University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2015
B. Rouben
UOIT
ENGR2500U
2015 Sept.Dec.
Assignment 1
3 Problems, of which 2 will be marked, 25 marks total
Due Monday September 21, 6 pm latest
1. [Will not be marked, but you should still do it]
Point particle a of mass 1 and speed 8 (in the LAB)(arbit
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
2.2: SEPARABLE EQUATIONS
What it means for an ODE to be separable 2.1, and recognizing if a
given differential equation is separable or not;
How to solve a separable first order ODE 1.
2.3: LINEAR EQUATIONS
How to recognize linear firstorder
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
2.4: EXACT EQUATIONS
Recognizing if a firstorder differential equation is exact 2.2;
Solving exact differential equations 1;
To find (where possible) an integrating factor which makes a firstorder
ode exact 2, and to subsequently solve the e
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
4.4: UNDETERMINED COEFFICIENTS. SUPERPOSITION APPROACH (covered
on Assign #2 but not in lecture . . . will only be tested on this section in
short answer or multiple choice questions)
The form of the particular solution to be assumed.
4.6: VARI
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
%
% adjust the following (READ THROUGH GREEN LINE COMMENTS TO FIND THEM):
%
IVP: x0,y0,dy/dx=F(x,y);
%
step size h (this is set up as a row matrix with one
entry for each h value in the question);
%
xlast the x value of the desired approximation
%
x0=0;
y
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
5.1: LINEAR MODELS: INITIALVALUE PROBLEMS
Setting up the model for a mass on a spring, and the form of the various forces that affect its motion;
Understand the distinction between damped and undamped oscillations (both in terms of the equatio
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
5.2: LINEAR MODELS: BOUNDARY VALUE PROBLEMS
Solve problems involving beams satisfying various boundary conditions such as embedded, free, and/or simply supported 3;
Solve various applications of 2nd order and higher boundary value
problems. In
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
4.2: REDUCTION OF ORDER
The technique reduction of order" and how to use it to construct a
second linearly independent solution given one solution to a linear
2nd order equation 1,1.
4.3: HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
3.1: LINEAR MODELS
Set up linear differential equations (with appropriate initial conditions)
as mathematical models for a variety of physical phenomena, and
solve the resulting equations;
Interpret solutions of differential equations in the co
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW (same as on previous notes)
5.1: LINEAR MODELS: INITIALVALUE PROBLEMS
Setting up the model for a mass on a spring, and the form of the various forces that affect its motion;
Understand the distinction between damped and undamped oscillations (
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
%
% adjust the following (READ THROUGH GREEN LINE COMMENTS TO FIND THEM):
%
IVP: x0,y0,dy/dx=F(x,y);
%
step size h (this is set up as a row matrix with one
entry for each h value in the question);
%
xlast the x value of the desired approximation
%
x0=0;
y
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2015
B. Rouben
UOIT
ENGR2500U
2015 SeptemberDecember
Assignment 2
4 Problems (3 to be marked), 25 marks total
Due Monday September 28, 6 pm
1. [8 marks; 2 marks per part]
Natural uranium contains the following isotopes in abundance by number of atoms:
234U,
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
1.1: DEFINITIONS AND TERMINOLOGY
Basic concept of a dierential equation 1.1;
Familiarity with the vocabulary of dierential equations: ODE 1.2 vs
PDE 1.3, linear vs nonlinear 1.4, order of an equation, systems of equations, etc.;
Ability to rec
University of Ontario Institute of Technology (UOIT)
Differential Equations for Engineers
MATH 2860

Fall 2013
PREVIEW
o 12.1: SEPARABLE PARTIAL DIFFERENTIAL EQUATIONS
Familiarity with the vocabulary of partial differential equations: lin
ear vs nonlinear, order of an equation, homogeneous vs nonhomoge
neous;
Understand what it means to solve a partial diff