MAT 303
FALL 2012
MIDTERM I
Problem 1. A car traveling at 30 mi/h (44 f t/s) gradually speeds up
during 10 seconds with the acceleration given by
a(t) = 0.06t2 + 2.4 (f t/s2 ).
Find the distance it ha
Quiz 1 with solutions
Problem 1. Show that the function y (x) =
the equation
2xy = (2x + 1)y
xex is a solution of
on the innite segment (0, +).
Solution. Using the product rule for dierentiation, we o
i. (Q, Pb.)
Solve differential equations: 42, (15' (/5 )
Solve the initial value problem 3.
A cup of tea at temperature 80C was left on a table in the kitchen,_
Where the temperature is 26C. After 20
REVIEW FOR MIDTERM: MAT 303, FALL 2013
(1) Indicate whether each of the following dierential equations is linear,
separable and/or exact. Find the general solution to each dierential equation. (An equ
Homework 7
Alexandra Viktorova
November 3, 2016
Problem 1: [Reduction of order] Show that if y1 is a solution of the dierential equation
y + p1 (t)y + p2 (t)y + p3 (t)y = 0
(1)
then y2 = y1 v is a new
MAT 303, Problem Set 04
Problems 2.1: 9: The time rate of change of a rabbit population P is
proportional to the square root of P. At time t = 0 (months) the population
numbers 100 rabbits and is incr
MAT 303, Problem Set 07
Problems 3.3: 9,10: Find the general solutions of the differential equations in Problems 1 through 20.
y 00 + 8y 0 + 25y = 0
5y (4) + 3y (3) = 0
Problems 3.3: 23, 26:
21 thro
MAT 303, Problem Set 10
Problems 5.1: 3: Find AB and BA given
A=
2 0 1
3 4 5
1
3
and B = 7 0
3 2
Problems 5.1: 9, 10: In Problems 9 and 10, verify the product law for
differentiation, (AB)0 = A0 B +
MAT 303, Problem Set 11
Problems 5.3: 31: A represents a 2 2 matrix.
Use the definitions of eigenvalue and eigenvector (Section 5.2) to prove
that if is an eigenvalue of A with associated eigenvector
MAT 303, Problem Set 12
Problems 5.5: 1, 4: Find general solutions of the systems in Problems
1 through 22.
2 1
x0 =
x
1 4
3 1
0
x =
x
1 5
Problems 5.6: 25, 27: Each coefficient matrix A in Problems
MAT 303: CALCULUS IV WITH APPLICATIONS
FALL 2016
GENERAL INFORMATION
Instructor. Raluca Tanase
Email: [email protected]
Office: Math Tower 4120
Office hours: M 12pm in MLC, W and Th 12pm
MAT 303, Lecture 01, Spring 2017
Course Description:
A differential equation is an equation relating unknown functions and
their derivatives. In this course we will study ordinary differential equatio
MAT 303
FALL 2012
NAME :
Final Exam
ID :
THERE ARE TEN PROBLEMS. EACH PROBLEM HAS THE SAME VALUE 10 POINTS.
SHOW YOUR WORK
DO NOT TEAROFF ANY PAGE
NO CALCULATORS
NO CELLS ETC.
ON YOUR DESK: ONLY test
MAT 303
FALL 2012
NAME :
Final Exam
ID :
THERE ARE TEN PROBLEMS. EACH PROBLEM HAS THE SAME VALUE 10 POINTS.
SHOW YOUR WORK
DO NOT TEAROFF ANY PAGE
NO CALCULATORS
NO CELLS ETC.
ON YOUR DESK: ONLY test
MAT303
WM
Summer
MAT
o
o
303
:
syllabus
:
higher
order
linear
systems
of
linear
office hour
Math
A
equations
Monday
once
:
equations
P

is
Thur
Assignment every Thursday
August
3
and
'
TEEHAN
wtgrrh
MAT 303, Midterm Review
The midterm will cover the material we have learned so far (also including this week). The exam problems will be based on the homework problems.
Here we give a brief summary of
MAT 303, Problem Set 05
Problems 2.3: 2: Suppose that a body moves through a resisting medium
with resistance proportional to its velocity v, so that dv/dt = kv. (a) Show
that its velocity and positio
MAT 303, Problem Set 08
Problems 3.5: 2, 17, 20: In Problems 1 through 20, find a particular
solution yp of the given equation. In all these problems, primes denote
derivatives with respect to x.
y 0
MAT 303, Problem Set 08
Problems 4.1: 1, 4: In Problems 1 through 16, transform the given differential equation or system into an equivalent system of firstorder differential
equations.
x00 + 3x0 +
Assignment 6: due date March 23rd / 25th in Recitation Section
MAT303: Calculus IV
Problem 1 (2.3 no. 2): Suppose that a body moves through a resisting medium with
resistance proportional to its veloc
Assignment 9: due date April 20th / 22th in Recitation Section
MAT303: Calculus IV with applications
Problem 1: Consider the following matrices:
3 2 1
A= 0 4 3
5 2 7
0 3 2
B = 1 4 3
2 5 1
Find (a) 7A
ASSIGNMENT 7 DUE DATE MARCH 30TH / APRIL 1ST
Exercise 1 (3.2 no. 7,8): Use the Wronskian to prove that the given functions are linearly
independent on the indicated interval:
f (x) = 1,
f (x) = ex ;
g
Assignment 5: due date March 9th and 11th in Recitation Sections
MAT303: Calculus IV with Applications
Problem 2.1: 10. Suppose that the fish population P (t) in a lake is attacked by a disease
at tim
Assignment 8: due date April 13th / 15th in Recitation Section
MAT303: Calculus IV with applications
For the first problems you can consult 3.4 of the textbook. For Problem 4 see 4.1 and for
the last
The topics covered so far naturally fall into two groupsGeneral first order differential
equations and linear differential equations.
First order equations
Initial value problems. If you know the gen