PREVIEW
1.1: DEFINITIONS AND TERMINOLOGY
Basic concept of a differential equation 1.1;
Familiarity with the vocabulary of differential equations: ODE 1.2 vs
PDE 1.3, linear vs nonlinear 1.4, order
MATH 2860S12 Assignment #2
DUE DATE: This assignment is to be submitted entirely on
paper in your TA's assignment drop box by FRI July 20 at
noon. Hand in one perfect copy per group of 2.
Last Name
Fi
Academic Success Centre
[email protected]
http:/academicsuccess.uoit.ca
LaplaceTransforms
Laplace transforms are used for solving linear differential equations by converting integral and
differe
rsLuE Saw no: 5
MATH 2860U Midterm examination Page 2 of 6
1. (a) [3 marks] Find the integrating factor associated with the DE (but DO NOT solve
the DE!)
(x + njZ + (x + 2)y = 22w"
B FM -\L -x _ _
PREVIEW
2.3: LINEAR EQUATIONS
Solving a linear equation by introducing an appropriate integrating
factor 1.
2.4: EXACT EQUATIONS
Recognizing if a first-order differential equation is exact 2.2;
S
PREVIEW
12.1: SEPARABLE PARTIAL DIFFERENTIAL EQUATIONS
Familiarity with the vocabulary of partial differential equations: linear vs nonlinear, order of an equation, homogeneous vs nonhomogeneous;
U
PREVIEW
7.4: OPERATIONAL PROPERTIES II
Understand and apply the relationship between multiplication by t
and the derivative of the Laplace transform 7.1;
Basic concept of a convolution of two funct
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: H
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 applicatio
PREVIEW
6.3: SPECIAL FUNCTIONS
Basic understanding of power series from Calculus II, and how to work
with such series (e.g. differentiation, shifting index of summation) (this
is from 6.1);
General
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 fo
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;
PREVIEW (same as on previous notes)
5.1: LINEAR MODELS: INITIAL-VALUE PROBLEMS
Setting up the model for a mass on a spring, and the form of the various forces that affect its motion;
Understand the
PREVIEW
7.4: OPERATIONAL PROPERTIES II
Finding the Laplace transform of a periodic function 7.1.
7.5: THE DIRAC DELTA FUNCTION
Basic concept of a unit impulse function and the Dirac delta function
MATH 2860U
Midterm examination
Page 2 of 6
1. (a) [3 marks] Find the integrating factor associated with the DE (but DO NOT solve
the DE!)
dy
( x + 1) + ( x + 2)y = 2xex
dx
ANS:
(b) [3 marks] Determine
PREVIEW
7.2: INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES
Finding the Laplace transform for a given initial value problem;
Solving the resulting algebraic equation once a differential equation
PREVIEW (same as on previous notes)
5.1: LINEAR MODELS: INITIAL-VALUE PROBLEMS
Setting up the model for a mass on a spring, and the form of the various forces that affect its motion;
Understand the
PREVIEW
4.1: LINEAR DIFFERENTIAL EQUATIONS: BASIC THEORY
What it means for a 2nd order equation to be linear; what it means to
be homogeneous 4.3;
Familiarity with operator notation 4.4, and how to
PREVIEW
12.1: SEPARABLE PARTIAL DIFFERENTIAL EQUATIONS
Familiarity with the vocabulary of partial differential equations: linear vs nonlinear, order of an equation, homogeneous vs nonhomogeneous;
U
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 fo
Academic Success Centre
[email protected]
http:/academicsuccess.uoit.ca
Solving Homogeneous Linear Systems using
Eigenvalues and Eigenvectors
What are the eigenvalues and eigenvectors?
If A i
PREVIEW
8.2: HOMOGENEOUS LINEAR SYSTEMS
Re-writing a higher-order differential equation as a system of 1st-order
differential equations (examples 1,2,3).
Finding eigenvalues and eigenvectors for a
PREVIEW
8.1: PRELIMINARY THEORY
How systems of differential equations arise in modelling various physical phenomena;
Writing a linear system in matrix notation 1;
The classification associated wit
B. Rouben
UOIT
ENGR-2500U
2016 Sept.-Dec.
Assignment 4
6 Problems [4 for marking], 31 marks total
Due Thursday October 6, 6 pm latest
Solutions
1. [Not for marking]
What is the atomic density in a mat
B. Rouben
UOIT
ENGR-2500U
2016 Sept.-Dec.
Assignment 2
Assigned 2016/09/15
5 Problems, of which 4 will be marked; 30 marks total
Due Thursday 2016/09/22, 6 pm latest
1. [8 marks; 2 for (a), 2 for (b),
B. Rouben
UOIT
ENGR-2500U
2016 Sept.-Dec.
Assignment 1
Assigned 2016/09/08
4 Problems, of which 3 will be marked, 30 marks total
Due Thursday 2016/09/15, 6 pm latest
1. [Will not be marked; you should
Tutorial worksheet 1 Part 1 (Total time 16 mins)
Chapter 01: INTRODUCTION TO DIFFERENTIAL EQUATIONS
Project the following questions on the screen
Go through the red colored questions one by one (4 in