The 2250-1 and 2250-2 final exams consist of six problems, representing
chapters 3, 4, 5, 6, 7, 10. Each problem has multiple parts, similar to
midterms 1,2,3.

The following problems will be used as models for the problems
that will appear on the final exam. 

 Chapter 3: 3.1-16, 3.2-18, 3.3-18, 3.4-22, 3.5-21, 3.6-17, 3.6-32
 Chapter 4: 4.1-16, 4.2-28, 4.3-18, 4.4-20, 4.5-22
 Chapter 5: 5.1-33 to 5.1-42, 5.3-15, 5.3-28, 5.4-18, 5.5-4, 5.5-24,
   5.5-48, 5.6-12, 5.6-18
 Chapter 6: 6.1-23, 6.1-35, 6.2-25, 6.2-31
 Chapter 7: 7.1-18, 7.2-16, 7.3-18, 7.3-28
 Chapter 10: 10.1-29, 10.2-6, 10.2-12, 10.2-23, 10.3-8, 10.3-21,
   10.3-38, 10.4-18

Sun May  2 12:16:50 MDT 2004

2250-1 and 2250-2 final exam in-class Spring 2004 information

Remove 10.4-13 and 10.5-9 from the final exam syllabus. These
topics were not covered in both classes, so to be fair, neither
class is responsible.

The final exam for 2250-1 is organized as follows. The 2250-1
final exam is similar.

        Differential Equations and Linear Algebra 2250-2
                  Final Exam 10:30am 3 May 2004

Instructions. The time allowed is 120 minutes. The examination
consists of six problems, one for each of chapters 3, 4, 5, 6, 7,
10, each problem with multiple parts. A chapter represents 20
minutes on the final exam.

Each problem represents several textbook problems numbered (a),
(b), (c), ... . Choose the problems to be graded by check-mark
X; the credits should add to 100.

Calculators, books, notes and computers are not allowed.

Answer checks are not expected or required. First drafts are
expected, not complete presentations.

Please submit exactly six separately stapled packages of
problems, one package per chapter.

=================================================================
Ch3. (Linear Systems and Matrices)
% Chapter 3: 3.1-16, 3.2-18, 3.3-18, 3.4-22, 3.5-21, 3.6-17,
% 3.6-32

[40%] Ch3(a): Find the inverse matrix by the RREF method.

[60%] Ch3(b): Find the value of x_i by Cramer's Rule in the
system Cx=b, given C and b below.

[40%] Ch3(d): Determine all values of k such that the system Rx=f
has infinitely many solutions and then display the solution
formula for x.

=================================================================
Ch4. (Vector Spaces)
% Chapter 4: 4.1-16, 4.2-28, 4.3-18, 4.4-20, 4.5-22

[40%] Ch4(a): Cite or state a determinant test to detect the
independence or dependence of fixed vectors [10%]. Apply the test
to the vectors below [25%]. Report independent or dependent [5%].

[60%] Ch4(b): Proof about subspaces.

[60%] Ch4(c): Find a basis of fixed vectors for the solution
space of Ax=0.

[40%] Ch4(d): Find a 4x4 system of linear equations for the
constants a, b, c, d in the partial fractions decomposition below
[10%]. Solve for a, b, c, d, showing all RREF steps [25%]. Report
the answers [5%].

=================================================================
Ch5. (Linear Equations of Higher Order)
% Chapter 5: 5.1-33 to 5.1-42, 5.3-15, 5.3-28, 5.4-18, 5.5-4,
% 5.5-24, 5.5-48, 5.6-12, 5.6-18

[30%] Ch5(a): Using the recipe for higher order
constant-coefficient differential equations, write out the
general solutions of the two equations below.

[30%] Ch5(b): Problem on a damped spring-mass system.

[40%] Ch5(c): Determine (from the table on page 331 of the
textbook) the final form of a trial solution for y_p according to
the method of undetermined coefficients. Do not evaluate the
undetermined coefficients!

[30%] Ch5(d): Find the steady-state periodic solution.

=================================================================
Ch6. (Eigenvalues and Eigenvectors)
% Chapter 6: 6.1-23, 6.1-35, 6.2-25, 6.2-31

[30%] Ch6(a): Find the eigenvalues of the matrix A.

[35%] Ch6(b): Diagonalization and eigenpairs.

[35%] Ch6(c): Proof.

[30%] Ch6(d): Give an example in eigenanalysis.

=================================================================
Ch7. (Linear Systems of Differential Equations)
% Chapter 7: 7.1-18, 7.2-16, 7.3-18, 7.3-28

[40%] Ch7(a): Solve a 2x2 system of differential equations.

[40%] Ch7(b): Solve a 2x2 system with complex eigenvalues.

[60%] Ch7(c): Apply the eigenanalysis method to solve a system x'
= Ax.

[40%] Ch7(d): Brine tank problem.

=================================================================
Ch10. (Laplace Transform Methods)
% Chapter 10: 10.1-29, 10.2-6, 10.2-12, 10.2-23, 10.3-8, 10.3-21,
%  10.3-38, 10.4-18
% Removed: 10.4-13, 10.5-9

It is assumed that you have memorized the basic Laplace integral
table and know the basic rules for Laplace integrals. No other
tables or theory are required to solve the problems below. If you
don't know a table entry, then leave the expression unevaluated
for partial credit.

[30%] Ch10(a): Find f(t) by partial fraction methods.

[30%] Ch10(b): Apply Laplace's method to find a formula for
L(x(t)). Do not solve for x(t)!

[35%] Ch10(c): Apply Laplace's method to the system to find a
formula for L(y(t)). Do not solve for y(t)!

[35%] Ch10(d): Solve for x(t), given L(x(t)).

[35%] Ch10(e): Find L(f(t)), given f(t).

=================================================================
End of final exam