Instructors Solutions Manual
PARTIAL DIFFERENTIAL
EQUATIONS
with FOURIER SERIES and
BOUNDARY VALUE PROBLEMS
Second Edition
H. ASMAR
NAKHLE
University of Missouri
Contents
Preface
Errata
1
v
vi
A Preview of Applications and Techniques
1
1.1 What Is a Part
Lectures on
Partial Differential Equations
By
G.B. Folland
Tata Institute of Fundamental Research
Bombay
1983
Lectures on
Partial Differential Equations
By
G.B. Folland
Lectures delivered at the
Indian Institute of Science, Bangalore
under the
T.I.F.R. I.
PARTIAL DIFFERENTIAL EQUATIONS
SERGIU KLAINERMAN
1. Basic definitions and examples
To start with partial differential equations, just like ordinary differential or integral
equations, are functional equations. That means that the unknown, or unknowns,
we
Ch 7.1: Introduction to Systems of First
Order Linear Equations
A system of simultaneous first order ordinary differential
equations has the general form
x1 = F1 (t , x1 , x2 , K xn )
x2 = F2 (t , x1 , x2 , K xn )
M
xn = Fn (t , x1 , x2 , K xn )
where eac
Problems and Solutions
for
Partial Differential Equations
by
WilliHans Steeb
International School for Scientific Computing
at
University of Johannesburg, South Africa
Yorick Hardy
Department of Mathematical Sciences
at
University of South Africa, South A
J. David Logan
Department of Mathematics
University of Nebraska Lincoln
Applied Partial Differential
Equations, 3rd ed.
Solutions to Selected
Exercises
February 14, 2015
SpringerVerlag
Berlin Heidelberg NewYork
London Paris Tokyo
Hong Kong Barcelona
Buda
Extended Solutions for Instructors
for the Book
An Introduction to Partial Differential Equations
Yehuda Pinchover and Jacob Rubinstein
1
Chapter 1
1.1 (a) Write ux = af 0 , uy = bf 0 . Therefore, a and b can be any constants such that
a + 3b = 0.
1.3 (a)
9
Numerical Solution of Partial Differential Equations
9.0
Classification of Partial Differential Equations
We now consider general secondorder partial differential equations (PDEs) of the form
Lu = autt + buxt + cuxx + f = 0,
(1)
where u is an unknown f
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 2: Coulombs Law,
Electric Force, and Electric
Field
August 16, 2016
Tuesday
Objectives
Calculate the net electric force on a point
charge exerted by a system of point
charges and arbitrary charge distribution
!
Determine the electric field due to a
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
August 26, 2016 (Friday)
TOPIC 6: APPLICATION OF GAUSS
LAW
OBJECTIVE
!
Use Gauss Law to calculate the electric field
generated at a point by highly symmetrical
charge distributions
SYMMETRY AND
GAUSSIAN SURFACE
SYMMETRY
There are three types of
applicable
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
August 24, 2016 (Wednesday)
TOPIC 5: ELECTRIC FLUX AND
"
GAUSS LAW
OBJECTIVES
Evaluate the electric flux through a surface
given the electric field
! Relate the electric flux thru a closed surface
to the total charge inside and outside the
surface
!
ELEC
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 1: Electric Charges,
Conductors, Insulators, and
Charge Induction
August 12, 2016
Friday
Objectives
Apply the dichotomy, quantization, and
conservation of charge
!
Given the initial/final charge distribution,
calculate the final/initial charge distr
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 3:
Electric Field Calculation by
Continuous Body
August 17, 2016
Wednesday
Objectives
Evaluate the electric field at a point in
space due to a system of arbitrary charge
distribution
Electric Field due to a
Continuous Charge Distribution
In the co
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
August 30, 2016 (Tuesday)
TOPIC 7: CONDUCTORS
OBJECTIVE
!
Predict the charge distribution induced on
the surface of a conductor in the presence of
a static charge and external electric field
ELECTROSTATIC EQUILIBRIUM
A redistribution of charges that cance
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 9: Electric Potential
September 2, 2016!
(Friday)
Objectives
Evaluate
the potential at any point in a
region containing point charges.!
Determine the electric potential
function at any point to continuous
charge distributions.
ELECTRIC POTENTIAL
E
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 10: Equipotential
Surface and Conductors
September 6, 2016!
(Tuesday)
Objectives
Given
the equipotential lines, evaluate
the electric field vectors, nature of the
electric field sources, and electrostatic
potential.!
Calculate the work done on a p
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 8:
Electric Potential Energy
August 31, 2016"
(Wednesday)
Objectives
Calculate
the potential energy of a
point charge in a uniform external
electric field"
Calculate the potential energy of a
system of point charges"
Calculate the minimum work n
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 4: Electric Field
Lines and Electric Dipoles
August 23, 2016
Tuesday
Objectives
Given the electric field lines, deduce the
electric field vectors and the nature of
electric field sources.
!
Determine the motion and/or the stability
of the electric d
Introduction to Assembly Language Programming and Digital Circuits
DCS CS 21

Spring 2015
Topic 11: Capacitors
September 7, 2016
(Wednesday)
Objectives
Deduce the effects on the capacitance, charge,
and potential difference on simple capacitors
(e.g. parallel  plate, spherical, cylindrical)
when geometry, potent
Computer Problem 7.6
CS 236
John Patrick S. Laanan
Problem
Interpolating the data points
Should give an approximation to the square root function
Question A: Compute the polynomial of degree
eight that interpolates these nine data points. Plot
the resul
Computer Problem 8.1
CS 236
John Patrick S. Laanan
Problem
Since
one can compute an approximate value for using numerical
integration of the given function.
* http:/www.integralcalculator.com/
a. Use the midpoint, trapezoid, and Simpson
composite quadr