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Of
Volume No. 2 Issue No. 2, 2014
C o n t e n t s
S. No. Title Page No.
1.
2.
3.
4.
1
17
32
38
Delineation Of Groundwater Potential Zones
In Coimbatore District, Tamil Nadu,
Using Remote Sensing And Gis Techniques
P. Meenakshi, K. Kannadasan and A. Ganesh
Green Energy Production Technology For Clean Environment And Carbon Trading Potential
From Poultry Litter In Namakkal Taluk, Tamil Nadu, India Using Gis
Dr. P. Gunasekaran and Dr. A. Ganesh
A Village Model Of Sustainable Development
M.Pal
Technology In Mathematics Education
Presentation Of Material Developed For First Year
Calculus Topics – Formal-Definition Of Limit
Barun Maity
December, 2014

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Int. J. Geosci. & Tech. Vol. 2 (2) 2014, pp. ISSN: 2321-2144
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DELINEATION OF GROUNDWATER POTENTIAL
ZONES IN COIMBATORE DISTRICT, TAMIL NADU
USING REMOTE SENSING AND GIS TECHNIQUES
P. Meenakshi 1
, K. Kannadasan 2
and A. Ganesh 3
1 & 2
– Research Scholar & 3
– Professor Department of Geography,
School of Geosciences, Bharathidasan University, Tiruchirappalli
Email : aganesh2001@gmail.com
Water is one of the most essential com-
modities for mankind and the largest
available source of freshwater lays under-
ground. (Todd, 1980). The water resource
not only supports the human existences
but also it is a vital input for all develop-
mental activities. Though the freshwater
resources are popularly used, because
of the uncertainties in its availability with
respect to various factors like vagaries of
monsoon, limited accessibility , pollution
and sometimes due to political reasons,
the degree of reliability on the surface wa-
ter resources becomes restricted or low.
Nowadays groundwater resources play
an important role in meeting demands
on water supply because of regional cli-
INTRODUCTION
Key Words: Groundwater Potential, GIS, Coimbatore, Weightage, Geomorphology.
1-16
Ín the present study, the groundwater potential zone of Coimbatore district is deline-
ated by the integration Remote Sensing and Geographic Information System (GIS)
techniques. The thematic maps such as geology, geomorphology, lineaments, slope
and land use/land cover are prepared from IRS -1C, Survey of India (SOI) Toposheets
of scale 1:50,000 and from already existing maps. The map layers are assigned with
suitable and then integrated in the GIS environment to generate the groundwater po-
tential zones. The occurrence of the groundwater is controlled by the factors such as
slope, geomorphology, soil and drainage of the region. The map was classified into
four categories, viz., very good, good, moderate, and poor zones. The flood plains,
weathered pediplains shows good to moderate groundwater potential zones in the
study area. About 50 per cent of the study area shows moderate to good groundwater
potential zones whereas only 8 per cent accounts for very good groundwater potential
in the study area.
AbstractAbstract
(Date of Receipt : 16-10-2014; Date of Acceptance for Publication : 10-11-2014 )
Pages: 16 References: 28

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Int. J. Geos. & Tech. Vol. 2 (2) 2014, pp. ISSN: 2321-2144
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mate change and scanty surface water
resources or their unsustainability. (Sener,
2006).
Several factors govern the occurrence
and flow of groundwater in an area in-
cluding topography, geologic structures,
extent of fractures, secondary porosity,
landforms, LULC, climatic conditions and
interrelationships between these factors.
(Mukherjee, 1996). In order to determine
the location of aquifer, quality of ground-
water, physical characteristics of aquifers,
etc., in any basin, test drilling and stratig-
raphy analysis are the most reliable and
standard methods.(Chowdhary. et. al.,
2005). In India 65 % of the total area is un-
derlain by hard rock formations. The oc-
currence of groundwater is confined to
fractures and weathered horizons in the
hard rock terrain. Therefore efficient man-
agement and planning of groundwater in
these areas is of the utmost importance.
(Saraf.et. al., 1998).
With the development of new technolo-
gies like Remote Sensing and GIS , the
data can be acquired for large areas on
both spatial and temporal basis even for
the areas inaccessible becomes possible.
The Remote Sensing technique is cost ef-
fective which facilitates quick and better
mapping of natural resources than the
conventional survey methods. The Re-
mote Sensing data integrated in the GIS
environment provides an effective tool for
the delineation of groundwater potential
zones.
Several researchers have attempted to
evaluate the groundwater potential zones
using several methods.P.C.Chatterji.et.al.
(1980) have done groundwater explo-
1-16
ration based on the geomorphological
features in Rajasthan desert. Pradeep. K.
