jalaaSayaaoM ka isqait Anausaar samainvat p`caalana
REAL TIME INTEGRATED OPERATION OF
RESERVOIRS
Government of India
Central Water Commission
Reservoir Operation Directorate
April-2005
jalaaSayaaoM ka isqait Anausaar samainvat p`caalana
REAL TIME INTEGRAT
Evaporation
Terminology
Evaporation process by which liquid
water passes directly to the vapor phase
Transpiration - process by which liquid
water passes from liquid to vapor through
plant metabolism
Sublimation - p
process by
y which water
passes dir
Stability Analysis of
Gravity Dams
Question
Section of a gravity dam is given.
Examine its stability at the base. The
earthquake forces may be taken as
equivalent to 0.1 g for horizontal forces and
0.05 g for vertical forces. The uplift may be
taken as eq
MA2020 Differential Equations (July - November 2014)
Assignment Sheet- 1 (Covering Quiz-I Syllabus)
1. Solve:
dy
(a) x dx
+ y = x3 y 6
dy
+ y = y 2 log(x)
(b) x dx
dy
(c) (x2 y 3 + xy) dx
= 1
(d)
dy
dx
+ (2x tan1 y x3 )(1 + y 2 ) = 0
x
x
(e) (1 + e y )dx
Differential Equations [MA2020]: An outline/Syllabus
Geometrical meaning of a first order differential equation
Separable differential equations :
Sections : K 1.2 K1.3
Exact differential equations, Integrating factors :
Section: K 1.5
Linear differential
MA2020 Differential Equations (July - November 2014)
Assignment Sheet- 2 (Covering Quiz-II Syllabus)
1. Prove that Pn (x) =
on n is even or odd
PN
(1)r (2n2r)!
r=0 2n r! (nr)! (n2r)!
2. Prove the Rodrigues formula Pn (x) =
1
xn2r where N is
1 dn
(x2
n!2n
ANSWER 1
> x = 4.5;
> y = 3.6;
> x + y
ans =
8.1000
> x * y
ans =
16.2000
> (x/y)^(1/3)
ans =
1.0772
ANSWER 2
No, the varible names are not equivalent in MATLAB. Variable names are case sensitive.
ANSWER 3
(a) The statement is true.
(b) The statement is f
Elasticity and Its
Application
Chapter 5
Elasticity . . .
is a measure of how much buyers and
sellers respond to changes in market
conditions
allows us to analyze supply and
demand with greater precision.
Price Elasticity of Demand
Price elasticity of d
l l
1.
2.
3.
5.
MA2020 Differential Equations
(July - November 2014)
Assignment Sheet~ 3
(a) Derive dAlemberts solution to the wave equation
2 271/
9572 :83? fort>0, oo <x< 00,
with u(:c,0) = f(m) and gx, 0) 9(33 ) ~00 < a: < 00.
(b); Using the result o
Money Growth and Inflation
Chapter 28
Inflation
Inflation is an increase in the
overall level of prices.
The Classical Theory of Inflation
The quantity theory of money is used to
explain the long-run determinants of the
price level and the inflation rate.
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
Academic Calendar ODD Semester Jul-Nov 2017
Days
Sat
Sun
Mon
Tue
Wed
July 2017
August 2017
1
2
3
4
5
1
2
Thu
6
3
Fri
7
Sat
8
Sun
NCC Camp beings
4
September 2017
Last date for
Enrolment with
fine
Last date for
sending
The Costs of
Production
Chapter 13
The Costs of Production
The Law of Supply:
Firms are willing to produce and
sell a greater quantity of a good when
the price of the good is high.
This results in a supply curve that
slopes upward.
The Firms Objective
The
Measuring a Nations Income
Chapter 22
Microeconomics
Microeconomics
is the study of how
individual households and firms make
decisions and how they interact with
one another in markets.
Macroeconomics
Macroeconomics is the study of the
economy as a whole
Supply, Demand and
Government Policies
Chapter 6
Supply, Demand, and
Government Policies
In a free, unregulated market system,
market forces establish equilibrium prices
and exchange quantities.
While equilibrium conditions may be
efficient, it may be tr
Interdependence and
the Gains from Trade
Chapter 3
Interdependence and Trade
Consider your necessary items in a typical day:
Alarm clock
Computer/laptop
Mobile
Dress material
Food
Car/scooter
././././
././
and you havent been up for more than 5 hours yet!
HS3002: Principles of Economics
Learning Objectives
Define
Economics
Explain the three big questions that
economists seek to answer
Explain ten principles that define the
economic way of thinking
Describe how economists go about their
work
Learning Ob
CH2010 Chemical Engineering Thermodynamics
Tutorial-1
Date: 04.08.2017
Topic: Intermolecular interactions
Problems:
1. The London disperion interaction is directly related to the polarizabilities of the corresponding
Instruction Set Architecture
BITS Pilani
Pilani Campus
S Mohan
Addressing Modes
An instruction must contains the information
about:
How to get the operands?
Called as ADDRESSING MODES
Essentially it tells where the operands are available and
how to ge
Feedback
4.
This is not an identity, because it is not true for all values of x. For example, x = 0 provides a
counterexample:
.
10.
Use the Pythagorean identity to rewrite this as:
.
Factor this equation as:
.
You can now see that the solution is given b
Creating Vectors
The c() function can be used to create vectors of objects.
>
>
>
>
>
>
x
x
x
x
x
x
<-
c(0.5, 0.6)
c(TRUE, FALSE)
c(T, F)
c("a", "b", "c")
9:29
c(1+0i, 2+4i)
#
#
#
#
#
#
numeric
logical
logical
character
integer
complex
Using the vector()
Textual Formats
dumping and dputing are useful because the resulting textual format is edit-able, and in the case
of corruption, potentially recoverable.
Unlike writing out a table or csv file, dump and dput preserve the metadata (sacrificing some
reada
Removing NA Values
A common task is to remove missing values (NAs).
> x <- c(1, 2, NA, 4, NA, 5)
> bad <- is.na(x)
> x[!bad]
[1] 1 2 4 5
12/14
Removing NA Values
What if there are multiple things and you want to take the subset with no missing values?
> x
Subsetting a Matrix
Matrices can be subsetted in the usual way with (i,j) type indices.
> x <- matrix(1:6, 2, 3)
> x[1, 2]
[1] 3
> x[2, 1]
[1] 2
Indices can also be missing.
> x[1, ]
[1] 1 3 5
> x[, 2]
[1] 3 4
4/14
Subsetting a Matrix
By default, when a s
Subsetting
There are a number of operators that can be used to extract subsets of R objects.
[ always returns an object of the same class as the original; can be used to select more than one
element (there is one exception)
[ is used to extract elements
Names
R objects can also have names, which is very useful for writing readable code and self-describing
objects.
> x <- 1:3
> names(x)
NULL
> names(x) <- c("foo", "bar", "norf")
> x
foo bar norf
1
2
3
> names(x)
[1] "foo" "bar" "norf"
24/27
Names
Lists ca
Objects
R has five basic or atomic classes of objects:
character
numeric (real numbers)
integer
complex
logical (True/False)
The most basic object is a vector
A vector can only contain objects of the same class
BUT: The one exception is a list, whi
Missing Values
Missing values are denoted by NA or NaN for undefined mathematical operations.
is.na() is used to test objects if they are NA
is.nan() is used to test for NaN
NA values have a class also, so there are integer NA, character NA, etc.
A Na