWhere is this?
    
  • Call Number: QH51 .G55 2019
    
  • Number of Items:1
    
  • Status:Available
    

   
• Library of Congress Subjects:Natural history--Mathematical models.
  Mathematics in nature.
  
• Description:xvii, 260 pages : illustrations, map ; 25 cm
  
• Summary:"This short textbook introduces students to the concept of describing natural systems using mathematical models. The authors highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and mechanisms and results are illustrated in graphical form wherever possible."--Provided by publisher.
  
• Notes:Includes bibliographical references and index.
  
• ISBN:9781786393104 hardcover alkaline paper
  1786393107 hardcover alkaline paper
  9781786393135 paperback alkaline paper
  1786393131 paperback alkaline paper
  9781786393111 electronic publication
  9781786393128 electronic book
  
• Contents:Machine generated contents note: 1.1. Global Climate Change and Our First Model
  1.1.1. Introduction and motivation
  1.1.2. first look at some data and the importance of units
  1.1.3. Using variables for our data and summarizing the data with tables
  1.1.4. Plotting our data for a visual summary
  1.1.5. Making assumptions about physical processes
  1.1.6. first model using equations and making predictions
  1.1.7. Comparing data and models with plots and lines of best-fit
  1.2. Linear Model
  1.2.1. Using parameters and estimating unknowns
  1.2.2. Using residuals and the sum of squared residuals to measure model accuracy
  1.2.3. constant model
  1.2.4. zero-intercept model
  1.2.5. Using transformations to simplify data and model building
  1.2.6. Using transformations to fit the linear model
  1.2.7. Fitting the linear model in practice: variance, covariance and trend-lines
  1.2.8. best-fit linear model and extrapolations
  1.3. Beyond Linear Models
  1.3.1. Quadratic models
  1.3.2. Polynomial models
  1.4. Conclusions and Key Results
  1.5. Resources for Further Study
  2.1. Rapid Growth of Microbial Populations
  2.1.1. Salmonella and Ebola
  2.1.2. Setting out the problem I: choosing our variables and units
  2.1.3. Setting out the problem II: data visualization
  2.2. Exponential Model
  2.2.1. growth of bacterial populations: the physical process and idealizations
  2.2.2. growth of bacterial populations: a simple model
  2.2.3. exponential model
  2.2.4. Exponential curves
  2.2.5. Applying the exponential model to data
  2.2.6. Simplifying the problem using transformations of data: exponentiation and logarithms
  2.2.7. Building an exponential model of population growth: log-plots and linear fits
  2.2.8. Extrapolating and checking our physical assumptions
  2.3. Difference Equations
  2.3.1. Stating modelling assumptions with difference equations and the constant model
  2.3.2. difference equation for the linear model
  2.3.3. difference equation for the exponential model
  2.3.4. Initial values for difference equations and discrete versus continuous models
  2.4. Conclusions and Key Results
  2.5. Resources for Further Study
  3.1. Growth of the Total Human Population
  3.1.1. importance of predicting the size of the total human population
  3.1.2. Setting out the problem
  3.1.3. Using functions to transform data
  3.1.4. Transformations and inverse functions
  3.1.5. exponential model revisited I: using functions to transform our data
  3.1.6. exponential model revisited II: using functions to transform our models
  3.2. Exponential-Quadratic Model
  3.2.1. Late population growth: the exponential model
  3.2.2. quadratic model for log-populations
  3.2.3. Comparing the exponential and exponential-quadratic models
  3.2.4. Extrapolating with the exponential and exponential-quadratic models
  3.3. Quadratic Difference Equations and Population Models
  3.3.1. Developing difference equations with data and fitting
  3.3.2. Late time population growth: a quadratic difference equation
  3.3.3. Applying difference equations as recurrence relations
  3.3.4. Comparing the long-term behaviour of our models
  3.4. Conclusions and Key Results
  3.5. Resources for Further Study
  4.1. Introduction to Chronological Dating
  4.1.1. Chronological dating, human history and the geological timescale