Jain (1998), K. Shankar(2002), Srinivasa
Rao (2004) and Jagadeeswara Rao.et.
al., (2004) applied Remote sensing in the
identification of groundwater potential
zones.
However, the fullest potential of the two
technologies i.e. Remote Sensing data
and GIS can be appreciated when they
are integrated for the delineation ground-
water potential zones. Saraf and Choud-
hary(1998), Obi Reddy.et. al., (2000), Nag.
SK.(2005), Sahu.2006),Dinesh Kumar.et.
al., (2007), Suja Rose.et. al., (2009),Prasad
Et.al (2007), Sreedhar Ganapuram (2009),
Preeja.KR(2011), Assadi (2012) Pandi-
an(2013) , Ramakrishman(2014) have in-
tegrated Remote sensing data in the GIS
environment for the delineation of ground-
water potential zones. Basudeo Rai(2005)
Srivastava (2006) and Sahu(2006) used
geophysical techniques along with the
remote sensing and GIS environment for
groundwater exploration Jaisankar.et. al.,
(2001), Kavitha Misra (2006) and Teixei-
ra(2008) combined hydro geomorphol-
ogy with GIS for mapping of groundwater
potential zones.Sreedevi.et. al., (2005) and
studied groundwater prospect in Pageru
river basin based on morphometric char-
acteristics.Manik Gupta(2010), Ram Ava-
tar(2010), Ganesh Babu(2004) carried
out multicriteria analysis using weighted
aggregation method associated with GIS
for the delineation of groundwater poten-
tial zones. MK.Gumma et. al., (2013) have
done groundwater potential assessment
with spatial modeling using GIS in Ghana.
Due to the vagaries of monsoon, the river
system is the main sources of the surface

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COIMBATORE DISTRICT: THE
STUDY AREA
1-16
water irrigation, which could not serve the
requirements of the farmers. Hence, the
irrigation through open wells, Dug wells
and Dug Cum Bore wells supplement
plays a considerable role in supplement-
ing the surface water requirements in the
study area. Exploitation of groundwater
resources has increased in the past dec-
ades, leading to the over-consumption of
groundwater, which eventually causes
ecological problems such as decreased
groundwater levels, water exhaustion,
water pollution and deterioration of water
quality.(Magesh 2012.)
Therefore an attempt has been made to
delineate the groundwater potential zones
in the Coimbatore district, Tamil Nadu in-
tegrating remote sensing and GIS.
The study area, Coimbatore district lies
between 10 ̊ 13’15’’ - 11̊ 24’ 26 ‘’ North Lati-
tudes and 76 ̊ 58 ‘52 ‘’ – 77 ̊ 06 ‘28 ‘’ East
Longitude covering 4714.18. sq.km(Fig.1).
The Coimbatore district is bounded on the
west and south by steeply rising moun-
tains of Western Ghats with the maximum
elevation of 2493 mts above Mean sea
level. The district consists of undulating
plain sloping gradually from west to east.
The climate of the Coimbatore district is
subtropical in nature. The mean tempera-
ture varies between 41 o
C to 29 o
C with
the highest temperature of 41 o
C record-

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1-16
ed in the month of May and the minimum
temperature of 27.6 0
C in the month of
December. The district receives an aver-
age rainfall of 647.20 mm from both the
southwest and northeast monsoon sea-
son with maximum rainfall received dur-
ing the northeast monsoon season (Oc-
tober and November).
METHODOLOGY
To demarcate the groundwater potential
zones different thematic maps were pre-
pared by integrating topographic maps
on 1:50000 scale, existing maps and sat-
ellite images in GIS environment using
Arc GIS 10 software. The base map
of Coimbatore district was prepared from
Survey of India topographic maps on
1:50000 scale (58A11, A12, 58 B9-16, 58
E3-E4, E8, F1-5). Various thematic maps
such as geomorphology, geology, soil,
drainage, landuse/landcover were pre-
pared and were converted into a raster
format. The slope, drainage density and
lineament density were calculated using
ArcGIS Spatial Analyst tool.
The weighted overlay method was em-
ployed to generate groundwater potential
zones. Each thematic map layers were as-
signed appropriate weightages (Wt.) and
Feature score(Wi) were given to each
thematic features depending on their ca-
pability to hold groundwater(Table.1).
The layers were integrated and analysed
using weighted aggregation method. In
this method, the resultant groundwater
potential map generated was based on
the total weight of the final integrated
map derived as the sum or product of the
weights assigned to different thematic
map layers according to their suitability.
