ESAM 311-3 Problem Set 6
Due in class on Friday, May 22
Evaluate the following integrals using residues. Please make sure to give a reason for eliminating
the contribution from any large contour.
1.
R
ESAM 311-3 Problem Set 8
This homework will not be collected. However, a problem like this may appear on the final exam
for the course. These problems are taken directly from Chapter 10 problems on Te
ESAM 311-3 Problem Set 7
Due in class on Monday, June 1
Evaluate the following integrals using residues. Please make sure to give a reason for eliminating
the contribution from any large contour.
1.
R
ESAM 311-3 Problem Set 1
Read Chapter 1 of the text and do the following problems.
Note: Solutions must be neatly written and your arguments and the steps of your calculations must be easy for
the gra
ESAM 311-3 Problem Set 2
Read Chapters 2 and 3 of the text and do the following problems.
Note: Solutions must be neatly written and your arguments and the steps of your calculations must be easy for
ESAM 311-3 Problem Set 5
Due in class Friday, May 15.
Read Chapters 6 of the text and do the following problems.
Note: Solutions must be neatly written and your arguments and the steps of your calcula
ESAM 311-3 Problem Set 4
Due in class Friday, May 8.
Read Chapters 5 of the text and do the following problems.
Note: Solutions must be neatly written and your arguments and the steps of your calculat
ESAM 311-3 Problem Set 3
Due in class Friday, April 24.
Read Chapter 4 of the text and do the following problems.
1. a) Each of the following equations describes an arc in the complex plane for 0 t 1.
ES_APPM 322 Homework 4 Solutions
1. Classification of Fixed Points
Identify the type of fixed point and sketch the phase portrait for linear system x = Lx for the 3 cases
1 2
0
2
1
2
L1 =
L2 =
L3 =
1
322 Applied Dynamical Systems
Syllabus
Class Information
Lectures are TuTh 3:30-5 in M416 (applied math conference room)
Professor: Hermann Riecke, Office Tech M458, [email protected]
TA: C
Applied Nonlinear Dynamics 322
Spring 2016
Hermann Riecke
Problem Set 4
Thursday, April 21, 2016
due Thursday, April 28, 2016
1. Classification of Fixed Points
Identify the type of fixed point and ske
Applied Nonlinear Dynamics 322
Spring 2016
Hermann Riecke
Problem Set 1
Thursday, March 31, 2016
due Thursday, April 7, 2016
The numbered problems are taken from Nonlinear Dynamics and Chaos by S.H. S
Applied Dynamical Systems
Midterm, May 6, 2014
Name:
Spring 2014
Riecke
Score
Instructions:
1. Print your name on this page in the space provided.
2. If you need extra space, use the back of a page
an
Applied Nonlinear Dynamics 322
Spring 2016
Hermann Riecke
Problem Set 5
Friday, April 29, 2016
due Tuesday, May 10, 2016
1. Poincare-Bendixson Theorem
Consider the dynamical system
x = y + x3 x x2 + y
Applied Nonlinear Dynamics 322
Spring 2016
Hermann Riecke
Problem Set 2
Thursday, April 7, 2016
due Thursday, April 14, 2016
1. Vector Fields and Bifurcations
For each of the following dynamical syste
Applied Nonlinear Dynamics 322
Spring 2016
Hermann Riecke
Problem Set 3
Thursday, April 14, 2016
due Thursday, April 21, 2016
1. Scaling at SNIC
Consider the following dynamical system on a circle
d
=
Some additional plots for Problem 3, illustrating the dynamics:
Problem 2
(a)
The plots of V and w are for initial conditions at (0, 0).
Different initial conditions converge to the invariant circle.
Chapter 1
Introduction to spectral theory
1.1
An ODE problem
Before dealing with partial differential equations, lets revisit ordinary differential equations, e.g.,
d xE
D AxE
dt
with x.0/
E
D xE0 :
(
Chapter 3
Greens Functions and Distribution theory
3.1
Introduction to the Greens function method for solving ODEs1
Consider the 1-D wave equation for a stretched string with harmonic forcing
't t
c 2
Chapter 6
Regular and singular boundary value problems
Now that weve learned how to use the Greens function to derive eigenfunction expansions and
transforms associated with boundary value problems, i
Chapter 2
The basic differential equations
Before delving into solution methods, its worth motivating things a bit. We do this by considering
some partial differential equations that come up in variou
Chapter 4
Inner Products and Adjoints
4.1
Eigenfunction Expansions
The next thing we need to do is better understand the expansions of the type,
f .x/ D
1
X
fn sin.nx/ ;
nD1
fn D
2
f ./ sin.n/ d ;
0
a
Chapter 5
Spectral Theory of 2nd-order Differential Operators1
5.1
The Greens function method
Recall that one way of looking at an eigenvalue problem for an operator L is to consider the forced
proble
411-1 Final Exam Solutions
1. Consider the half-plane problem
r 2 g D .x x0 / .y y0 / for
y; y0 > 0 and
1 < x; x0 < 1 ;
with gy D 0 on y D 0. In how many ways can this problem be solved using transfor
411-1 Homework 3
1. What is .x 2
2. What is
a2 / equal to in the sense of distributions?
d
H.x 2
dx
3. Solve x 2
a2 / equal to in the sense of distributions?
du
D 0 in the sense of distributions.
dx
411-1 Homework 2
1. The goal of this problem is to develop a general way to determine the specific form of the
Laplacian in different coordinate systems. [Note: you only have to do the parts (a)-(g);
411-1 Homework 4
1. By modifying the method used in class (or using some other way, such as the one outlined
on page 119 of Stakgold), show that
Z 1
sin kx
lim
f .x/ dx D f .0/:
k!1
x
1
Solution: Here
411-1 Homework 1
1. If z D x C iy, D C i and 2 D z, determine and in terms of x and y. (Hint: first eliminate
to find a quadratic equation for 2 in terms of x and y.) This gives a way to calculate co
Fall 2015
ESAM 441-1 PS2
1. The goal of this problem is to develop a general way to determine the specific form of the
Laplacian in different coordinate systems. [Note: you only have to do the parts (
411-1 Homework 5
1. Use two different spectral representations to find the solution of Laplaces equation for
'.x; y/ in the rectangular region 0 < x < 1, 0 < y < b, with the boundary conditions '.x; 0