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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.
Ordinary differential equations (ODEs) are widely used in various fields such as physics, engineering, biology, and economics to model dynamic systems. They describe phenomena like population growth, motion of objects under forces, electrical circuits, and heat transfer. In engineering, ODEs are crucial for analyzing systems' behavior, such as in control theory and signal processing. Additionally, they play a vital role in predicting changes over time in systems governed by continuous change.
The abbreviation PDE stands for partial differential equation. This is different from an ordinary differential equation in that it contains multivariable functions rather than single variables.
All types of engineering professions use the quadratic formula since it applies to ordinary differential equations.
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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.
J. C. Butcher has written: 'Numerical Methods for Ordinary Differential Equations' -- subject(s): Differential equations, Mathematics, Nonfiction, Numerical solutions, OverDrive 'The numerical analysis of ordinary differential equations' -- subject(s): Differential equations, Numerical solutions, Runge-Kutta formulas
Leon Lapidus has written: 'Numerical solution of ordinary differential equations' -- subject(s): Differential equations, Electronic data processing, Numerical analysis, Mathematics
Granville Sewell has written: 'The numerical solution of ordinary and partial differential equations' -- subject(s): Data processing, Differential equations, Mathematics, Nonfiction, Numerical solutions, OverDrive, Partial Differential equations 'Computational Methods of Linear Algebra' -- subject(s): OverDrive, Mathematics, Nonfiction
Sze-Bi Hsu has written: 'Ordinary differential equations with applications'
Witold Hurewicz has written: 'Lectures on Ordinary Differential Equations' 'Ordinary differential equations in the real domain with emphasis on geometric methods' -- subject(s): Differential equations
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)
You'll find ordinary differential equations (ODEs) being used in chemical engineering for many things, such as determining reaction rates, activation energies, mass transfer operations, heat transfer operations, and momentum transfer operations.
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Melvin R. Scott has written: 'Invariant imbedding and its applications to ordinary differential equations' -- subject(s): Boundary value problems, Differential equations, Invariant imbedding, Numerical solutions
Morris Tenenbaum has written: 'Ordinary differential equations' -- subject(s): Differential equations