Differential Equations

Change of variables in partial differential equations (PDEs) involves substituting new variables to simplify the equation or convert it to a more solvable form. This technique can help reduce the complexity of the PDE, making it easier to analyze or solve. Common transformations include linear transformations, coordinate shifts, or non-linear substitutions, and they often exploit symmetries or specific features of the problem. Ultimately, the goal is to facilitate finding solutions or gaining insights into the behavior of the system described by the PDE.

To translate a word problem into a mathematical sentence, first identify the key elements such as quantities, relationships, and operations involved. Assign variables to unknowns and translate phrases into mathematical symbols, like using "+" for "more than" or "=" for "is." Organize the information logically, ensuring that the equation reflects the relationships described in the problem. Finally, review the sentence to ensure it accurately represents the original scenario.

Newton's equation of cooling is a differential equation. If K is the temperature of a body at time t, then dK/dt = -r*(K - Kamb) where Kamb is the temperature of the surrounding, and r is a positive constant.

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.

The second term in the ratio is 1.

60 minutes in an hour, 24 hours in a day, 365 days in a year.

365 X 24 X 60 X 1.5 = 788,400 minutes.

this questions isn't specified enough to be answered

Some partial differential equations do not have analytical solutions. These can only be solved numerically.

ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.

The number of moves required to solve the Hanoi tower is 2m + 1 . Therefore for a tower of five disks the minimum number of moves required is: 31.