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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.
Differential equations are crucial in chemical engineering for modeling dynamic processes such as reaction kinetics, mass transfer, and heat exchange. For instance, the rate of a chemical reaction can be described by ordinary differential equations (ODEs) that relate concentration changes over time. In reactor design, engineers use these equations to optimize conditions for maximum yield. Additionally, partial differential equations (PDEs) can model spatial variations in concentration and temperature within reactors or separation units.
Analysis of differential equations involves studying the properties and behaviors of equations that relate a function to its derivatives. This field encompasses various methods for solving ordinary differential equations (ODEs) and partial differential equations (PDEs), as well as examining existence, uniqueness, and stability of solutions. Techniques such as qualitative analysis, numerical approximation, and transform methods are commonly employed to understand the dynamics described by these equations in diverse applications across physics, engineering, and biology. Ultimately, the goal is to gain insights into how systems evolve over time or space based on their governing equations.
Ordinary differential equations (ODEs) are widely used in various daily life applications, such as modeling population dynamics in ecology, where they help predict the growth of species over time. They are also crucial in engineering for designing systems like electrical circuits and control systems, optimizing performance and stability. Additionally, ODEs play a role in finance, aiding in the modeling of investment growth and risk assessment. In medicine, they are used to model the spread of diseases and the effects of medications on the human body.
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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
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.
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.
Olusola Akinyele
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
Fred Brauer has written: 'Linear mathematics; an introduction to linear algebra and linear differential equations' -- subject- s -: Linear Algebras, Linear Differential equations 'Mathematical models in population biology and epidemiology' -- subject- s -: Mathematical models, Population biology, Epidemiology 'Problems and solutions in ordinary differential equations' -- subject- s -: Differential equations, Problems, exercises