Introduction | Even determined systems | Overdetermined systems | Equalities only | Equalities and inequalities | Underdetermined systems | Equalities, inequalities and approximate equations | Equalities and inequalities and a target function | solving sets of linear equations with sparse matrices | solve, Solve.tridiag, Solve.banded | Banded matrices in the Matrix package | Solve.block | datasets | Notes | Bibliography

General reaction transport equation in one dimension | one-dimensional finite difference grids and properties in ReacTran | one-dimensional reactive-transport modelling in ReacTran | volumetric advective-diffusive transport in an aquatic system | Transport in two dimensions | finally

Introduction | Constants and datasets | Physical functions | Dissolved gasses | Seawater properties | Conversions | Finally

Converting large data sets from long to cross-table format | Quickly analysing and plotting several columns from a matrix | Resolution and mapping to sigma coordinates | Plotting two-dimensional velocity data | Plotting temporally variable particle distributions | Finally

Preamble | Reading data | Plot bathymetry and grid | integrated velocities | Quivers at selected time points | surface elevation, for selected time steps | surface temperature, for selected time steps | mean temperature along a NS-depth and a SW-depth transect | time-averaged vertical velocities at several depths | time-averaged horizontal velocity vectors at several depths | NE and SW transects of time-averaged flows | plotting irregular transects, along a ship track | Finally

Intro | Images and contours | persp3D | Backgrounds and axes annotations | View and shading perspectives | Ribbons and histograms | Color keys | Combined persp3D and image or contour | Two more to go

Introduction | Functions image2D and persp3D | slices and isosurfaces | surf3D | Functions based on image | Composite figures | plotting with legends and colorkeys | Issues | Finally

Introduction | The elements of an object of class aquaenv | Using AquaEnv | Extending AquaEnv | Abbreviations for references used throughout the code and in the helpfiles | References for the elements of an object of class aquaenv

A steady-state model of oxygen in a marine sediment | Global sensitivity analysis : Sensitivity ranges | Local sensitivity analysis : Sensitivity functions | Fitting the model to the data | Running a Markov chain Monte Carlo | Finally

Introduction | colors | Rotating | ellipses | Cylinders, rectangles, multigonals | Other shapes | arrows, arrowheads | Miscellaneous | And finally

Chapter 1. Introduction | Chapter 2. Model formulation | chapter 3. Spatial components and transport | chapter 4. Parameterisation | chapter 5. Model solution - analytical methods | chapter 6. Model solution numerical methods | chapter 7. Stability and steady state | chapter 8. Multiple time scales and equilibrium processes | chapter 9. Discrete time models | chapter 9. Discrete time models, b | chapter 11. Testing and validating the model | And finally

Introduction | The test model | Local sensitivity analysis | Multivariate parameter identifiability | Fitting the model to data | MCMC | Model prediction | Monte Carlo applications | Discussion | The Fortran version of the model

Introduction | The example model | Global sensitivity | Local sensitivity | Multivariate sensitivity analysis | Fitting the model to data | Markov chain Monte Carlo | Distributions | Examples | Finally

Introduction | Function modMCMC | Sampling from a normal distribution | Sampling from a lognormal distribution | The banana | A simple chemical model | Fitting a nonlinear model | Finally

Fitting a Monod function | Finally

Finding roots of nonlinear equations in R and rootSolve | Steady-state analysis | Boundary value problems | writing functions in compiled code | Gradients, Jacobians and Hessians | Finally

Notations and flow matrix conventions | Arguments to network index functions | Network indices | Changes in later versions

Partial differential equations | A parabolic PDE | A hyperbolic PDE | An elliptic PDE