Models with Differential Equations
Exploring Modeling with Data and Differential Equations Using R
Preface
Models with Differential Equations
1
Models of Rates with Data
2
Introduction to R
3
Modeling with Rates of Change
4
Euler’s Method
5
Phase Lines and Equilibrium Solutions
6
Coupled Systems of Equations
7
Exact Solutions to Differential Equations
Parameterizing Models with Data
8
Linear Regression and Curve Fitting
9
Probability and Likelihood Functions
10
Cost Functions and Bayes’ Rule
11
Sampling Distributions and the Bootstrap Method
12
The Metropolis-Hastings Algorithm
13
Markov Chain Monte Carlo Parameter Estimation
14
Information Criteria
Stability Analysis for Differential Equations
15
Systems of Linear Differential Equations
16
Systems of Nonlinear Differential Equations
17
Local Linearization and the Jacobian
18
What are Eigenvalues?
19
Qualitative Stability Analysis
20
Bifurcation
Stochastic Differential Equations
21
Stochastic Biological Systems
22
Simulating and Visualizing Randomness
23
Random Walks
24
Diffusion and Brownian Motion
25
Simulating Stochastic Differential Equations
26
Statistics of a Stochastic Differential Equation
27
Solutions to Stochastic Differential Equations
References
Models with Differential Equations
Preface
1
Models of Rates with Data