1. 1. Modelling with diffsol
2. 1. 1.1. Explicit First Order ODEs
   2. 1. 1.1.1. Example: Population Dynamics
   3. 1.2. Higher Order ODEs
   4. 1. 1.2.1. Example: Spring-mass systems
   5. 1.3. Discrete Events
   6. 1. 1.3.1. Example: Compartmental models of Drug Delivery
      2. 1.3.2. Example: Bouncing Ball
   7. 1.4. Hybrid ODEs
   8. 1. 1.4.1. Example: Dosing Protocols
      2. 1.4.2. Example: Epidemic SIR with policy switching
   9. 1.5. DAEs via the Mass Matrix
   10. 1. 1.5.1. Example: Electrical Circuits
   11. 1.6. PDEs
   12. 1. 1.6.1. Example: Heat Equation
       2. 1.6.2. Example: Physics-based Battery Simulation
   13. 1.7. Forward Sensitivity Analysis
   14. 1. 1.7.1. Example: Fitting a predator-prey model to data
   15. 1.8. Backwards Sensitivity Analysis
   16. 1. 1.8.1. Example: Fitting a spring-mass model to data
       2. 1.8.2. Example: Weather prediction using neural ODEs
3. 2. Specifying ODE problems
4. 1. 2.1. The builder
   2. 2.2. Tolerances
   3. 2.3. DiffSL
   4. 2.4. Rust closures
   5. 1. 2.4.1. Explicit
      2. 2.4.2. Implicit
      3. 2.4.3. Mass matrix
      4. 2.4.4. Root finding
      5. 2.4.5. Forward Sensitivity
      6. 2.4.6. Adjoint Sensitivity
      7. 2.4.7. Automatic differentiation
      8. 2.4.8. Sparse problems
   6. 2.5. OdeEquations trait
   7. 1. 2.5.1. Non-linear functions
      2. 2.5.2. Constant functions
      3. 2.5.3. Linear functions
      4. 2.5.4. ODE systems
      5. 2.5.5. Parameters
5. 3. Creating a solver
6. 1. 3.1. Initialisation
   2. 3.2. Tableau
7. 4. Solving the problem
8. 1. 4.1. Manual time-stepping
   2. 4.2. Interpolation
   3. 4.3. Stopping
   4. 4.4. Forward Sensitivities
9. 5. Performance
10. 1. 5.1. Stiff vs Non-Stiff
    2. 5.2. Events and Multistep Solvers
11. 6. Using diffsol from other languages
12. 1. 6.1. Python
    2. 6.2. C and other languages
    3. 6.3. WebAssembly
    4. 6.4. WebAssembly with JIT
13. 7. Benchmarks
14. 1. 7.1. Sundials
    2. 7.2. Python (Diffrax & Casadi)