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 obtain
1
y = ( xex ) = 2x ex + xex .
Thus,
2xy =
xex + 2
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 has traveled in these 10 seconds and its velocity at the
Homework 1
Dyi-Shing Ou
September 10, 2016
1.1.26
Plugin the given y to the left hand side
[cos x (x + C) sin x] + (x + C) cos x tan x
= [cos x (x + C) sin x] + (x + C) sin x
= cos x
This equals to the right hand side. Therefore, y(x) = (x + C) cos x is a
Homework 2
Tim Ryan
September 19, 2016
1.3.11
Problem
Determine whether the existence of at least solution of the initial value problem is guaranteed by Thm. 1 of the
section and, if so, if its uniqueness is guaranteed.
dy
= 2x2 y 2 ; y(1) = 1
dx
Solution
Assignment 11: due date May 6th
MAT303: Calculus IV
Solve the following problems that you can find on the textbook. Moreover dont forget to fill
out the on-line evaluation.
Edition 4
4.2: 2, 12, 8
5.2: 27
5.6: 5, 10
Edition 5
4.2: 2, 12, 8
5.2: 27
5.7: 5,
Assignment 10: due date April 29th
MAT303: Calculus IV
Solve the following problems that you can find on the textbook:
Edition 4
5.4: 6, 7, 12, 13
5.2: 11, 23
5.5: 25, 27
Edition 5
5.5: 6, 7, 12, 13
5.2: 11, 23
5.6: 25, 27
1
MAT 303, Problem Set 01
These problems are from Sections 1.1 and 1.2 in the textbook Differential equations and boundary value problems by C. H. Edwards, D. E.
Penney, D. T. Calvis ( 5th edition). This homework is due in recitation on
the week of Jan 30,
MAT 303, Problem Set 03
Problems 1.5: 3,14: Find general solutions of the differential equations
in Problems 1 through 25. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with
respect to
MAT 303, Problem Set 02
Problems 1.3: 14, 15, 16: A more detailed version of Theorem 1 says
that, if the function f (x, y) is continuous near the point (a, b), then at least
one solution of the differential equation y 0 = f (x, y) exists on some open
inte
MAT 303: CALCULUS IV WITH APPLICATIONS
FALL 2016
GENERAL INFORMATION
Instructor. Raluca Tanase
Email: [email protected]
Office: Math Tower 4-120
Office hours: M 1-2pm in MLC, W and Th 1-2pm in Math Tower 4-120
Lecture and Recitations.
LEC 01 MW
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 equations
including first order equations, linear equations of
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 equation implicitly dening y as function of x is an accept
CHAPTER 2.
8. (a) .8
(b) .3
(c)
0
10. Let R and N denote the events, respectively, that the students wears a ring and wears a
necklace.
(a) P(R U N) = 1 - .6 = .4
(b) .4 = P(R U N) = P(R) + P(N) - P(RN) = .2 + .3 - P(RN)
Thus, P(RN) = .1
11. Let A be the
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 velocity v, so that dv/dt = kv. (a) Show that its velocity a
CSE355/AMS345 Homework 1
Jie Gao
September 16, 2014
The following problems are due on September 16th.
1. Guarding the walls. (10pts) Construct a polygon P and a placement of guards such that the guards
see every point of P , but there is at least one poin
AMS 311 - HW1 Feedback
TA: Mengqiao Wang [email protected]
Notes:
1. If you submit homework as several loose pages, please staple them. Thank you very much!
2. I am very careful inputting your grade into the Blackboard. However, if there is a m
AMS 210 Homework #1 (75 points)
Due Date: Feb 7, 2013
1. (20 points) Reduce each of the following systems of linear equations into
their echelon form. For each linear system, indicate whether there should
be a single solution, innitely many solutions, or
AMS 210 Homework #2 (75 points)
Due Date: Feb 14, 2013
1. (15 points) For each pair of points in Rn , express the line which passes
through the two points as a parametrized set of vectors.
(a) (0, 0) and (1, 2)
(b) (1, 3, 5) and (2, 4, 7)
(c) (3, 3, 3, 3)
ADDITIONAL PROBLEMS FOR HW 11
Let G,H denote two groups. A mapping f : G H is homomorphism of
groups if f (g1 g2 ) = f (g1 )f (g2 ) is true for all g1 , g2 G. A homomorphism
of groups is an imbedding of groups if it is one-to-one. A homomorphism of
groups
SOLUTIONS FOR MIDTERM: MAT 303, FALL 2013
(1) Find the general solution to each dierential equation.
(a) (10 points) y (3) + 2y (2) 4y (1) 8y = 0
Solution: The characteristic equation is r3 + 2r2 4r 8 = 0: r = 2
is a root of multiplicity one, and r = 2 is
SOLUTIONS TO MIDTERM FOR MAT312/AMS351; FALL
2013
Instructions: Complete each of the following 5 problems in the spaces
provided. Be sure to show some work, or give an explanation, in support of
each of your answers. The use of notes, books, computers, ca
MAT 303: CALCULUS IV WITH APPLICATIONS, FALL
2013
Course Description
Most of the fundamental principles of the sciences are expressed mathematically in the form of dierential equations. This course discusses some basic
methods for solving ordinary dierent
SOLUTION TO 72 IN SECTION 1.6
3
Substitute = y into ry = (1 + (y )2 ) 2 to get
3
(i) r = (1 + 2 ) 2 .
By seperating the variables in (i) and then integrating we get
(ii) r
d
3
(1+2 ) 2
=
1dx = x + C1 .
By substituting = tan() into the left hand side of th
MAT 303 Spring 2013
Calculus IV with Applications
Midterm #1 Practice Problems
1. Solve the following initial value problems:
(a) xy0 = y + x2 , y(1) = 0
(b) y0 = 6e2xy , y(0) = 0
(c) y0 = 2x y +
1
,
x2
y (1) = 2
(d) (1 + x )y0 = 4y, y(0) = 1
(e) v0 1x v