| Description |
1 online resource (379 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- List of Figures -- Welcome -- I. Models with Differential Equations -- 1. Models of Rates with Data -- 1.1. Rates of change in the world: a model is born -- 1.2. Modeling in context: the spread of a disease -- 1.3. Model solutions -- 1.4. Which model is best? -- 1.5. Start here -- 1.6. Exercises -- 2. Introduction to R -- 2.1. R and RStudio -- 2.2. First steps: getting acquainted with R -- 2.3. Increasing functionality with packages -- 2.4. Working with R: variables, data frames, and datasets |
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2.5. Visualization with R -- 2.6. Defining functions -- 2.7. Concluding thoughts -- 2.8. Exercises -- 3. Modeling with Rates of Change -- 3.1. Competing plant species and equilibrium solutions -- 3.2. The Law of Mass Action -- 3.3. Coupled differential equations: lynx and hares -- 3.4. Functional responses -- 3.5. Exercises -- 4. Euler's Method -- 4.1. The flu and locally linear approximation -- 4.2. A workflow for approximation -- 4.3. Building an iterative method -- 4.4. Euler's method and beyond -- 4.5. Exercises -- 5. Phase Lines and Equilibrium Solutions -- 5.1. Equilibrium solutions |
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5.2. Phase lines for differential equations -- 5.3. A stability test for equilibrium solutions -- 5.4. Exercises -- 6. Coupled Systems of Equations -- 6.1. Flu with quarantine and equilibrium solutions -- 6.2. Nullclines -- 6.3. Phase planes -- 6.4. Generating a phase plane in R -- 6.5. Slope fields -- 6.6. Exercises -- 7. Exact Solutions to Differential Equations -- 7.1. Verify a solution -- 7.2. Separable differential equations -- 7.3. Integrating factors -- 7.4. Applying the verification method to coupled equations -- 7.5. Exercises -- II. Parameterizing Models with Data |
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8. Linear Regression and Curve Fitting -- 8.1. What is parameter estimation? -- 8.2. Parameter estimation for global temperature data -- 8.3. Moving beyond linear models for parameter estimation -- 8.4. Parameter estimation with nonlinear models -- 8.5. Towards model-data fusion -- 8.6. Exercises -- 9. Probability and Likelihood Functions -- 9.1. Linear regression on a small dataset -- 9.2. Continuous probability density functions -- 9.3. Connecting probabilities to linear regression -- 9.4. Visualizing likelihood surfaces -- 9.5. Looking back and forward -- 9.6. Exercises |
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10. Cost Functions and Bayes' Rule -- 10.1. Cost functions and model-data residuals -- 10.2. Further extensions to the cost function -- 10.3. Conditional probabilities and Bayes' rule -- 10.4. Bayes' rule in action -- 10.5. Next steps -- 10.6. Exercises -- 11. Sampling Distributions and the Bootstrap Method -- 11.1. Histograms and their visualization -- 11.2. Statistical theory: sampling distributions -- 11.3. Summary and next steps -- 11.4. Exercises -- 12. The Metropolis-Hastings Algorithm -- 12.1. Estimating the growth of a dog -- 12.2. Likelihood ratios for parameter estimation |
| Notes |
Description based upon print version of record |
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12.3. The Metropolis-Hastings algorithm for parameter estimation |
| Subject |
Biological models-Data processing
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Differential equations.
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R (Computer program language)
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Biological models -- Data processing
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Differential equations
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R (Computer program language)
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| Form |
Electronic book
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| ISBN |
9781000776782 |
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1000776786 |
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