May 10, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Sample nal exam
1. For the system
x=
1 1
x
5 3
(a) Find the general solution
(b) Find equilibrium solutions and determine their stability
(c) Sketch the phase portrait
2. Solve the initial-value problem
MATH 351, Review for Midterm 2
Test topics
1. Linear equations of second order: examples with damped mass-spring system and electrical circuits (1.3.6,
Example 1.14, pp.24-25)
2. Initial-value problem, existence/uniqueness; superposition principle, genera
March 25, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 6
Due Thu. April. 1, 2010, in class.
1. Problems 4, 7, 8, Section 3.5, pp. 122124.
2. Transform the following higher-order equations into a system of rst order, and write
the syste
March 23, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 5
Due Thu. Mar. 25, 2010, in class.
1. Problems 1, 5, 6, 11, 14, 15, 17 (a), (d), (e) in Section 3.4 (pp. 115-117).
2. Problems 1 (d), (e); 5, Section 3.6, pp. 126127.
3. Problems
March 23, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 4
Due Thu. Mar. 18, 2010, in class.
1. Problems 3, 8, 9, 10, 12, section 3.2 (pp. 94-95).
2. Show that a particular solution of the equation
u + pu + qu = f1 (t) + f2 (t)
can be fo
February 23, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 3
Due Tue. Feb. 23, 2010, in class.
In the following two problems y denotes the unknown function, and x the independent
variable.
1. Solve the following linear equations
(a) xy
February 4, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 2
Due Thu. Feb. 11, 2010, in class.
1. (Population dynamics) At low population densities it may be dicult for an animal
to reproduce because of a limited number of suitable mates
February 4, 2010
MATH 351, Spring 2010
Prof. V. Panferov
Homework Assignment 1
Due Tue. Feb. 2, 2010, in class.
1. Verify that the initial-value problems
u = 1 u2 ,
u(0) = 0,
and u = 1 + u2 ,
u(0) = 0
2t
have solutions u(t) = e2t 1 and u(t) = tan t, respe