The final output map was then reclassi-
fied into 4 potential zones as shown in
(Fig:10) The methodology followed to
determine the groundwater potential is
shown in Fig.2
Fig.2. Methodology for Delineating the Groundwater Potential Zone.

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1-16
RESULT AND DISCUS-
SION
The thematic map layers prepared for the
integrated analysis (Fig.3-9) and the re-
sultant groundwater potential zones map
(Fig.10) generated are discussed in detail
in the following sections.
GEOMORPHOLOGY
Geomorphic features plays a major role in
the controlling the infiltration, movement
and occurrence of groundwater since it
influences to large extent the precipitation
distribution and the amount of precipita-
tion that become runoff and groundwa-
ter recharge. The study area is an up-
land plateau region with many hillocks
and undulation topography with gentle
slope towards east for the hilly terrain in
the west. The geomorphic features in the
study area are of structural and fluvial
origin. The geomorphic units have been
classified as Linear Ridge , Inselbergs,
Residual hills ,Denudational hills, In-
selbergs, Pediment, Shallow weathered
buried pediplains, Moderately weathered
buried pediplains,Colluvial fans and Valley
fills(Fig.3).
Fig.3. Geomorphology of Coimbatore District

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Table: 1.Weightages for thematic layers and corresponding feature scores

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1-16
The structural hills exhibits complex
folding, fracturing criss crossed by
numerous fracture and joints which
facilitates infiltration but mostly act
as a run off zones. Linear ridges and
Pediments are gently sloping and
undulating rock surface covered
with the remnants of weathering
and denudational action. The denu-
dational hills are marked by sharp
to blunt crest lines with rugged tops
indicating that the surface runoff at
the upper reaches of the hills has
caused hill erosion.Residual hills are
the end products of the process of
pediplanation are residual hillocks
with steep slopes because of ero-
sion. Inselbergs are mostly barren
rocky rounded small hills. Ground-
water potential in these units is gen-
erally very poor except along the
intersection of lineaments and frac-
tures zones where the groundwa-
ter presence is moderate. Among
the geomorphic units structural hill,
denudational hill, linear ridge, re-
sidual hill, Pediments are consid-
ered as moderate to poor potential
zones. Bajadas mainly exixts along
the foothills comprises of detrital
materials of various lithology and
grain size. Pediplains are formed as
the result of continuous process of
pediplanation gently sloping, char-
acterized by high porosity, perme-
ability and infiltration.
The groundwater prospect in this
unit is generally very good but var-
ies with thickness of the weathering
materials. Valley fills and colluvial
fans composed of unconsolidated
formations comprising of both ma-
terials of fluvial origin such as sand,
fine silt and other detrital materials
with high porosity and permeability
resulting in high infiltration rate. The
groundwater prospect of pediplains,
Bajadas, Colluvial fans and valley
fills are good to very good.
Slope
Slope analysis is an important pa-
rameter in geomorphic studies. The
gradient of slope plays a significant
role in controlling the infiltration
into the subsurface. Infiltration is
inversely related to the slope since
steep slopes generates high run off
at the time of rainfall with less time
to infiltrate resulting in less poten-
tial for groundwater occurrence. In
the areas with gentle slopes with
slow run off and adequate resi-
dence time increasing infiltration
rate favours groundwater recharge.
The slope was estimated from the
Digital Elevation Model which was
obtained from the SRTM DEM data
and reclassified as 0 o
-3 o
(Very gen-
tly sloping, 5 o
-10 o
(Moderate),
10 o
-15 o
(Moderately Steep), and
>15 o
(Steep)(Fig.4).The areas with
0 o
-3 o
slope has very high ground-
water potential since the rate of in-
filtration is high and about 75% of
the study area has been identified
with very gentle sloping topogra-
phy. The areas with 5 o
-15 o
slope
with undulating terrain with high
run off presents moderate ground-
water potential zone whereas the
areas with more than 20 o
slope
has poor or no groundwater po-
tential zones.

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Fig.4. Slope of Coimbatore District
SOIL
Soils have a significant place in determin-
ing the infiltration of the water into the
subsurface. The infiltration rate of the soil
mainly depends on the texture of the soil.
In the study area soils are classified on
Fig. 5. Soil of Coimbatore District
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the basis of their permeability, infiltration
and runoff potential.
Coarse grained soils infiltrate more wa-
ter because of high permeability than
the fine grained soils with low perme-
ability and the groundwater potential is
good in coarse textured soils. The soil in
the region has been grouped based on
their texture as Sandy Loam, Sandy clay
loam and Clay loam (Fig.5). Majority of the
study area i.e. 58 % is occupied by Sandy
Loam soil which has high infiltration rate
and low run off potential.
