MAT2384: Ordinary Dierential Equations and Numerical Methods
Dr. Robert Smith?
General Introduction
0.1
0.1.1
Basic Denitions
Dierential equation
A dierential equation is an equation involving an unkn
1. Integrating factor y 2 , answer 4x2 y 2 ex cos y + 3x = 1.
2. Undetermined coecients; homogeneous general solution yh = c1 e2x +
c2 ex ; particular solution yp = 2xe2x + 3 sin x cos x; solution to
MAT 2384 3X
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
Final Exam
July 20, 2009
Instructor: Dr. Steve Desjardins
Duration: 3 hours
Name:
Student Number:
Instructions:
 Print your name and student n
University of Ottawa
MAT 2384 Midterm Exam
Mar 1, 2017, Duration: 80 Minutes.
Instructor: Robert Smith?
Family Name:
First Name:
Do not write your student ID number on this front page. Please write yo
MAT 2384 A
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
TEST #1
October 16, 2015
Instructor: Dr. Steve Desjardins
Duration: 80 minutes
Name:
Student Number:
Instructions:
 Print your name and student
NEAT 2384 3X
DIFFERENTIAL EQUATIONS
AND NUNIERICAL NIETHODS
TEST #1
June 1? 2016
Instructor: Dr. Steve Desjarclins
Duration: 80 mhlutes
Student Number:
Instructions:
— Print your name and Student mu
MAT 2384 A
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
TEST #2
November 20, 2015
Instructor: Dr. Steve Desjardins
Duration: 80 minutes
Name:
Student Number:
Instructions:
 Print your name and studen
ORDINARY DIFFERENTIAL
EQUATIONS
LAPLACE TRANSFORMS
AND NUMERICAL METHODS
FOR ENGINEERS
by
Steven J. DESJARDINS
and
Rmi VAILLANCOURT
e
Notes for the course MAT 2384 3X
of Steven J. DESJARDINS
Spring 20
1
Solving equations by iteration
Suppose we want to solve
f (x) = 0.
(1)
There are no general formulas for this (except in a few simple cases). Thus, any solution depends almost entirely
on numerical
1
MAT 2384BFall 2017Assignment #4
To be submitted in class on Friday, November 3rd at 10:00 AM
Family Name
Given Name
Student Number
Please print the assignment and write solutions in the space pro
1
MAT 2384BFall 2017Assignment #5
To be submitted in class on Friday, November 17 at 10:00 AM
Family Name
Given Name
Student Number
Please print the assignment and write solutions in the space prov
MAT2384 B ORDINARY DIFFERENTIAL
EQUATIONS AND NUMERICAL METHODS
FALL 2016
Instructor: Dr. Petko Kitanov
Office: 585 King Edward (KED), Room 302
Phone: 6135625800, Ext. 2082
Email: [email protected]
MAT2384: Ordinary Differential Equations and Numerical Methods
Dr. Robert Smith?
1
Solving equations by iteration
Suppose we want to solve
f (x) = 0.
(1)
There are no general formulas for this (except
MAT2384: Ordinary Differential Equations and Numerical Methods
Dr. Robert Smith?
General Introduction
0.1
0.1.1
Basic Definitions
Differential equation
A differential equation is an equation involving
Splines
A type of modelfitting that
Assumes the data is excellent
Adapts the model to the data
Is good for interpolating between data
points.
Splines
Linear
Cubic
Join the
dots
Fit smooth
curves
I
42
Nonhomogeneous Linear Systems
We can now expand our discussions to include nonhomogeneous linear systems; that is, systems
that can be written as
x = Px + g
where g is a nonzero vectorvalued funct
1
Solving equations by iteration
Suppose we want to solve
f (x) = 0.
(1)
There are no general formulas for this (except in a few simple cases). Thus, any solution depends almost entirely
on numerical
MAT 2384 A
Assignment # 1
due Friday, September 22nd
Solvethe following initial value problems:
1. y 1 + y 2 y 0 = xex , y(1) = 3
2. (2x + 1) dx + (4y + 2) dy = 0, y(2) = 1
3. (x + 2y) dx x dy = 0, y(
MAT 2384 C
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
MIDTERM
March 4, 2015
Instructor: Dr. Steve Desjardins
Duration: 80 minutes
Name:
Student N umber:
Instructions:
Print your name and student
MAT2384 BOrdinary differential Equations and Numerical Methods
Midterm Exam (Fall 2017)
Professor: Joseph Khoury. Duration: 80 minutes
Last Name: ab;
First Name:
Student Number:
This is a closed
DERIVATIVE RULES & FORMULAS
RULES
y = c, c is a constant
y = cf, c is a constant
y = f +g
y=fg
y=fg
y=
f
g
y = fog(x)= f(g(x)
y = 0 ;
y = c(f )
y = f + g
y = f  g
y = f g + f g
y =
y = f (g(x) g
MAT 2384 C
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
MIDTERM
February 12, 2014
Duration: 80 minutes
1 ' 
Name:
Student Number:
Instructions:
 Print your name and student. number 011 this page.

MAT 2384 3K
DIFFERENTIAL EQUATIONS
AND NUMERICAL METHODS
NIIDTERM
_.J,!1_11e 19, 3011
Instructor: Dr. Steve Desjardins
Duration: 80 minutes
Name:
Student Number:
Instructions:
 Print your name and
: /Mf 23 A 4.11:7. am #9, J/ufmkr
2; y .13: he ~2n+/ y() O, yKa): /
'W Maga9 y=0 avg/.444
W 5914412523 (14 = m (I+/)/=0
w 4,; jun 96" + c134 mad rule. Maw
. Fix): anx jxr/ :,) yinJ: axzenf 15415
MAT 2384Fall 2017Assignment #1
To be submitted in class on Friday, September 22
. V
Family Name M
Givnn Name
Student Number
o Please print the assignment and write solutions in the space provided.
0