- #1

nizi

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- Homework Statement
- In the following second-order partial differential equation for ##f## with ##x## and ##t## as independent variables, ##a## and ##b## as constants, and ##g## as a known function with ##t## as the only independent variable, is the mathematically correct notation for the third term on the left-hand side ##\frac{ dg }{ dt }## as below, or ##\frac{ \partial g }{ \partial t }##?

- Relevant Equations
- $$a \frac{ \partial^2 f}{ \partial x^2 } + b \frac{ \partial f }{ \partial t } + \frac{ dg }{ dt } = 0$$

Some may say that ##\frac{ \partial g }{ \partial t }## is correct because it is a term in a partial differential equation, but since ##g## is a one variable function with ##t## only, I think ##\frac{ dg }{ dt }## is correct according to the original usage of the derivative and partial derivative symbol.

The original usage of the partial derivative symbol is to express the rate of change of a multivariable function of two or more variables when all variables except the variable to be used in the differentiation are fixed, and the notation ##\frac{ \partial g }{ \partial t }## implies that ##g## is not a one variable function, which would be somewhat inaccurate.

The original usage of the partial derivative symbol is to express the rate of change of a multivariable function of two or more variables when all variables except the variable to be used in the differentiation are fixed, and the notation ##\frac{ \partial g }{ \partial t }## implies that ##g## is not a one variable function, which would be somewhat inaccurate.

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