DRAINAGE DENSITY
It reflects the characteristics of surface as
well as subsurface formation. It indicate
closeness spacing of channels as well as
the nature of surface materials. The more
the drainage density lesser the ground-
water potential and lower drainage den-
sity indicates probability of groundwa-
ter prospect. A low network of drainage
courses in a place is indicative of pres-
ence of highly resistant or highly permea-
ble rocks in the surface, while a high den-
sity is characterized by hilly terrain and
areas underlain by weak or impermeable
rock(Karanth). The drainage density map
was categorized as Very Low (0-2), Low(2-
4), Moderate(4-6), High(>6) and classes
and nearly half of the study area belongs
to very low density class which indicates
high groundwater potential zones)(Fig.6).
Fig.6. Drainage Density of Coimbatore District
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LINEAMENT DENSITY
In the hard rock areas, the movement
and occurrence of ground water de-
pends mainly on the secondary porosity
and permeability resulting from folding,
faulting, fracturing etc.(Obi Reddy .et. al.,
2000). Lineaments are linear or curvilin-
ear pattern features which results from
faulting and fracturing which causes in-
creased secondary porosity and perme-
ability of the rocks. They are the conduits
of groundwater movement and generally
associated with the stream courses.
They are important in rocks where sec-
ondary permeability and porosity domi-
nate the intergranular characteristics
combine in secondary openings and
influence weathering, soil water and
ground water movement. The intersec-
tion of lineaments found in the low elevat-
ed areas are marked as favorable sites of
groundwater existence. Areas with high
lineament density indicate high intensity
of fracturing which reveals the presence
of high groundwater potential. The line-
ament density map was reclassified into
Low(0.2-0.4), Moderate(0.4-0.6),High(>0.8)
Fig.7. Lineament Density of Coimbatore District
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classes and most of the area belongs
very low density category(Fig.7). High lin-
eament density is associated with Fissile
Hornblende Biotite gnessis and Garneti-
ferrous Quartzoferrous regions whereas
very high lineament density is found in
Charnockite rock units.
GEOLOGY
The study area is underlain by uncon-
solidated, porous formations and consoli-
dated hard rock formations of Archaean
age. The district is occupied by hard con-
solidated crystalline rocks of charnockite
groups such as charnockite, Ultramafic
and pyroxene granulites and metamor-
phic rocks of khondalitic group such as
garnetiferougneiss –silimanite gneiss,
Calc –granulite and Limestone, Fissile
Hornblende biotite gneiss and Pink mig-
matite of Migmatite complex. The Am-
phibolite and Basic anorthosite of Saty-
amanagalam group, Granite, Laterite,
with relatively low infiltration due to less
or absence of weathering makes the area
less favourable for groundwater occur-
rence. The dominant rock types found
in the region are Charnockite and Fissile
Hornblende biotite gneiss(Fig.8).. These
rocks are extensively weathered and
overlain by recent alluvium and colluvium
materials such as gravely pebbles, sand,
and silt which has high infiltration rate
and has high groundwater potential.
Fig.8. Geology of Coimbatore District
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The groundwater developments in these
rocks depend on the secondary porosity
due to weathering and fracturing. Thus
the groundwater availability in these
rocks is mainly confines to the presence
of fractures and the level of infiltration in
the faults and fractures. The foliations of
these metamorphic rocks serve as planes
of weakness and facilitate flow and stor-
age of groundwater. The depth and extent
of the weathered regolith is also known
to be important for groundwater yields in
crystalline rocks.
LAND USE / LAND COVER
The land use of the study area were identi-
fied from the IRS LISS III image and stand-
ard visual interpretation methods were
used to demarcate the land use category
present in the study area. The major type
of land use in the study area are agricul-
tural land, built up land , Scrubs, current
fallow , water bodies and forest(Fig.9). The
dominant type of landuse is forest (43%)
followed by fallow land and built up land.
Fig.9. Land Use / Land Cover of Coimbatore District
Demarcation of Groundwater Poten-
tial Zones
The groundwater potential zone of the
study area was delineated by integrating
the various thematic maps with suitable
weightages assigned to each feature of
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the study area using Remote Sensing and
GIS techniques. The resultant groundwa-
ter potential zones were then categorized
into Very Good, Good, Moderate and Poor
Categories (Fig.10). The category “Very
Good – Good” groundwater potential
zones in the study are found associated
with the, agricultural land,water bod-
ies and scrub land which possess high
infiltration capacity. The slope, Linea-
ment Density and drainage density also
plays a considerable role in developing
groundwater potential of the area. Out
of the total study area 4717.18 sq.km of
the study area, only 7.84% of the area
is identified with very good groundwa-
ter potential is found in Southeastern
part of the area, the zones of good and
moderate potential occupy 25.22% and
21.17% of the study area respectively.
