A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 200 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 200 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x =
3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 200 degrees Celsius. The ends of
the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x. t) be the
temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1).
Put us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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