University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B44H
2013
Assignment # 1
Due date: Tuesday, October 1st, 2013
Readings: 1. Elementary Differential Equations and Boundary Value problems, 9e
by William E. Boyce & Ri

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University of Toronto at Scarborough
Department of CMS, Mathematics
MAT B44F
2015/16
Problem Set #3
Due date: in tutorial, week of Nov 16, 2015
Do the following problems from Boyce-Di Prima.
S.
S.
S.
S.
S.
3.5: 7, 9 (9th ed: 5,7)
3.6: 6, 10, 13, 14, 16
5.

Mathematics MATB44, Assignment 4, December 2015
Solutions to Selected Problems
7.1 # 22
1. Tank 1 initially contains 30 gal of water and 25 oz of salt, and Tank 2
initially contains 20 gal of water and 15 oz of salt. Water containing 1
oz/gal of salt flow

University of Toronto at Scarborough
Department of CMS, Mathematics
MAT B44F
2014/15
Problem Set #4
Due date: in tutorial, week of November 30
NOTE: Unlike previous assignments, most questions from Part A will be graded.
NOTE 2: I suggest you start with P

Mathematics MATB44, Assignment 1
Solutions to Selected Problems
1. Solve
x(1 + y 2 )dx + y(1 + x2 )dy = 0
This is of the form
M (x, y)dx + N (x, y)dy = 0
My = Nx = 2xy
so it is exact.
The solution is
F (x, y) = C
where
Fx = M
and
Fy = N
So
Fx = x + xy 2
x

Mathematics MATB44, Assignment 2
Solutions to Selected Problems
Question 1.
Solve
4y 00 12y 0 + 9y = 0
Soln: The characteristic equation is
4r2 12r + 9 = 0
The solutions are
r=
24
144 16 9
=3
8
(repeated root)
So the solutions are
y = e3x
and
y = xe3x
Qu

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TI-30X B
and
TI-30X S
The most recently calculated result is stored to the variable
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Press % i (Ans displays on the screen), or
Press any oper

MATB44 Assignment 3 201516 Solutions
Question 1.
Find a particular solution yp of each of the following equations.
(a) y 00 + 16y = e3x
(c) y 00 + 2y 0 3y = 1 + xex
Solution:
Question 1(a):
y 00 + 16y = e3x
Solution to homogeneous equation is
y1 = cos(4x)

4. Floating Point Numbers
Chapt. 5
ITEC 1011
Introduction to Information Technologies
Exponential Notation
The following are equivalent
representations of 1,234
123,400.0
x 10-2
12,340.0
x 10-1
1,234.0
x 100
123.4
x 101
12.34
1.234
x 102
x 103
The repres

University of Toronto at Scarborough
Department of CMS, Mathematics
MAT B44F
2015-16
Problem Set #2
Due date: In tutorial, week of October 5, 2015
The following problems from Boyce-Di Prima are suggeested for practice.
S.
S.
S.
S.
3.1
3.2
3.3
3.4
#9
#5
#

3
LECTURE #1. INTRODUCTION
1.1 Differential equations and Mathematical Modeling.
~Why do we study differential equations?
-Why do they deserve such a great attention?
The low of universe is written in the language of mathematics. To ﬁnd solutions to
diffe

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University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Fall 2013
MAT B44 (Ordinary Differential Equations)
GENERAL INFORMATION
Instructor:
Dr. N.Cheredeko
Office:
IC484
Telephone: (416) 287-7226
E-mail: n.cheredeko@utoronto.ca

Assignment # 0
MAT B44
Due Date: September 11th, 2013 (Hand in at the beginning of the lecture)
Review of Integration
Textbook: J.Stewart, Single Variable Calculus,Early Transcendentals, 6e &7e
Definite Integral. Application of Fundamental Theorem of Calc

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT B44H
2013
Assignment # 2
Due date: Tusday, October 22nd, 2013
Readings:
1. Elementary Differential equations and Boundary Value problems,
William E. Boyce & Richard

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Final Examination
MATB44H Dierential Equations I
Examiner: L. Jerey
Date: December 17, 2009
Duration: 3 hours
FAMILY NAME:
GIVEN NAMES:
STUDENT NUMBER:
DO NOT OPEN THIS BO

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
FINAL EXAMINATION
MATB44H Dierential Equations I
Examiner: N. Cheredeko
Date: December 18, 2010
Duration: 180 minutes
DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO.
F

B44 MIDTERM
1. cfw_10 Find general solution to the given differential equation (use UV-
substitution) 1page
x 2 y! + xy = x 2 sin x
2. cfw_10Reduce the given equation to separable equation and find its general

LECTURE #4
LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS.
MIXTURE PROBLEMS
Large amount of real life mixture problems involves changes in concentration
and amount of solute and solvent. Lets consider generalized problem
1. Brief formulation of the real world

CHAPTER 7. ———~
Section 7.8
2. Setting x = g tT results in the algebraic equations
(4? 106348)
The characteristic equation is r2 = 0, with the single root r = 0. Substituting 7' = 0
reduces the system of equations to 251 — £2 = 0. Therefore the only eig

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B44F
2015-16
Problem Set #1
Due date: in tutorial, week of Sept. 21, 2015
Do the following problems from Boyce-Di Prima.
S. 2.4: #27
S. 2, Miscellaneous problems (page 13