MA205 Final Exam Information (Intersession 2014)
1. The nal exam will be on June 19, Thursday during 12:00noon - 2:30pm
at BA102.
2. No more regular oce hours. New oce hours are June 17, Tuesday,
10:00-12:00noon.
3. It is a closed book exam.
4. The exam i
MA205 Lab 6 Report - Series Solutions of Dierential Equations
Name:
Student Number:
Lab
Fall 2013
1. [9 marks] Consider the Van der Pol Equation:
y +
1
y 2 1 y + y = 0 with initial values y(0) = 1, y (0) = 0
10
The Van der Pol equation has applications in
MA205 Lab 3 Report - Linear Dierential Equations - Part 1
Name:
Student Number:
Lab
Fall 2013
1. [6 marks] Find the general solution to each of the following linear homogeneous dierential equations with
constant coecients.
(a) 4
d2 y
16y = 0
dx2
Solving
MA205 Lab 1 Report - Introduction to Dierential Equations
Name:
Student Number:
1. [6 marks] For each of the following:
Lab
Fall 2013
i) State the independent and dependent variables.
ii) Determine a dierential equation modelling the situation.
iii) State
MA205 Lab 2 Report - First Order Dierential Equations
Name:
Student Number:
Lab
Fall 2013
1. [3 marks] Indicate (by circling) whether each of the following dierential equations is separable, linear, exact,
or a combination of the three. Extra space is pro
MA205 Lab Report 3 Prep
Second Order Linear Dierential Equations with Constant Coecients
1. Substitution:
See the lab prep for the previous lab report. In particutlar, look at the Bernoulli stu.
2. Homogeneous Dierential Equations with Constant Coe:
d2 y
MA170 Week 12 Report - Bonds
Name:
Student Number:
Lab:
Winter 2013
1. [15 marks] A 1-year $15000 bond is redeemable at par and pays quarterly coupons at j4 = 6%:
(a) If the bond is priced to yield a rate of j4 = 8%; without any calculations, explain whet
MA170 Week 11 Report - Sinking Funds; Bonds
Name:
Student Number:
Lab:
Winter 2013
1. [5 marks] A sinking fund that earns interest at a rate of j2 = 13:5% is created so that the Mathematics
Department can purchase $60000 of computer equipment in 1.5 years
MA170 Week 10 Report - Amortized Loans
Name:
Student Number:
Lab:
Winter 2013
1. [11 marks] Ben purchases a car for $36000. The car dealerships offers Ben nancing with an interest rate of
j26 = 3:25% over a 6 year period which they say results in bi-weekl
MA205 Lab 5 Report - Laplace Transforms
Name:
Student Number:
Lab
Fall 2013
1. [11 marks] Consider the following hyperbolic functions:
sinh(t) =
et et
,
2
cosh(t) =
et + et
2
Use Tables 7.1 and 7.2 in the text to determine the Laplace transform of each of
MA205 Lab 1 Report - Introduction to Dierential Equations
Name:
Student Number:
1. [6 marks] For each of the following:
Lab
Fall 2014
i) State the independent and dependent variables.
ii) Determine a dierential equation modelling the situation.
iii) State
MA205 Lab 2 Report - First Order Dierential Equations
Name:
Student Number:
Lab
Fall 2014
1. [4 marks] Indicate (by circling) whether each of the following dierential equations is separable, linear, exact,
or a combination of the three. Extra space is pro
MA205 Lab 1 Report - Introduction to Dierential Equations
Name:
Student Number:
1. [9 marks] For each of the following:
Lab
Winter 2015
i) State the independent and dependent variables.
ii) Determine a dierential equation modelling the situation.
iii) Sta
MA205 Lab 3 Report - Linear Dierential Equations - Part 1
Name:
Student Number:
Lab
Fall 2012
1. [9 marks] Find the general solution to each of the following linear homogeneous dierential equations with
constant coecients.
(a)
d2 y
dy
4
+ 8y = 0
2
dx
dx
S
MA205 Lab 2 Report - First Order Dierential Equations
Name:
Student Number:
Lab
Fall 2012
1. [3 marks] Indicate (by circling) whether each of the following dierential equations is separable, linear, exact,
or a combination of the three. Extra space is pro
MA205 Lab 1 Report - Introduction to Dierential Equations
Name:
Student Number:
1. [6 marks] For each of the following:
Lab
Fall 2012
i) State the independent and dependent variables.
ii) Determine a dierential equation modelling the situation.
iii) State
MA205 Lab 4 Report - Linear Dierential Equations - Part 2
Name:
Student Number:
Lab
Fall 2014
1. [3 marks] State the general form of a particular solution (do not solve for the particular solution) to
y + 3y y = g(t) when:
(a) g(t) = 3t2 e2t .
