Part I
Circle what you think is the correct answer. +3 for a correct answer, 1 for a wrong answer, 0 for no
answer.
1. The ODE y | y = ace3, has the solution, , w H . 7 . , .
(a) C + $302 (b) C + a:2
MATH 256 Midterm 2 March 20, 2014.
Last name:
First name:
I attend the tutorial in room:
Student #:
MATH 105
MATH 203 (circle one)
Place a box around each answer so that it is clearly identified. Poin
Math 256 Midterm 2
University of British Columbia
March 24, 2015, 2:00 pm to 3:20 pm
Last name (print):
First name:
ID number:
This exam is closed book with the exception of a single 8.5x11 formula sh
MATH 256 Midterm 2 March 20, 2014.
Last name:
First name:
I attend the tutorial in room:
Student #:
MATH 105
MATH 203 (circle one)
Place a box around each answer so that it is clearly identified. Poin
MATH 256 Midterm 2 March 15, 2016.
Last name:
First name:
Student #:
Tutorial (circle one): T2A - Cole, T2B - Shirin, T2C - Dhananjay, T2D - Xiaoyu, T2E - Catherine, T2F - Will
Place a box around each
Math 256 Midterm #1 February 7, 2013
Name: Student number:
Open Book Section
Prob. l. (16mg) m
Consider the nonhomogeneous ODE
dZy/dtz * y = an?
(i) Find the two fundamental solutions to the homogeneo
. tudent no. in ink Section Instructor Name PRINT in ink
5,. 0L u T! o A) 5
MATH 256
Midterm Test 1
2015 October 7
Time: 50 minutes. This is a closed book examination: no books, notes, electronic calc
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 256, Section 103
Midterm Exam I October 3, 2014
Name
Signature
Student Number
This exam consists of 4 question
MATH 256 Midterm 1 February 2, 2016.
Last name:
Solution/marking key First name:
Student #:
Place a box around each answer so that it is clearly identified. Point values are approximate and may
differ
MATH 256 Midterm 1 February 2, 2016.
Last name:
First name:
Student #:
Place a box around each answer so that it is clearly identified. Point values are approximate and may
differ slightly in the fina
Example Problems Math 256 Midterm #1
Closed Book Section
_
Sample problems from 2011 Midterm
Note: In some of the problems, = d/dt
Prob. 1. (3 pts.) Here is a second order differential equation:
MATH 256 Midterm 1 February 6, 2014.
Last name:
First name:
Student #:
Place a box around each answer so that it is clearly identified. Point values are approximate and may
differ slightly in the fina
Chapter 10: Partial differential equations and Fourier series
Heat equation: Let u(x, t) be the temperature in a thin heatconducting bar of length L (where x is position and t is time).
2
u u
=
.
x2
t
MATH 256 Midterm 2 March 15, 2016.
Last name: First name: Student #:
Tutorial [circle one]: TEA - Cole, T2B - Shirin, T2C - Dhananjay, T2D - Xiaoy'u1 T2E - Catherine, T2F - Will
Place a box around eac
1
Numerical/Graphical Methods
The definition of a derivative:
y(x + ) y(x)
dy
= Lim0
dx
But from the ODE we also know that dy/dx = F (x, y). Hence, taking a small but finite value of we
arrive at the
Periodic functions and boundary conditions
A function is periodic, with period T , if it repeats itself exactly after an interval of length T . i.e. y(x) = y(x+
T ) for any x. Evidently, the derivativ
Math 256. Sample final questions.
No formula sheet, books or calculators!
Part I
Circle what you think is the correct answer. +3 for a correct answer, 1 for a wrong answer, 0 for no answer.
1. The ODE
PDEs
For a function, u(x, t), of two variables, x and t, the general form of a PDE is
F (x, t, u, ux , ut , uxx , uxt , utt , .) = 0
for some function F , where
ux =
u
,
x
ut =
u
,
t
uxx =
2u
,
x2
utt
Math 256. Midterm 2.
No formula sheet, books or calculators! Include this exam sheet with your answer booklet!
Name:
Part I
Circle what you think is the correct answer. +3 for a correct answer, 1 for
ODEs: one seeks a function of a single variable (e.g. y(x) that satisfies a differential equation a given
relation between the function and its derivatives (y, y 0 , y 00 , .).
PDEs: one seeks a funct
1
The inhomogeneous problem
Recall the ODE:
ay 00 + by 0 + cy = f (x)
with constants a, b and c, and f (x) a prescribed function.
An example: y 00 + y = ex . Notice that if y ex , then all three terms
1
Laplace transforms
The Laplace transform is defined by the integral
Z
Lcfw_y(t) =
est y(t)dt = y(s)
0
Within the integral a new variable s appears. Thus the transform is a function of s; we add the
1
Homogeneous systems of ODEs
We now deal with the system of first-order equations,
d
x = Ax,
dt
where x(t) is a (column) vector of length n and A is an n n matrix.
Practically, we will consider A to
Student no. (in ink)
Section/Instructor
Name (PRINT in ink)
MATH 256
Midterm Test 2
2015 November 13
This test consists of six pages (pages 2, 4, 6 are blank). A table of Laplace transforms
is on page
The Trace-Determinant Plane
An efficient way to classify first-order linear systems of the form
d~
a b
~
Y = AY
A=
c d
dt
where A is a 2 2 real-valued matrix is to locate the system on the Trace-Deter