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. DAEs via the Mass Matrix
   8. 1. 1.4.1. Example: Electrical Circuits
   9. 1.5. PDEs
   10. 1. 1.5.1. Example: Heat Equation
       2. 1.5.2. Example: Physics-based Battery Simulation
   11. 1.6. Forward Sensitivity Analysis
   12. 1. 1.6.1. Example: Fitting a predator-prey model to data
   13. 1.7. Backwards Sensitivity Analysis
   14. 1. 1.7.1. Example: Fitting a spring-mass model to data
       2. 1.7.2. Example: Weather prediction using neural ODEs
3. 2. Diffsol APIs for specifying problems
4. 1. 2.1. DiffSL
   2. 2.2. Rust closures
   3. 1. 2.2.1. Explicit
      2. 2.2.2. Implicit
      3. 2.2.3. Mass matrix
      4. 2.2.4. Root finding
      5. 2.2.5. Forward Sensitivity
      6. 2.2.6. Sparse problems
   4. 2.3. OdeEquations trait
   5. 1. 2.3.1. Non-linear functions
      2. 2.3.2. Constant functions
      3. 2.3.3. Linear functions
      4. 2.3.4. ODE systems
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. Benchmarks
10. 1. 5.1. Sundials
    2. 5.2. Python (Diffrax & Casadi)