Solving Aux
MA205 Lab 6 Report - Series Solutions of Dierential Equations
Name:
Student Number:
Lab
Fall 2014
1. [5 marks] Consider the initial value problem
y = y + x2 , y(0) = 1.
Determine the rst 5 non-zero terms in the Taylor series that approximates the solution
MA205 Lab 5 Report - Laplace Transforms
Name:
Student Number:
Lab
Fall 2014
1. [4 marks] Use the Denition 1 (on page 353 of the text of in the lab prep) to nd the Laplace Transform of:
1 t,
0,
f (t) =
1
L cfw_f (t) (s)
(1 t)e
=
st
dt +
0
=
=
1 st
(1 t)
e
MA205 Lab 3 Report - Linear Dierential Equations - Part 1
Name:
Student Number:
Lab
Fall 2014
1. [10 marks] The Logistic Growth Model is a dierential equation that models population growth:
L (t) = (a rL(t)L(t)
Where a and r are constants.
1
1
and r =
, e
MA170 Week 10 Report - Amortized Loans
Name:
Student Number:
Lab:
Winter 2013
1. [11 marks] Ben purchases a car for $36000. The car dealerships offers Ben nancing with an interest rate of
j26 = 3:25% over a 6 year period which they say results in bi-weekl
MA170 Week 9 Report - General Annuities
Name:
Student Number:
Lab:
Winter 2013
1. [5 marks] Recall Question #3, Week 7, where a couple was saving for their daughter's education by investing
in a fund earning interest at j2 = 4% for 19 years. Suppose that
MA170 Week 7 Report - Annuities
Name:
Student Number:
Lab:
Winter 2013
1. [3 marks] Celina purchases land in Costa Rica for $200 000. She puts $50000 down and pays the balance with
quarterly payments (starting 3 months from now) for 15 years. If interest
MA205 Lab Report 2 First Order Differential Equations
Name:
Student Number:
Intersession 2013
1. [6 marks] For each of the following differential equations, use the with(DEtools): package and the
odeadvisor(.); and dsolve(.); commands (substituting approp
MA205 Lab Report 2 Notes
Linear Ordinary Differential Equations:
General Form: an (x)
dn y
+ an
dxn
1 (x)
dn 1 y
dy
+ : + a1 (x)
+ a0 (x)y = g(x)
n 1
dx
dx
Has Order n with independent variable x and dependent variable y
Note: Our goal in this course is t
MA205 Lab 4 Report - Linear Differential Equations - Part 2
Name:
Student Number:
Lab
Fall 2014
1. [3 marks] State the general form of a particular solution (do not solve for the particular solution) to
y 00 + 3y 0 y = g(t) when:
(a) g(t) = 3t2 e2t .
(b)
MA205 Lab 2 - First Order Differential Equations
Name:
Student Number:
Winter 2017
1. [3 marks] Indicate (by circling) whether each of the following differential equations is separable, linear, exact or
none of these. (If you believe it is None, simply do
Lihan Wang
Assignment Homework Assignment 2 W17 due 01/23/2017 at 11:59pm EST
(x + 4)y)0 = x1 + 4x2 .
Integration on both sides now yields
1. (1 pt) Solve the separable differential equation
p
dy
10x 3y x2 + 1 = 0
dx
subject to the initial condition: y(0)
Lihan Wang
Assignment MA205W17 Assignment1 due 01/09/2017 at 11:59pm EST
MA205 W17
Linear
1. (1 pt) Determine the order of the given differential equation and state whether the equation is linear or nonlinear.
s
2
d2y
dy
=
5
+
2
dx
dx
(correct)
Correct
MA205 Lab Notes
Text References: 4.2 - 4.4, 6.2
Homogeneous Differential Equations with Constant Coeff (4.2, 4.3, 6.2)
dy
d2 y
For DEs of the form: a 2 + b
+ cy = 0
where a, b,and c are constants
dx
dx
To find the general solution y(x):
Determine the roo