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If you are a scientist, engineer or mathematician, there are too many examples to list. If you aren't, then there are basically none, except in finance.
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
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.
Herman Betz has written: 'Differential equations with applications' -- subject(s): Differential equations
There is no application of differential equation in computer science
Zeev Schuss has written: 'Theory and applications of stochastic differential equations' -- subject(s): Stochastic differential equations
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Kent Franklin Carlson has written: 'Applications of matrix theory to systems of linear differential equations' -- subject(s): Differential equations, Linear, Linear Differential equations, Matrices
Jianhong Wu has written: 'Theory and applications of partial functional differential equations' -- subject(s): Functional differential equations
Lars Garding has written: 'Cauchy's problem for hyperbolic equations' -- subject(s): Differential equations, Partial, Exponential functions, Partial Differential equations 'Applications of the theory of direct integrals of Hilbert spaces to some integral and differential operators' -- subject(s): Differential equations, Partial, Hilbert space, Partial Differential equations
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Carbon dating would be one thing...
Applications of ordinary differential equations are commonly used in the engineering field. The equation is used to find the relationship between the various parts of a bridge, as seen in the Euler-Bernoulli Beam Theory.
Jerrold Stephen Rosenbaum has written: 'Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits' -- subject(s): Differential equations, Electronic circuits, Numerical solutions, Stiff computation (Differential equations)
P. Quittner has written: 'Superlinear parabolic problems' -- subject(s): Differential equations, Elliptic, Differential equations, Parabolic, Differential equations, Partial, Elliptic Differential equations, Parabolic Differential equations, Partial Differential equations