I was solving a physics problem and the solution involves solving a differential equation that's of the form: $$ \bigg ( \frac {dx} {dt} \bigg)^2 + \bigg ( \frac {dy} {dt} \bigg)^2 = a^2 $$ By guessing, ...
Differential-algebraic equations are important for mathematical modeling and scientific computation. If you write down the mathematical laws for some chemical, electrical, or physical system, you often will just end up with a system of equations involving parameters, various partial derivatives and purely algebraic quantities. Maybe you also get some equations involving integrals. Now ...
I have a problem understanding how to define a linear or non-linear Differential equation. These are my answers to the questions, however, my teacher's answers are not the same as mine. Questions ...
Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...
Engadget: MIT solved a century-old differential equation to break 'liquid' AI's computational bottleneck
MIT solved a century-old differential equation to break 'liquid' AI's computational bottleneck
The right question is not "What is a differential?" but "How do differentials behave?". Let me explain this by way of an analogy. Suppose I teach you all the rules for adding and multiplying rational numbers. Then you ask me "But what are the rational numbers?" The answer is: They are anything that obeys those rules. Now in order for that to make sense, we have to know that there's at least ...
Then one thinks of differential operators as a linear maps between such spaces. Often the space of all linear maps between two spaces is itself a vector space and so one can indeed start to manipulate differential operators as if they are ‘objects’ in their own right eg add them together.