TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.1 (Due Tuesday Jan. 29)
In Edwards and Penney: Section 3.8, problem 1 Section 9.5, problem 15 Section 9.7, problem 8 Section 9.7, problem 9

Prof. S.L. Phoenix
9/06/11
Math 3100
Method of Variation of Parameters for Higher Order Linear ODEs
Suppose we have the equation
L y y n p1 x y n1 pn1 x y 1 pn x y g x
(1)
which is eqn. (2) in E&P, except we use g x instead of f x . From the homogeneous

Prof. S.L. Phoenix
9/06/11
TAM 3100
Method of Undermined Coefficients: Two Useful Rules and a Table
Rule 1:
In solving L y f x suppose that no term appearing either in f x or in any of its
derivatives satisfies the homogeneous equation L y 0 . Then take a

Prof. S.L. Phoenix, 9/15/11
B&D Section 5.2: An Example
We use the power series solution method, expanding about x a 0 , to solve the differential
equation
y xy y 0
(1)
subject to the initial conditions
y 0 2, y 0 3
(2)
Here power series solution method m

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.14 (not to be handed in)
Questions 1 and 2 are based on the following Table, in which x=U.S. Population, y=World Population, and z=no.of employees in U.S. Federal Gov't., a

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.13 (Due Tuesday April 29)
1) A standard deck of 52 playing cards is shuffled and 10 cards are selected with replacement as follows: A card is drawn, it is written down, the

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.12 (Due Tuesday April 22)
1. Let Z be a random variable equal to the sum of the three numbers that appear when three dice are rolled. a. Determine and plot the probability

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.11 (Due Tuesday April 15)
1. Evaluate (a)
10 P3 ,
(b)
10 P1 ,
(c)
10 P10 ,
(d)
10 C3 ,
(e)
10 C1 ,
(f)
10 C10 .
2. How many different arrangements can be made o

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.10 (Due Tuesday April 8)
1. A bag is filled with 20 dice in the shape of the 5 Platonic solids (T=Tetrahedron, C=Cube, O=Octahedron, D=Dodecahedron, I=Icosahedron), in each

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.9 (Due Tuesday April 1) 1. The radial vibrations of a gas contained in a rigid spherical shell of radius unity is governed by the PDE: 2 1 = 2 2 (1) 2 t with the bound

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.8 (Due Tuesday March 25) 1. The following equation is called Hermite's equation: y - 2xy + 2py = 0 (1)
a. Obtain a solution to eq.(1) by power series. b. Find values of p s

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.7 (Due Tuesday March 11) 1. Beginning with the equation A(x)y + B(x)y + C(x)y + D(x)y = 0 first divide by A(x) and then multiply by p(x) = exp B(x) dx A(x)
Show that the re

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.6 (Due Tuesday March 4) 1. We have seen in class that the equation xy + y + xy = 0 has the general solution y = c1 J0(x) + c2 Y0 (x) (2) where J0 (x) is the Bessel function

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.5 (Due Tuesday Feb.26) 1. Determine whether x = 0 is an ordinary point, a regular singular point, or an irregular singular point for each of the following. In each case, use

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.4 (Due Tuesday Feb.19)
1. Find the general solution to the following two ODE's in the form of power series in x. Find the first three nonzero terms in each of two linearly

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand
Homework No.3 (Due Tuesday Feb.12) 1. Derive 2 u in circular cylindrical coordinates by using the chain rule, starting with 2 u = uxx + uyy and applying the transformation x = r cos , y

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.2 (Due Tuesday Feb. 5) 1. Using separation of variables on the following PDE's, obtain 2 ODE's for each. Underline in red all variable coefficients which occur in the ODE's.

S. L. Phoenix
TAM 3100 Fall 2011
Typical Prelim 1 Questions with respect to the the current organization of the
course (though more problems than typical).
1.
Consider the differential equation
y 4 y t At cos 2t
(a) Find four linearly independent solutio