First Order Partial Differential Equations, Part  1:
Single Linear and Quasilinear First Order Equations
PHOOLAN PRASAD
DEPARTMENT OF MATHEMATICS
INDIAN INSTITUTE OF SCIENCE, BANGALORE
Definition
Fir
Introduction and Basic Definitions
FirstOrder Partial Differential Equations
Course plan
Lecture Slot:
Division I(CSE, ECE) and II (EEE, EPH, MA&C)Slot C
Division III(ME, CE) and IV (BT, CL, CT)Slo
MA 201: Lecture  3
Solving quasilinear PDEs
Quasilinear FirstOrder PDEs
A first order quasilinear PDE is of the form
a(x, y , u)
u
u
+ b(x, y , u)
= c(x, y , u).
x
y
(1)
Quasilinear FirstOrder P
Surfaces orthogonal to a given system of surfaces
Nonlinear FirstOrder PDEs
Solving Cauchys problem for nonlinear PDEs
MA 201: Lecture  4
Nonlinear first order PDES
IIT Guwahati
MA201(2017):PDE
Surf
Classification of PDEs
Canonical forms
MA 201: Lecture  7
Second order PDEs: Classification and Canonical
forms
MA201(2017):PDE
Classification of PDEs
Canonical forms
Classification of PDEs
An ODE i
Compatible Systems and Charpits Method
Charpits Method
Some Special Types of FirstOrder PDEs
MA 201: Lecture  5
Charpit method
IIT Guwahati
MA201(2017):PDE
Compatible Systems and Charpits Method
Cha
Jacobi Method
Second order PDE
MA 201: Partial Differential Equations
Jacobi method for I order PDE
and
Introduction to II order PDE
IIT Guwahati
MA201(2017):PDE
Jacobi Method
Second order PDE
Jacobis
MA 201: Lecture  2
Methods of characteristics
MA201(2017):PDE
Example
Let us warm up with a simple example
ux = u + c, c is function of x, y .
MA201(2017):PDE
(1)
Example
Let us warm up with a simple
MA 201 MATHEMATICS III (PARTIAL DIFFERENTIAL EQUATIONS)
Topicwise reference for first order PDE
S. No.
1
2
3
4
5
Topics
Introduction to PDE, formation of PDEs,
origin of PDEs
Integral surface passing
MA 201, Mathematics III, JulyNovember 2016,
Fourier Transform (Contd.)
Lecture 17
Lecture 17
MA 201, PDE (2016)
1 / 26
Fourier Transform
For a given function f , the improper integral
Z
1
eit
2
Z
Z
Formal Languages and Automata Theory
D. Goswami and K. V. Krishna
November 5, 2010
Contents
1 Mathematical Preliminaries
3
2 Formal Languages
2.1 Strings . . . . . . . . . . . .
2.2 Languages . . . .
Motivating Examples
Compatible Systems and Charpits Method
Charpits Method
Some Special Types of FirstOrder PDEs
MA 201: Partial Differential Equations
Lecture  5
IIT Guwahati
MA201(2016):PDE
Motiva
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
Quasilinear FirstOrder PDEs
Formation of quasilinear FirstOrder PDEs
General solution quasilinear FirstOrder PDEs
The method of Lagrange
Solving a Cauchy Problem
MA 201: Partial Differential Equ
Surfaces orthogonal to a given system of surfaces
Nonlinear FirstOrder PDEs
Solving Cauchys problem for nonlinear PDEs
MA 201: Partial Differential Equations
Lecture  4
IIT Guwahati
MA201(2016):PDE
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 b
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
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
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]
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
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 s
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 int
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 (x
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 su
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

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 sa
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 likeliho
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 W