Ulsan National Institute of Science and Technology
statistics
MATH 211

Fall 2012
Syllabus
Course Information
Instructor Information
Course Code
Course Title
MTH 21103, MTH 21104
Statistics
Instructor
Office
Dougu Nam
EB4 6017
Year/Semester
School
2017/Spring
Life Sciences
Telepho
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks (20162)
Homework #1 (Chapter 1)
Assigned: 9/6 Tue
Due: 9/13 Tue, 5pm
Directions:
Submit your homework to TA @ 4031, Bldg. 106, until 5pm. No late
submission. Ea
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks (20162)
Homework #4 (Chapter 4)
Assigned: 11/03 Thu
Due: 11/10 Thu, 5pm
Directions:
Submit your homework to TA @ 4031, Bldg. 106, until 5pm. No late submission.
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks
Homework #4 solutions
Assignments (7 problems):
HW#41
Problem 6 (p. 369)
HW#42
Problem 7 (p. 369)
Direction: Assume that frame transmission time is d, and
there
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks
Homework #2 solutions
Assignments (5 problems):
HW#21
Problem 7 (p. 208)
HW#22
Problem 10 (p. 208)
HW#23
Problem 11 (p. 208)
HW#24
Problem 18 (p. 208)
HW#25
P
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks (20162)
Homework #5 (Chapter 5)
Assigned: 11/29 Tue
Due: 12/6 Tue, 5pm
Directions:
Submit your homework to TA @ 4031, Bldg. 106, until 5pm. No late submission.
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks (20162)
Exercises #2 (Chapter 6)
EX#21
Problem 8 (p. 625)
EX#22
Problem 17 (p. 626)
EX#23
Problem 25 (p. 626)
EX#24
Problem 28 (p. 626)
EX#21. Allocation for
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks
Homework #3 solutions
Assignments (5 problems):
HW#31
Problem 1 (p. 271)
HW#32
Problem 2 (p. 272)
HW#33
Problem 14 (p. 272)
HW#34
A channel has a bit rate of 4
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks (20162)
Exercises #1 (Chapter 4, ALOHA)
EX#11
Problem 2 (p. 369)
EX#12
Problem 3 (p. 369)
EX#13
Problem 4(a)(b) (p. 369)
EX#11. Pure ALOHA achieves the maximu
Ulsan National Institute of Science and Technology
Data Networks
MATH 314

Spring 2017
ECE314 Introduction to Data Networks
Homework #1 solutions
Assignments (5 problems):
HW#11
Problem 5 (p. 106)
Hint #1. Assume that the speed of signal is the same as the speed of
light, 300,000 km/s.
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 7.4: Basic Theory of Systems of First Order Linear
Equations
The general theory of a system of n first order linear equations
x1! = p11 (t ) x1 + p12 (t ) x2 + + p1n (t ) xn + g1 (t )
x2! = p21 (t
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 7.6: Complex Eigenvalues
!
We consider again a homogeneous system of n first order
linear equations with constant, real coefficients,
x1! = a11 x1 + a12 x2 + + a1n xn
x2! = a21 x1 + a22 x2 + + a2
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 7.8: Repeated Eigenvalues
!
We consider again a homogeneous system of n first order
linear equations with constant real coefficients x' = Ax.
If the eigenvalues r1, rn of A are real and different
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 10.1:TwoPoint Boundary Value Problems
In many important physical problems there are two or more
independent variables, so the corresponding mathematical
models involve partial differential equati
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 9 : Nonlinear Differential Equations and
Stability
Ch 9.1: The Phase Plane: Linear Systems
There are many differential equations, especially nonlinear
ones, that are not susceptible to analytical
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 9.3: Almost Linear Systems
In Section 9.1 we gave an informal description of the stability
properties of the equilibrium solution x = 0 of the 2 x 2 system
x' = Ax. The results are summarized in T
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 10.4: Even and Odd Functions
Before looking at further examples of Fourier series it is useful
to distinguish two classes of functions for which the EulerFourier formulas for the coefficients can
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
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 , xn )
x2! = F2 (t , x1
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 6.2: Solution of Initial Value Problems
The Laplace transform is named for the French mathematician
Laplace, who studied this transform in 1782.
The techniques described in this chapter were deve
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 5.4: Euler Equations; Regular Singular Points
Recall that the point x0 is an ordinary point of the equation
d2y
dy
P( x) 2 + Q( x) + R( x) y = 0
dx
dx
if p(x) = Q(x)/P(x) and q(x)= R(x)/P(x) are a
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 2.4: Differences Between Linear and Nonlinear Equations
Recall that a first order ODE has the form y' = f (t, y), and is
linear if f is linear in y, and nonlinear if f is nonlinear in y.
Examples
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 5.2: Series Solutions Near an Ordinary Point, Part I
!
!
In Chapter 3, we examined methods of solving second order
linear differential equations with constant coefficients.
We now consider the ca
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 3.2: Fundamental Solutions of Linear Homogeneous
Equations
Let p, q be continuous functions on an interval I = (, ),
which could be infinite. For any function y that is twice
differentiable on I,
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 1.1: Basic Mathematical Models;
Direction Fields
Differential equations are equations containing derivatives.
Ex>
Motion of fluids
Motion of mechanical systems
Flow of current in electrical circ
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 3.4: Repeated Roots; Reduction of Order!
!
Recall our 2nd order linear homogeneous ODE
ay! + by! + cy = 0
where a, b and c are constants.
Assuming an exponential soln leads to characteristic equ
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 2.9: First Order Difference Equations
!
!
Although a continuous model leading to a differential equation
is reasonable and attractive for many problems, there are some
cases in which a discrete mo
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 4.3: Nonhomogeneous Equations: Method of
Undetermined Coefficients
The method of undetermined coefficients can be used to
find a particular solution Y of an nth order linear, constant
coefficient,
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 4.1: Higher Order Linear ODEs: General
Theory!
!
An nth order ODE has the general form
dny
d n1 y
dy
P0 (t ) n + P1 (t ) n1 + ! + Pn1 (t ) + Pn (t ) y = G(t )
dt
dt
dt
We assume that P0, Pn, and
Ulsan National Institute of Science and Technology
Differential Equations
MATH 101

Spring 2017
Ch 2.6: Exact Equations and Integrating Factors
Consider a first order ODE of the form
M ( x, y ) + N ( x, y ) y = 0
Suppose there is a function such that
x ( x, y ) = M ( x, y ), y ( x, y ) = N (