Merge pull request #575 from ChrisRackauckas-Claude/docs-improvements-20251229-195633

Documentation improvements: fix grammar and clarity issues

Author: ChrisRackauckas

docs/src/libs/datadrivensparse/sparse_regression.md

@@ -1,12 +1,12 @@
 # DataDrivenSparse
 
-DataDrivenSparse provides a universal framework to infer system of equations using sparse regression. Assume the system:
+DataDrivenSparse provides a universal framework to infer systems of equations using sparse regression. Assume the system:
 
 ```math
 y_{i} = f(x_{i}, p, t_i, u_{i})
 ```
 
-Then might be able to express the unknown function $f$ as a linear combination of basis elements $\varphi_i : \mathbb R^{n_x} \times \mathbb R^{n_p} \times \mathbb R \times \mathbb R^{n_u} \mapsto \mathbb R$ .
+We might then be able to express the unknown function $f$ as a linear combination of basis elements $\varphi_i : \mathbb R^{n_x} \times \mathbb R^{n_p} \times \mathbb R \times \mathbb R^{n_u} \mapsto \mathbb R$ .
 
 ```math
 y_i = \sum_{j=1}^k \xi_k ~ \varphi_k\left(x_i, p, t_i, u_i \right)

docs/src/problems.md

@@ -16,7 +16,7 @@ problem = DiscreteDataDrivenProblem(X, t, U, p = p)
 problem = DiscreteDataDrivenProblem(X, t, (x, p, t) -> u(x, p, t))
 ```
 
-Similarly, a [`ContinuousDataDrivenProblem`](@ref) would need at least measurements and time-derivatives (`X` and `DX`) or measurements, time information and a way to derive the time derivatives(`X`, `t` and a [Collocation](@ref collocation) method). Again, this can be extended by including a control input as measurements or a function and possible parameters:
+Similarly, a [`ContinuousDataDrivenProblem`](@ref) would need at least measurements and time-derivatives (`X` and `DX`) or measurements, time information, and a way to derive the time derivatives (`X`, `t`, and a [Collocation](@ref collocation) method). Again, this can be extended by including a control input as measurements or a function and possible parameters:
 
 ```julia
 # Using available data
@@ -65,7 +65,7 @@ DirectDataDrivenProblem
 DataDrivenDataset
 ```
 
-A `DataDrivenDataset` collects several [`DataDrivenProblem`s](@ref problem) of the same type but treats them as a union for system identification.
+A `DataDrivenDataset` collects several [`DataDrivenProblem`](@ref problem)s of the same type but treats them as a union for system identification.
 
 ## Concrete Types