The zone of poor groundwater poten-
tial occupies 45.75% of the study area
which lies in the area with steep slope
and high drainage density.
Fig.10. Groundwater Potential Zones
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CONCLUSION
The delineation of groundwater poten-
tial zones in Coimbatore district of Tamil
Nadu using Remote Sensing and GIS
techniques proves to be an valuable tool
in assessing the groundwater resourc-
es of the area and helps in better man-
agement of the water resources of the
study area. Topographic maps, Satel-
lite images and existing data were used
to prepare thematic map layers such as
geomorphology, geology, soil, drainage,
landuse/landcover, drainage density,
slope, and lineament density and appro-
priate weightages were assigned to each
of the layers. The individual features are
allocated with feature score according to
their ability to hold water in the subsur-
face and integrated in the GIS environ-
ment to generate groundwater potential
zones through Intersect tool in ArcGIS
.10. The composite map indicates that
about 46% of the study area is found with
good to moderate groundwater potential
zones. These zones are mainly associat-
ed with geomorphological features such
as weathered pediplains, Colluvial plains,
flood plains and Pediments. The linea-
ments along with gentle sloping areas
facilitate the augmentation of the ground-
water resources in the area and serves
as the aquifer zones. The resultant map
generated indicates that remote sensing
and GIS play a commendable in evalu-
ating the groundwater resources and the
map could be used for various purpos-
es such as sustainable management of
groundwater resources as well as map-
ping of groundwater prospect zones for
further exploration purposes and for iden-
tification of conservation sites where the
groundwater availability is critical.
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GREEN ENERGY PRODUCTION TECHNOLOGY FOR
CLEAN ENVIRONMENT AND CARBON TRADING
POTENTIAL FROM POULTRY LITTER IN NAMAKKAL
TALUK, TAMIL NADU, INDIA USING GIS
Dr. P. Gunasekaran.* & Dr. A. Ganesh **
* Assistant Professor, Dept. of Geography, Government Arts College (Aut), Coimbatore,Tamil Nadu, India,
** Professor and Chair, School of Geosciences, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India
Email : gunagri@gmail.com, aganesh2001@gmail.com.
Every day when the sunrays reach earth,
a group of gasses called greenhouse gas-
es such as water vapour, carbon-di-oxide,
Fossil fuels consumption is believed to be the primary factor contributing to serious
environmental problems, such as global warming, climate change and acid rain. If
the temperature rise is not controlled, our future generation is going to witness many
more climate change connected tragedies like water scarcity, migration of people due
to seawater inundation in the coastal areas, reduction in food grain production, reces-
sion in the economic growth of the countries etc. The Intergovernmental Panel on
Climate Change predicts that there will be a temperature rise of about 1.4 to 5.8 o
C dur-
ing 2100. Carbon is the common denominator in all polluting gases that cause global
warming. Carbon dioxide is the gas most commonly thought of as a greenhouse gas.
It is responsible for about half of the atmospheric heat retained by trace gasses. Almost
all the countries are now seriously thinking on controlling the fossil fuel use so as to
arrest global warming. There is growing interest in installing anaerobic digesters tech-
nology on farms to use poultry litter as a biogas resource for both economic value and
environmental benefit. The carbon trade is an idea that came about in response to the
Kyoto Protocol. Biogas is an environmental friendly, clean, cheap, and versatile fuel
generating from poultry litter. Namakkal taluk has a tremendous poultry litter potential
to earn carbon credits by setting site based energy substitution projects like biogas
plants through GIS technique. In this study, we propose a generalized mathematical
model that will estimate the economic viability and feasibility of a programmatic Clean
Development Mechanism based biogas plant project for green energy self sufficiency
and carbon trading in Namakkal Taluk, Tamil Nadu, India. Taking these into account,
the present status of the green energy potential and carbon trading are assessed.The
study shows that, the green energy potential is 234 megawatt per day. The enriched
methane gas potential available in the study area is 70,328 cubic metres per day.
INTRODUCTION
Key Words: Poultry Litter, Anaerobic Digester Technology, Biogas, Enriched Methane
Gas, Green Energy, Carbon Trading, Clean Environment, Sustainable Development.
