0.5 Green's Functions

0.5 Green's Functions

• Nuclear reaction produces heat inside a fuel rod.

• The temperature variation along a rod's length is less than along a radius because the rod is 3 m long and 1 cm in diameter.
• The rod's temperature is treated as a function of the radial variable alone.

• We need to know the derivative of the function.

• Let's apply the boundary condition.

• The two integrals can be combined into one.

• The formula was given in Eq.

• The Green's function can be solved by constructing it.

• The boundary conditions need to be satisfied.

• This is the correct solution.
• There are many ways to arrive at the same result.
• It's an efficient way to get the solution.

• Let's take a look at the calculations and see if there is a problem.

• We summarize in a conclusion.

• A unique solution is given when it exists.

• We might try to get a solution by the usual method.

• There is no solution to the problem stated.

• 2 as the case may be.

• The Green's function is stated in the exercises.

• Review questions can be found on the CD.

• The given boundary value problem can be solved in Exercises 1-15.

• The equation is not straight forward.

• The interval should be noted.

• To find a second independent solution of the differential equation, use a variation of parameters.
• The solution is given in parentheses.

• The boundary value problem can be solved in closed form.

• A straight shaft has violent behavior at certain times of rotation.

• The existence of nonzero solutions to the boundary value problem can be found with a formula for the values of angular velocity.

• Air pollutantSO2 reacts with water to form sulphuric acid.
• Acid rain occurs if the water is in the air or in the snow.

• The concentration is in the air.

• 2 is related to stress.

• Show that the relation is a differential equation.