All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.
Chat with our AI personalities
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
Partial differential equations are great in calculus for making multi-variable equations simpler to solve. Some problems do not have known derivatives or at least in certain levels in your studies, you don't possess the tools needed to find the derivative. So, using partial differential equations, you can break the problem up, and find the partial derivatives and integrals.
Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
What's the question?
Very often because no analytical solution is available.