  4.1.2. Models as functions and inverting models
  4.1.3. change in atomic populations through radioactive decay: fractional populations
  4.2. Exponential Model Applied to Decay
  4.2.1. radioactive decay of atoms
  4.2.2. exponential decay of populations: bacterial death and radioactive decay
  4.2.3. exponential model base-e: irrational numbers and the exponential function
  4.2.4. exponential model for 224Ra: fitting and interpreting the parameters
  4.2.5. Predicting ages with fractional populations
  4.3. Differential Equations
  4.3.1. Instantaneous speeds and average speeds
  4.3.2. Approximating derivatives with differences
  4.3.3. Defining derivatives with differences and calculating them with differentiation
  4.3.4. Differentiation rules for common functions
  4.3.5. idea of differential equations and their approximation with difference equations
  4.3.6. Predicting ages with populations: multiple populations
  4.3.7. Predicting the age of the Earth from zircon
  4.4. Conclusions and Key Results
  4.5. Resources for Further Study
  5.1. Improving Measures of the Goodness of Fit
  5.1.1. Conservation and distribution of species
  5.1.2. Species-area relationships for butterflies
  5.1.3. Measuring goodness of fit with a single value: the coefficient of determination R2
  5.1.4. Calculating the baseline SSR with variance
  5.1.5. Calculating R2 with Pearson's correlation coefficient and covariance
  5.2. Power-Law Model
  5.2.1. Using R2 with transformations for model development
  5.2.2. Linear models for log-log data and power-laws
  5.2.3. Power-law curves
  5.2.4. Understanding our failures: using residuals for error analysis
  5.3. Models with Multiple Predictors
  5.3.1. Data with multiple predictors: representation of data and using categories
  5.3.2. Using multiple features for prediction
  5.3.3. Plotting models with multiple features
  5.3.4. multiple linear model, and interactions
  5.3.5. Writing the polynomial model as a multiple linear model
  5.3.6. Linear least-squares problems
  5.3.7. general framework for models with interactions
  5.3.8. problem of overfitting and increasing R2
  5.3.9. Fitting with R software and using adjusted R-squared
  5.3.10. Simplifying models by setting parameters to zero
  5.3.11. Errors in data and standard errors of best-fit values
  5.3.12. Using statistical hypothesis testing to simplify models
  5.4. Conclusions and Key Results
  5.5. Resources for Further Study
  6.1. Introduction: A Binary Response Model for Vegetation Damage
  6.1.1. Natural environmental damage
  6.1.2. first look at some data
  6.1.3. Binary classification: a model for predicting vegetation damage from gas concentration
  6.2. Building a Simple Model for Classification: The Linear Model and a Step Function
  6.2.1. linear model for concentration and distance
  6.2.2. Fitting the constant model and minimization of functions
  6.2.3. Minimization of functions using differentiation
  6.2.4. Fitting the constant model using differentiation
  6.2.5. Finding the SSR of the linear model
  6.2.6. Simplifying the SSR with summation rules
  6.2.7. Minimizing functions with multiple inputs: partial derivatives
  6.2.8. Minimizing functions with multiple inputs: simultaneous equations
  6.2.9. Fitting the linear model
  6.2.10. Predicting vegetation index from distance
  6.2.11. danger of predictions made with certainty
  6.3. Statistical Models
  6.3.1. ideas of probability and statistical models
  6.3.2. statistical model for the vegetation index and SO2 concentration
  6.3.3. Building an improved statistical model with a sigmoid function
  6.3.4. Comparing statistical models to data with likelihoods and log-likelihoods
  6.3.5. simple statistical model for the concentration and distance
  6.3.6. Using Gaussian functions for statistical models
  6.3.7. Probability density functions
  6.3.8. Maximum likelihood estimation
  6.4. Conclusions and Key Results
  6.5. Resources for Further Study
  A1. Modelling Toolbox
  A2. Exponent Laws
  A3. Logarithmic Identities
  A4. Differentiation Rules
  A5. Using Common Inbuilt Functions
  A6. List of Parameter Values and Results to 10 Significant Figures.