Motivating Examples
Compatible Systems and Charpits Method
Charpits Method
Some Special Types of First-Order PDEs
MA 201: Partial Differential Equations
Lecture - 5
IIT Guwahati
MA201(2016):PDE
Motivating Examples
Compatible Systems and Charpits Method
Ch
MA 201: Second Order Linear PDE
Canonical Transformation
Lecture - 6
MA201(2016):PDE
A second order PDE with two independent variables x and y is
given by
F (x, y , u, ux , uy , uxy , uxx , uyy ) = 0.
(1)
What is the linear form?
The unknown function u(
Quasi-linear First-Order PDEs
Formation of quasi-linear First-Order PDEs
General solution quasi-linear First-Order PDEs
The method of Lagrange
Solving a Cauchy Problem
MA 201: Partial Differential Equations
Lecture - 3
IIT Guwahati
MA201(2016):PDE
Quasi-l
Surfaces orthogonal to a given system of surfaces
Nonlinear First-Order PDEs
Solving Cauchys problem for nonlinear PDEs
MA 201: Partial Differential Equations
Lecture - 4
IIT Guwahati
MA201(2016):PDE
Surfaces orthogonal to a given system of surfaces
Nonli
MA 201: Convergence of Fourier Series
Lecture - 9
MA201(2016):PDE
Convergence of Fourier Series for Periodic Functions
Example
Recall that Fourier Series of the function f (x) = x for L x L is
given by
2L X
1
nx
(1)n+1 sin
.
n=1
n
L
Observe that value o
MA 201: Finite Vibrating string Problem
Introduction to Fourier Series
Lecture - 8
MA201(2016):PDE
IBVP for Vibrating string with no external forces
We consider the problem in a computational domain
(x, t) [0, L] [0, )
The IBVP under consideration consi
MA 101 (Mathematics I)
Sequence : Summary of Lectures
A sequence of real numbers or a sequence in R is a mapping f : N R.
Notation: We write xn for f (n), n N and so the notation for a sequence is (xn ).
Examples:
1. Constant sequence: (a, a, a, .), where
Riemann Integral: Motivation
Riemann Integral: Motivation
Partition of [a, b]: A nite set cfw_x0 , x1 , ., xn [a, b] such that
a = x0 < x1 < < xn = b.
Riemann Integral: Motivation
Partition of [a, b]: A nite set cfw_x0 , x1 , ., xn [a, b] such that
a =
An innite series in R is an expression
n=1
where (xn ) is a sequence in R.
xn ,
An innite series in R is an expression
xn ,
n=1
where (xn ) is a sequence in R.
More formally, it is an ordered pair (xn ), (sn ),
where (xn ) is a sequence in R,
and sn = x1
A sequence of real numbers or a sequence in R
is a mapping f : N R.
A sequence of real numbers or a sequence in R
is a mapping f : N R.
Notation: We write xn for f (n), n N
and so the notation for a sequence is (xn ).
A sequence of real numbers or a seque
Differentiability and Derivative: Let D R and let x0 D such
that there exists an interval I of R satisfying x0 I D.
Differentiability and Derivative: Let D R and let x0 D such
that there exists an interval I of R satisfying x0 I D.
A function f : D R is s
MA 101 (Mathematics - I)
Innite Series : Summary of Lectures
An innite series in R is an expression
xn , where (xn ) is a sequence in R.
n=1
More formally, it is an ordered pair (xn ), (sn ), where (xn ) is a sequence in R and
sn = x1 + + xn for all n N.
MA 101 (Mathematics I)
Integration : Summary of Lectures
Riemann Integral: Motivation
Partition of [a, b]: A nite set cfw_x0 , x1 , ., xn [a, b] such that a = x0 < x1 < < xn = b.
Upper sum & Lower sum: Let f : [a, b] R be bounded. For a partition P = cfw
Denition: Let D(= ) R and let f : D R.
Denition: Let D(= ) R and let f : D R.
We say that f is continuous at x0 D if for each > 0, there
exists > 0 such that |f (x) f (x0 )| < for all x D satisfying
|x x0 | < .
Denition: Let D(= ) R and let f : D R.
We sa
MA 101 (Mathematics I)
Dierentiation : Summary of Lectures
Dierentiability and Derivative: Let D R and let x0 D such that there exists
an interval I of R satisfying x0 I D.
(x
A function f : D R is said to be dierentiable at x0 if lim f (x)f 0 0 ) (or equ
Chapter 24
Logistic Regression
Content list
Purpose of logistic regression
Assumptions of logistic regression
The logistic regression equation
Interpreting log odds and odds ratio
Model t and likelihood function
SPSS activity a logistic regression analysi
Logistic Regression
Chapter 8
Aims
When and Why do we Use Logistic
Regression?
Binary
Multinomial
Theory Behind Logistic Regression
Assessing the Model
Assessing predictors
Things that can go Wrong
Interpreting Logistic Regression
Slide 2
When And
Getting Started in
Linear Regression using R
(with some examples in Stata)
(ver. 0.1-Draft)
Oscar Torres-Reyna
Data Consultant
otorres@princeton.edu
http:/dss.princeton.edu/training/
R
Stata
Using dataset Prestige*
Used in the regression models in the fol
Some useful graphic tools in R
Renee X. de Menezes
R Users Group - 7th February 2006
Example 1: Legend
Legends can be included in all sorts of graphs
Here we wish to include them in a densities graph of normalized
chips
R Users Group - 7th February 2006
Statistics 191:
Introduction
to Applied
Statistics
Jonathan
Taylor
Department of
Statistics
Stanford
University
Statistics 191: Introduction to Applied Statistics
Simple Linear Regression: Diagnostics
Jonathan Taylor
Department of Statistics
Stanford Univ
Using R for Linear Regression
In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional entries (all current as of version R-2.4.1). Samp
Association Analysis,
Logistic Regression,
R and S-PLUS
Richard Mott
http:/bioinformatics.well.ox.ac.uk/lectures/
Logistic Regression in Statistical
Genetics
Applicable to Association Studies
Data:
Binary outcomes (eg disease status)
Dependent on geno
CSSS 508: Intro to R
3/03/06
Logistic Regression
Last week, we looked at linear regression, using independent variables to predict a
continuous dependent response variable.
Very often we want to predict a binary outcome: Yes/No (Failure/Success)
For examp
Newsom
Data Analysis II
Fall 2012
1
Logistic Regression
Overview: Logistic and OLS Regression Compared
Logistic regression is an approach to prediction, like Ordinary Least Squares (OLS) regression.
However, with logistic regression, the researcher is pre
A Handbook of Statistical Analyses
Using R
Brian S. Everitt and Torsten Hothorn
CHAPTER 4
Analysis of Variance: Weight Gain,
Foster Feeding in Rats, Water
Hardness and Male Egyptian Skulls
4.1 Introduction
4.2 Analysis of Variance
4.3 Analysis Using R
4.3
Convex Optimization Boyd & Vandenberghe
1. Introduction
mathematical optimization
least-squares and linear programming
convex optimization
example
course goals and topics
nonlinear optimization
brief history of convex optimization
11
Mathematical o
CS 101: ALGORITHMS ASSIGNMENT
International Institute of Information Technology, Bangalore
Faculty: Prof. G.N.S. Prasanna
NOTE: Either Submit .m file or snapshot for these questions.
1. Consider MH1 hostel building of IIIT Bangalore with the rooms as show
Queuing Theory
Introduction
Queuing
theory provides a
mathematical basis for understanding
and predicting the behavior of
communication networks.
It
is extremely useful in predicting and
evaluating system performance.
Queuing
theory has been used for
oper