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WELL LOGGING TECHNIQUES AND FORMATION EVALUATIONAN OVER VIEW
By Shri S. Shankar , DGM(Wells)
INTRODUCTION:
Once the prospect generation is made based on seismic and geological surveys, location
for drilling is released based on the most probable structure
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Geography AS Notes
Long & Cross Profiles
By Alex Jackson
A Rivers Course
The course a river takes is split into three stages, the upper, middle and lower
stage. In the upper stage, the river is close to its source and high above its ba
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Classifying Rivers - Three Stages of River Development
River Characteristics - Sediment Transport - River Velocity - Terminology
The illustrations below represent the 3 general classifications into which rivers are placed
according to specific characteris
The Calculation of Activity
Handlers of radioactive materials must be able to calculate the activity of the materials
they handle and the wastes generated.
The following formula can be used to calculate the activity of a radioactive material at
any point
Chapter 5
Methods for ordinary
differential equations
5.1
Initial-value problems
Initial-value problems (IVP) are those for which the solution is entirely known
at some time, say t = 0, and the question is to solve the ODE
y 0 (t) = f (t, y(t),
y(0) = y0
Chapter 7
Spectral Interpolation,
Differentiation, Quadrature
7.1
7.1.1
Interpolation
Bandlimited interpolation
While equispaced points generally cause problems for polynomial interpolation, as we just saw, they are the natural choice for discretizing the
Chapter 6
Fourier analysis
(Historical intro: the heat equation on a square plate or interval.)
Fouriers analysis was tremendously successful in the 19th century for formulating series expansions for solutions of some very simple ODE and PDE.
This class s
Chapter 4
Nonlinear equations
4.1
Root nding
Consider the problem of solving any nonlinear relation g(x) = h(x) in the
real variable x. We rephrase this problem as one of nding the zero (root)
of a function, here f (x) = g(x) h(x). The minimal assumption
Chapter 3
Interpolation
Interpolation is the problem of fitting a smooth curve through a given set of
points, generally as the graph of a function. It is useful at least in data analysis (interpolation is a form of regression), industrial design, signal p
Elementary Numerical Analysis
Prof. Rekha P. Kulkarni
Department of Mathematics
Indian Institute of Technology, Bombay
Module No. # 01
Lecture No. # 02
Polynomial Approximation
Today we are going to consider approximation by polynomials of a continuous fu
Elementary Numerical Analysis
Prof. Rekha P. Kulkarni
Department of Mathematics
Indian Institute of Technology, Bombay
Module No.# 01
Lecture No. # 03
Interpolating Polynomials
Today, we are going to consider polynomial interpolation; it is one of the imp
Elementary Numerical Analysis
Prof. Rekha P. Kulkarni
Department of Mathematics
Indian Institute of Technology, Bombay
Module No.# 01
Lecture No. # 01
Introduction
In numerical analysis, we are mainly interested in implementation and analysis of
numerical
Chapter 2
Integrals as sums and
derivatives as dierences
We now switch to the simplest methods for integrating or dierentiating a
function from its function samples. A careful study of Taylor expansions
reveals how accurate the constructions are.
2.1
Nume
Chapter 1
Series and sequences
Throughout these notes well keep running into Taylor series and Fourier se
ries. Its important to understand what is meant by convergence of series be
fore getting to numerical analysis proper. These notes are sef-contained,
18.330 : Homework 4 : Spring 2012 : Due Tuesday April 3
1. (1pt) Compute 31/3 to 10 digits of accuracy using Newtons method. Explain how you obtained your
answer.
2. One method to find the solution of the equation x = (x) for some function is to use the f
18.330 : Homework 2 : Spring 2012 : Due March 1
1. (1 pt) Let and be real numbers. If a quantity f (h) is O(h ) as h 0, show that
h f (h) = O(h+ ).
2. (2 pts) Consider the midpoint rule,
Z
1
f (x) dx ' h
0
N
1
X
j=0
1
f (j + )h),
2
h = 1/N.
Draw a picture
18.330 : Homework 3 : Spring 2012 : Due March 15
1. (2.5pts) Design a one-sided second-order accurate finite difference formula to approximate f 0 (0) from
the samples f (0), f (h), and f (2h), by differentiating an adequately chosen interpolation polynom
18.330 : Homework 8 : Spring 2012 : Not due
Fourier exercises (05/15):
1. Show that a C p periodic function (p 1) has Fourier series coefficients that decay like |k|p .
2. Show that the error of the trapezoidal rule for integrating a C p periodic function
18.330 : Homework 6 : Spring 2012 : Due Thursday April 26
1. (7pts) Consider the mixed Neumann-Dirichlet boundary-value problem
u00 = f,
x [0, 1],
u0 (0) = 0,
u(1) = 0.
a) Find the eigenvalues and eigenfunctions for this problem, i.e., find all the possib
18.330 : Homework 7 : Spring 2012 : Due Thursday May 3
1. (3pts) Prove the following properties of the Fourier transform (x, k R):
(a) Dilation: if g(x) = f (x/a) for a > 0, then g(k) = af(ak).
(b) Conjugation: if g(x) = f (x), then g(k) = f(k).
(c) Symme
18.330 : Homework 1 : Spring 2012 : Due February 23
1. (3 pts) Consider the convergent series1
1 1 1
= 1 + + .
4
3 5 7
(a) Is this series absolutely convergent or conditionally convergent? Justify your answer in a rigorous
fashion.
(b) Write a short progr
18.330 : Homework 5 : Spring 2012 : Due Tuesday April 12
1. (4 pts) Consider the initial-value problem for harmonic oscillations: y 00 (t) + 2 y(t) = 0, y(0) = y0 ,
y 0 (0) = y1 . In what follows, consider y0 = 0, y1 = 1, and = 1.
a) Solve the equation ex
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GATE 2013 : Geology And Geophysics
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GATE 2008 : Geology And Geophysics
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