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AbstractAbstract
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methane, nitrous oxide, etc. absorb heat
from the sun rays and make our planet
warm enough for us to survive. If the levels
of these gases in the atmosphere increase,
they will absorb more heat, and make the
earth too hot to live. This overheating of
the planet is called global warming. Since
1880 earth has warmed up by 0.8 o
C. This
increase in earth’s temperature has re-
sulted in a rapid melting of ice in Polar Re-
gions, higher sea levels, submergence of
low-lying islands and flooding of coastal
areas. Warmer temperatures have also
triggered climate change and the extinc-
tion of animal and plant species (9)
. An
increase in public awareness regarding
the negative impact of traditional power-
generating methods, especially coal and
oil-fired power stations, on the environ-
ment has created a demand for devel-
oping and using environmental friendly
renewable energy (2)
. Kapdi et. al., (8)
have
explained that biogas is produced by an-
aerobic digestion of biological wastes
such as cattle dung, vegetable wastes,
sheep and poultry droppings, municipal
solid waste, industrial waste water, land
fill, etc. generated huge quantities of com-
pressed methane, a gas with an immense
potential and an alternative source of
vehicle fuel. Gelegenis et. al., (4)
have ob-
served that biogas production from olive
mill wastewater by codigesting with dilut-
ed poultry manure at mesophillic condi-
tions. Hanandeh and Zein (6)
attempted to
study the energy from waste identified as
a source of green electricity and has been
used as a way of reducing greenhouse
gas emissions. Anaerobic Digestion may
yield better results from an environmental
and energy generation perspective. Salm-
inen and Rintala (14)
studied the potential
of anaerobic digestion for material recov-
17-31
ery and energy production from poultry
slaughtering by-products and wastes. The
anaerobic digestion is considered impor-
tant for the digestion of solid slaughter-
house wastes. Oliveira et. al., (10)
evaluated
the technical and economic character-
istics of power generation, using biogas
obtained from poultry litter in Brazil, and
highlighted the large energy potential and
the high poultry litter production in the re-
gion, which translates into an important
source of raw material for electricity gen-
eration. Aurich et. al., (1)
have emphasized
that the production of biogas as a renew-
able resource has emerged rapidly in
Germany and other countries with the ex-
pectation to substantially mitigate anthro-
pogenic Green House Gases. This study
analyzes the GHG mitigation potential of
using biogas based on cattle slurry and
corn to produce electrical and thermal
energy. Saenz et. al., (13)
have evaluated a
bio-filtration system for removing hydro-
gen sulfide and volatile fatty acids con-
tained in a gaseous stream from an an-
aerobic digester. The elimination of these
compounds allowed the potential use of
biogas in automobiles. Ramachandra (12)
used a Geographic Information Systems
to analyze biogas as one such alternative,
which can be obtained by anaerobic di-
gestion of animal residues and domestic
and farm wastes abundantly available in
Karnataka State. Goetz et. al., (5)
have at-
tempted to study the mapping and moni-
toring carbon stocks with satellite obser-
vations. Remote sensing measurements
relevant to mapping, above ground bio-
mass and relative merits and limitations
of each have been analyzed. Purohit and
Michaelowa (11)
have explained that Clean
Development Mechanism provides in-
dustrialized countries with an incentive to

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invest in emission reduction projects in
developing countries to achieve a reduc-
tion in CO2
emissions at lowest cost that
also promotes sustainable development
in the host country. Humbad et. al., (7)
have studied Clean Development Mech-
anism to reduce the green house gas
emissions by monetizing the reduction in
emissions and a tremendous potential to
earn carbon credits by setting up house-
hold based energy substitution or fuel
switching projects like biogas plants, so-
lar cookers and solar cells and smokeless
chulhas. Hence, the main objective of the
present study is to use Geographical In-
formation System to map the village wise
green energy potential for clean environ-
ment and carbon trading potential from
poultry in Namakkal Taluk, Tamil Nadu,
India and analyze the variability consider-
ing spatial aspects.
The compressed methane gas potential
available in the study area is 50,214 kg per
day. This compressed methane gas po-
tential is available to earn carbon credits,
clean environment and sustainable de-
velopment.
STUDY AREA
Namakkal taluk is located between 11o
and 11o
26’ N latitudes and 78o
02’ and 78o
28’ E longitudes. Namakkal taluk extends
over an area of 1513 km2
at a mean alti-
tude of about 300 m (Fig.1). Namakkal, the
taluk headquarter, is the only town in the
taluk which has 117 villages grouped un-
der six development blocks (3). Hills are
found on the northern and eastern part of
the taluk. Kolli Hills spreads over an area
of 371 km2
with peaks rising to 1300 m.
The taluk has semi-arid type of climate,
and Thirumanimutharu and Kaveri rivers
pass through this taluk (15). The maxi-
mum temperature ranges from 28.10 to
37.85 o
C and the minimum from 20.85
to 25.40 o
C. The mean annual rainfall of
the taluk is 730.5mm. Paddy is the main
crop, followed by cholam, maize, ground-
nut, cotton, sugarcane, tapioca, onion,
turmeric and pulses. Total population as
per 2011 Census of the taluk was 5,29,343
with density being 350 persons per km2
.
