EIGRP
Routing Protocols and
Concepts Chapter 9
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
Describe the background and history of Enhanced
Interior Gateway Routing Protocol (EIGRP).
Examine the basic EIGRP configur
OSPF
Routing Protocols and
Concepts Chapter 11
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
2
Introduction to OSPF
Background of OSPF
Began in 1987
1989
The Routing Table: A
Closer Look
Routing Protocols and
Concepts Chapter 8
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
Describe the various route types found in the routing
table structure.
Describe the routing ta
Introduction to Routing
and Packet Forwarding
Routing Protocols and
Concepts Chapter 1
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
Identify a router as a computer with an OS and
hardware designed for the routing pr
VLSM and CIDR
Routing Protocols and
Concepts Chapter 6
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
Compare and contrast classful and classless IP
addressing.
Review VLSM and explain the benefits of classless IP
add
Link-State Routing
Protocols
Routing Protocols and
Concepts Chapter 10
Version 4.0
2007 Cisco Systems, Inc. All rights reserved.
Cisco Public
1
Objectives
Describe the basic features & concepts of link-state
routing protocols.
List the benefits and requi
Appendix A
Solutions to selected exercises
Exercise 1.2: This exercise derives the probability of an arbitrary (non-disjoint) union of events, derives
the union bound, and derives some useful limit expressions.
a) For 2 arbitrary events A1 and A2 , show t
Numerical Analysis
2015 Fall
Linear Regression
Model Function Example
Air resistance
FU cd v
2
F ma
Newtons 2nd raw
FD mg
Regression
Statistic Measure of Location
Arithmetic mean: the sum of the individual
data points (yi) divided by the number of
points
Numerical Analysis
2015 Fall
Summary of the class
Part 1
Mathematical Model
Numerical Methods
Roundoff Errors
Truncation Errors
Part 2
Roots and Optimization
Bracketing Methods: Bisection
Open Methods: Newton-Rapthson,
Secant, Brents
Optimization:
Numerical Analysis
2015 Fall
Linear Least Squares
Linear Least-Squares
Regression
Linear least-squares regression is a method to
determine the best coefficients in a linear model for
given data set.
Best for least-squares regression means
minimizing the
Numerical Analysis
2015 Fall
Gauss Elimination
Solving systems
k1 k 2
k
2
0
k2
k3 k 2
k3
0 x1 m1 g
k3 x2 m2 g
k3 x3 m3 g
Graphical Method
For small sets of simultaneous equations, graphing
them and determining the location of the intercept
provid
Numerical Analysis
2015 Fall
Adaptive Methods and Stiff Systems
Runge-Kutta Methods
Runge-Kutta (RK) methods achieve the accuracy of a
Taylor series approach without requiring the calculation
of higher derivatives.
For RK methods, the increment function
Numerical Analysis
2015 Fall
Numerical Differentiation
Differentiation
The mathematical definition of a derivative
begins with a difference approximation:
y f xi x f xi
x
x
and as x is allowed to approach zero, the
difference becomes a derivative:
f xi
Numerical Analysis
2015 Fall
Numerical Integration
Method1
Newton-Cotes Formulas
The Newton-Cotes formulas are the most
common numerical integration schemes.
Generally, they are based on replacing a
complicated function or tabulated data with a
polynomi
Numerical Analysis
2015 Fall
Roots: Open Methods
Open Methods
Open methods differ from bracketing methods,
in that they require only a single starting value
or two starting values that do not necessarily
bracket a root.
Open methods may diverge as the
c
Numerical Analysis
2015 Fall
Eigenvalues
Example
Newtons 2nd raw
F ma
Dynamics of Three Coupled
Bungee Jumpers in Time
Is there an underlying pattern?
Mathematics
Up until now, heterogeneous systems:
[A] cfw_x = cfw_b Outside of the system.
What about hom
Numerical Analysis
2015 Fall
Polynomial Interpolation
Curve Fitting
Polynomial Interpolation
You will frequently have occasions to estimate
intermediate values between precise data points.
The function you use to interpolate must pass
through the actual
Numerical Analysis
2015 Fall
Optimization
Optimization
Optimization is the process of creating
something that is as effective as possible.
From a mathematical perspective,
optimization deals with finding the maxima
and minima of a function that depends
Numerical Analysis
2015 Fall
Initial-Value Problems
Model Function
dv
cd 2
g v
dt
m
Analytical solution
vt
gc
gm
d
tanh
t
cd
m
Numerical solution
cd
2
vti 1 vti g vti (ti 1 ti )
m
Ordinary Differential Equations
Methods described here are for sol
Numerical Analysis
2015 Fall
Roots: Bracketing
Roots
Roots problems occur when some function
f can be written in terms of one or more
dependent variables x, where the solutions to
f(x)=0 yields the solution to the problem.
These problems often occur whe
Numerical Analysis
2015 Fall
Linear Algebra
Example
Newtons 2nd raw
F ma
Example
In steady state
Example
k1 k 2
k
2
0
k2
k3 k 2
k3
0 x1 m1 g
k3 x2 m2 g
k3 x3 m3 g
Rank of the matrix ?
Overview
A matrix consists of a rectangular array
of elements
Numerical Analysis
2015 Fall
Numerical Integration
Integration
Integration:
I
f x dx
b
a
is the total value, or summation, of f(x) dx over the
range from a to b:
Integration
Newton-Cotes Formulas
The Newton-Cotes formulas are the most
common numerical
Numerical Analysis
2015 Fall
Fourier Analysis
Additional Clarifications
Solving General Linear Least
Squares Coefficients
The equation:
y a0 z0 a1z1 a2 z2 am zm e
can be re-written for each data point as a matrix
equation:
y Z a e
where cfw_y contains th
Numerical Analysis
2015 Fall
LU Factorization
LU Factorization
Recall that the forward-elimination step of
Gauss elimination comprises the bulk of the
computational effort.
LU factorization methods separate the timeconsuming elimination of the matrix [A
Numerical Analysis
2015 Fall
Chapter 11 & 12
Matrix Inverse
Recall that if a matrix [A] is square, there is
another matrix [A]-1, called the inverse of
[A], for which [A][A]-1=[A]-1[A]=[I]
The inverse can be computed in a column by
column fashion by gen
Numerical Analysis
2015 Fall
Splines
Fitting vs Interpolation
Superresolution
Oscillations
Introduction to Splines
An alternative approach to using a single
(n-1)th order polynomial to interpolate
between n points is to apply lower-order
polynomials in a
ECE440 - Midterm Review Notes
Probability review
You should be fluent with notions such as probability spaces, the axioms of probability and
their consequences, law of total probability and Bayes rule, discrete and continuous random
variables (RVs), expec
ECE440 - Introduction to Random Processes
Midterm Exam
November 5, 2014
Instructions:
This is an open book, open notes exam.
Calculators are not needed; laptops, tablets and cell-phones are not allowed.
Perfect score: 100 (out of 104, extra points are
ECE440 - Introduction to Random Processes
Midterm Exam
October 9, 2014
Instructions:
This is an open book, open notes exam.
Calculators are not needed; laptops, tablets and cell-phones are not allowed.
Perfect score: 100.
Duration: 75 minutes.
This e