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## Nomenclature

The following will be used throughout this course

`eps_step`- If and represent two successive approximations of a value , one condition for halting is that .
`eps_abs`- If and represent two successive approximations of a value , one condition for halting is that .
`f`- A function used in an algorithm, either for root finding () or an initial value-problem ().
`g`- A forcing function of a 2nd-order ordinary differnetial equation.
`i`- An index over a single space variable, usually .
`ix`,`iy`,`iz`- Indices over two or three space variables, , , and , respectively.
`k`- An index iterating over a time variable.
`M`- A matrix.
`m`- Either the row-dimension of a matrix
**M**(an*m*×*n*matrix) or an index of a vector. `n`- Either the column-dimension of a matrix
**M**(an*m*×*n*matrix) or a positive integer indicating the number of points into which an interval will be divided. `N_max`- A maximum number of steps or iterations.
`t_out`- An output column vector indicating the partition of a time interval .
`t_rng`- A time interval where , that is, from an initial time to a final time .
`x_rng`- A space interval over a variable where .
`u0`- The initial values (a vector) of -values where usually
`U_out(1,:) = u0`for a solution over time and a single space variable . `U0`- The initial values (a 2- or 3-dimensional array) of -values where usually
`U_out(1,:,:) = U0`or`U_out(1,:,:,:) = U0`for a solution over time and two or three space variables , , and . `u_out`- An output column vector of -values where usually
`y_out(1,:) = y0`for a solution over time. `U_out`- An output column vector of -values where usually
`y_out(1,:) = y0`for a solution over time. `y0`- An initial value (either a scalar or a column vector) of -values where usually
`y_out(1,:) = y0`for a solution over time. `y_out`- An output column vector of -values where usually
`y_out(1,:) = y0`for a solution over time.