By Philip Straffin (editor)

ISBN-10: 0883850850

ISBN-13: 9780883850855

Scholars see how calculus can clarify the constitution of a rainbow, advisor a robotic arm, or examine the unfold of AIDS. every one module starts off with a concrete challenge and strikes directly to offer an answer. The discussions are targeted, lifelike, and pay cautious consciousness to the method of mathematical modeling. routines, strategies, and references are supplied.

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**Extra resources for Applications of Calculus (Resources for Calculus Collection)**

**Sample text**

3 does not apply to this modified equation, because the diffusion coefficient is negative. Rather, an examination of the Fourier series solution for this modified equation would show that all wave numbers lead to growth, and the growth increases with the square of the wave number. 4. 3 Modified Equation Analysis for Explicit Centered Differences The modified equation analyses of the explicit upwind and explicit downwind schemes were very similar. However, in order to study the explicit centered difference scheme we will need to make the additional assumption that the modified equation error has an asymptotic expansion.

In other words, taking larger timesteps decreases the accuracy of the implicit upwind scheme; this result stands in contrast to our experiments with the explicit upwind scheme, in which the accuracy improved as the size of the timestep was increased. This is important to remember, because the temptation is to take larger timesteps with the implicit upwind method in order to decrease the cost of the scheme. 7 Explicit Centered Differences Our final example of finite difference schemes for linear advection will use a second-order spatial difference.

V) Type “xmgrace output” to plot the computational results. This information is contained in the README file. 2 Second Upwind Difference Program The second program is designed to be more modular than the first program. f Fortran main program for solving a linear advection problem over some specified time or number of timesteps. 2-11: GNUmakefile Makefile to compile and load the Fortran files. It is strongly suggested that the student maintain this basic style of organization for the code. The separation of initial and boundary conditions from the time integration will make the experimentation with alternative numerical schemes easier.

### Applications of Calculus (Resources for Calculus Collection) by Philip Straffin (editor)

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