About 55 per cent working population is
engaged in farming activities. The taluk
is known for egg production and sends
eggs to all over the country. Namakkal
is known as Egg City or Poultry Town. It
is also known for truck building industry.
Now in Namakkal taluk, 431 poultry farms
are located in 64 villages and the total
number of birds are 1,30,23,220. These
have been chosen for the present inves-
tigation.
MATERIAL AND METHODS
The present investigation is mainly based
on secondary data which is collected
from the various government and private
agencies in Tamil Nadu. In accordance
with collateral data, the SOI toposheet in
1:50,000 scale and maps from various or-
ganizations have been used for preparing
various thematic maps. Block map with
village boundaries were digitized to gen-
erate base layers using vector based soft-
ware. The village-wise spatial distribution
of poultry farms (2007-2008) data was col-
lected from District Poultry Development
Office, Namakkal. Simple statistical tech-
niques are used to calculate the percent-
age of spatial distribution of poultry birds,
estimation of poultry litter, estimation of

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POULTRY BIRDS AND POULTRY
LITTER
In Namakkal Taluk, the poultry farms
are located in 64 villages and the to-
tal number of birds are 1,30,23,220
in these poultry farms. The poultry
farms are not presented in 53 villag-
es. The spatial distribution of poultry
birds were analyzed using a GIS and
constitutes the basis for the estima-
tion and presentation of the avail-
able green energy potential. The
study shows that, the concentration
of poultry birds are at a high level
(more than 4 per cent) in six villages
(Table.1 and Fig.2). The main reason
is very good environment and in-
frastructural facilities present here.
Nineteen villages have 2 to 4 per
cent of poultry birds. In thirty nine
villages have less than 2 per cent
of poultry birds. Most of the poultry
farms are located along the trans-
portation lines and are having good
connectivity. This will help the rural
formers for increasing the income
from poultry farming and increase
the socio-economic condition of the
rural underprivileged society. The
physical quantity of poultry litter pro-
duced per day was estimated at the
village level, by using the average
amount of litter generated per bird.
The average amount of litter gener-
ated by a bird was assumed as 90
grams per day. Thus, the total quan-
tity of the poultry litter generated in
Namakkal taluk is about 1172 per
day (Table.1). The highest amount
of poultry litter were generated per
day was estimated at Marurpatty
and Ladduvadi villages, which gen-
erated 98 tonnes and 72 tonnes per
day (Fig.3). The moderate amount
(21 to 51 tonnes) of poultry litter was
generated by twenty villages. Forty-
two villages generated less than 20
tonnes of poultry litter per day. Poul-
try litter is a promising sustainable
energy resource that can help in re-
ducing the dependence on fossil fu-
els and to earn carbon credits.
biogas, green energy potential, enriched
methane gas, compressed methane gas
and carbon trading potential from poultry
litter.

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BIOGAS AND GREEN ENERGY
POTENTIAL
Biogas energy potential assessment is
based on compilation and computation
of poultry litter supply for energy genera-
tion. Farm wastes locally available are
used for extracting biogas from poultry lit-
ter. Assuming a production of 0.1 cu.m of
biogas from one kilogram of poultry liter,
it is estimated that Namakkal taluk can
produce biogas of 1,17,214 cu.m per day
(Table.1). Six villages are having highest
amount of biogas potential (Fig.4), the bi-
ogas production can totally go up to more
than 4200 cu.m per day. In nineteen vil-
lages, biogas production is between 1700
and 4200 cu.m per day. Thirty- nine vil-
lages have low level of biogas potential.
It may be less than 1700 cu.m per day. Bi-
oresource supplies are considered to as-
sess the energy potential in village-wise.
The theoretical potential is presented as
a thematic map of the total amount of bi-
ogas available in each village.
The estimation of green energy potential
was implemented in Geographical Infor-
mation System to obtain maps showing
village-wise variation of green energy po-
tential in the study area. Assuming that
one cubic metre of biogas may produce
two units of green electricity. The highest
amount of green energy potential per day
was estimated at six villages. It is about
more than 9 megawatt per day (Table.1
and Fig.5). Nineteen villages are estimat-
ed to possess 4 to 9 megawatt potential
per day. Thirty-nine villages produce low
level of green energy potential in less than
4 megawatt per day. Taking these into ac-
count, the great alternative green energy
potential assessed in Namakkal taluk is
2,34,000 KW (234 MW/day). The electric-
ity generated would be sold to the Tamil
Nadu State Electricity Board (TNEB) at
the rate of Rs. 4.50/KW. Namakkal Taluk
has the potential of income Rs. 10,53,000
per day.
