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mirinmari0
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Homework Equations
N/a
The Attempt at a Solution
I am wondering if this is the right direction in solving this. any input would be great! Sorry for the messy handwriting!
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Partial differential equations (PDEs) are mathematical equations that involve multiple independent variables and their partial derivatives. They are used to describe how a function or process changes over space and time.
The main difference between a partial differential equation and an ordinary differential equation is that PDEs involve multiple independent variables, whereas ODEs only involve one independent variable. Additionally, PDEs also involve partial derivatives while ODEs only involve ordinary derivatives.
PDEs are used to model many physical phenomena, such as heat transfer, fluid dynamics, electromagnetism, and quantum mechanics. They are also commonly used in engineering, economics, and other fields to solve problems involving multiple variables and their rates of change.
Some common techniques for solving PDEs include separation of variables, method of characteristics, Fourier transforms, and numerical methods such as finite difference and finite element methods.
To improve your understanding of PDEs, it is important to have a strong foundation in calculus and linear algebra. Additionally, practicing solving various types of PDEs and studying their applications in different fields can also help deepen your understanding.