Math 215/255 Section 103 (Gustafson): Written Assignment
3 Solutions
1. Solve exercise 1.4.9 in the online text.
Solution: let
y (t) = the mass (in kg) of toxic substance in Lake 1 at time t (in hours).
The initial condition is
y (0) = 500
(take the time
HOMEWORK 1 SOLUTIONS: MATH 215
Problem 1: In each case, solve for y (t):
a. y + 2y = 0 with y (0) = 1.
b. y + 2y = 3et with y (0) = 2.
1
c. y 2y = te2t with y ( 4 ) = 0.
d. ty 2y = t3 sin t with y ( ) = 0.
3
e. t3 y + 8t2 y = e(t
)
with y (1) = 1.
Solutio
MATH 215/255
Fall 2015
Assignment 2
Due date: October 02, 2015
1.4, 1.6, Brauns Book 1.9
1. Consider a pond that initially contains 10 million gal of fresh water. Water containing an undesirable chemical ows into the pond at the rate of 5 million gal/yr,
HOMEWORK 1: MATH 215
Due in class on Monday, Jan 20th
Show all relevant work for credit. You will be marked for your work and your answer as appropriate.
Working with others is encouraged but you must submit your own work and identify who you worked with
MATH 215/255
Fall 2015
Assignment 4
Due date: October 23, 2015
1. A small object of mass 1 kg is attached to a spring with spring constant 2 N/m. This
spring-mass system is immersed in a viscous medium with damping constant 3 N s/m.
At time t = 0, the mas
MATH 215/255
Fall 2015
Assignment 5
2.5.3, 2.6, 6.1
1
y + y + y = e2t sec(2t), < t < .
4
4
4
Hint: To use the method of variation of parameters, rewrite the DE so that the
coecient of y is 1 before solving the boxed system on page 74 of [Lebl].
1. Find a
MATH 215/255, Homework 3
1. Consider the ODE
y (t) = y t,
y(0) = 2.
(1)
(a) Find the exact solution to this problem, and show that y(1) 4.71xx. What are the next two
digits xx?
(b) Use Eulers method to approximate y (1) with (1) h = 0.5 (2) h = 0.25; and
HOMEWORK 2: Math 215 January 2014
1. Find the solution y(t) to
y =
3 2
1 2
y,
with y(0) =
3
3
.
Also, describe the behavior of the solution for large t.
2. Solve the following system of dierential equations with initial conditions and sketch the solution.
HOMEWORK 1: MATH 215/255
Due in class on Friday, Jan 22nd
Show all relevant work for credit. You will be marked for your work and your answer as appropriate.
Talking to other students about the problems is encouraged but you must submit your own work and
Notes on Diffy Qs
Differential Equations for Engineers
by Ji Lebl
r
October 20, 2014
2
A
Typeset in LTEX.
Copyright c 20082014 Ji Lebl
r
This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0
United States License. To v
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Required Output per shift
Where are the bottlenecks in the system
75 What is the daily output of the system?
How would you increase capacity?
1000
Average Job Size (boards)
60
Production hours per day
7.5
Working Days
Team Building
Emotional Intelligence Ethics
& Business
Why EI Teamwork
& Ethics in Business?
Harvard Business Review
NASA research air crashes concluded errors of
teamwork & communication can be a cause:
1. Pilots make poor decisions when acting on too li
Introduction to Operations
Management COMM 399
UBC
Tom Culham P. Eng, M.A. Sc., Ph. D.
398 Operations Management
Getting to Know Tom Culham
Office hours 1:30-3:15 Tue
Office HA 351, station 'OPLOG 1'
Telephone: 604 773 2489
Email: [email protected]
COURSE OUTLINE FOR MATH 215: DIFFERENTIAL EQUATIONS
Text: We will use the free online text in .pdf form Diy Qs: Dierential Equations
for Engineers, by Jiri Lebl. Please download the book from:
http:/www.jirka.org/diyqs/diyqs.pdf
For a few topics you will
PROBLEM 3: (20 Points)
By using Laplace transforms, ﬁnd the solution to the initial value problem
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MATH 215: MIDTERM 2: MARCH 20th 2014. (R. Froese, M. Ward)
Closed Book and Notes. 50 minutes. Total 50 points
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MATH 215: MIDTERM 1: February 6th 2015
Closed Book and Notes. 50 minutes. Total 50 points
PROBLEwW'i; (28 Points) Solve the ioilowing initial value problems for y(t) and then
determine the interval of existence of the solution:
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Team Analytical Assignment #1
Identification Removed
1
2.7
Time to bake bread - 12 minutes
Flow rate - to produce 4000 units / hour OR x units/min
Average Flow Rate (=4000) x Average Flow time (=12/16) = oven must be able to hold at least
800 units breads
MATH 215S - PRACTICE MIDTERM
Problem I. (18 points) Short answer questions. Here you only need to give the correct answer no
detailed explanations/ calculations are needed to support your answer.
(a) (2 points) Find a solution of the form y = tr of the eq
17-03-06
Announcements:
HW4 is posted may take more eort with
Matlab than previous get started early and
visit the TAs in LSK310 as needed. Due Friday,
March 17.
No oce hours this week
Webwork 8 will be posted by tomorrow. Due
Monday, March 13t
4/5/17
Notices
Notices
Final Exam: Friday, April 21st, 7PM.
In WOOD 2 (this section)
Exam will be TWO HOURS LONG
Final exam:
Office hours:
April 19 and 20, 10am-12pm
Webwork 11 deadline is deferred to Friday
10pm
Final exam list of topics will be po