ENRICHED AND COMPRESSED
METHANE GAS POTENTIAL
Natural gas has 75 to 98 per cent
methane with small percentages of
ethane, butane and propane while
biogas has about 60 per cent meth-
ane and 40 per cent carbon-di-oxide
and traces of nitrogen, sulphur and
moisture. It is possible to improve
the quality of biogas by removal of
CO2, H2S through scrubbing tech-
nique and enriching its methane
content up to the natural gas level.
Therefore, the eco friendly enriched
biogas potential is calculated and
assessed at village level. The total
amount of enriched methane gas
potential is 70,328 cubic metres per
day (Table.1) assessed in Namakkal
Taluk, Tamil Nadu, India. Six villag-
es are having high level of enriched
methane gas potential with more
than 2561 cu.m per day (Fig.6). The
moderate level distribution of en-
riched methane gas potential of be-
tween 1049 to 2560 cu.m per day,
is in nineteen villages. Thirty-nine
villages are estimated to have less
than 1048 cu.m per day. Enriched
methane gas potential presented in
the study area is a promising renew-
able energy resource, not only with
significant benefits with respect to
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the environment compared with
non-renewable fossil fuels, but also
as an alternative energy to meet en-
ergy demands.
There is large potential of enriched
methane gas to compressed meth-
ane gas potential available in Nam-
akkal Taluk to make it an alternate
fuel for vehicle. The present status
of the compressed methane gas po-
tential is assessed and maps have
been prepared in the study area. As-
suming that one cu.m of enriched
methane gas may produce 0.714 kg
of compressed methane gas, it is es-
timated that poultry droppings gen-
erated in Namakkal Taluk may pro-
duce about 50,214 kg compressed
methane gas per day (Table.1). In six
villages estimated high level is more
than 1829 kg per day (Fig.7) and in
nineteen villages it is estimated be-
tween 749 to 1828 kg per day. Thir-
ty- nine villages produce less than
748 kg of compressed methane gas
per day. This can be bottled in bio-
CNG cylinders and would be sold at
the approximate rate of Rs. 50 per
kg. Overall, the study revealed that
methane gas enrichment and com-
pression system is a profitable ven-
ture for rural areas due to availabil-
ity of large quantity of poultry litter.
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CARBON TRADING POTENTIAL
Projects that reduce methane emissions
are eligible to earn marketable assets,
generi¬cally called carbon credits. One
carbon credit usually represents the re-
duction of one metric tonne of carbon-di-
oxide or its equivalent in other greenhouse
gases such as methane and nitrous ox-
ide. Carbon credits are assets defined by
a variety of voluntary specifi¬cations, as
well as by national and international regu-
lations. Methane and nitrous oxide have
approximately 21 times and 310 times,
respectively, the heat-trapping capacity
of carbon-di-oxide. Reducing methane
by one tonne is equivalent to reducing
carbon-di-oxide by 21 tonnes (16). The
compressed methane gas potential avail-
able in Namakkal Taluk is 50 tonnes per
day. This compressed methane gas po-
tential is available to earn carbon credits.
This would be in the approximate rate of
Rs. 700 per tonne (10 euros for one Certi-
fied Emission Reduction). Namakkal Ta-
luk has the potential of additional income
of Rs. 35,000 per day or Rs. 10,50,000 per
month. This Clean Development Mech-
anism to reduce the green house gas
emissions and a tremendous potential to
earn carbon credits.
CONCLUSION
Proper management of poultry manure
as feed ingredient, fertilizer as well as a
safe biofuel with minimal negative impact
on environment. The Anaerobic Digester
gasification process offers considerable
energy recovery and reduces the emis-
sion of potential pollutants. Biogas energy
is a clean, pollution free and renewable
source of energy. The method of gener-
ating electricity from biogas resources is
one of the most effective ways to reduce
global warming emissions. Poultry litter
being generated continuously in Namak-
kal taluk may be profitably used, as it has
a potential of generating about 234 meg-
awatt of power per day. There is large
potential of enriched methane gas poten-
tial 70,328 cubic meter per day and com-
pressed methane gas potential 50,214 kg
Kilogram per day available in Namakkal
taluk, Tamil Nadu, India to make it an al-
ternate fuel for vehicle. This compressed
methane gas potential is available to
earn carbon credits. Namakkal Taluk has
the potential of additional income of Rs.
35,000 per day or Rs. 10,50,000 per month.
This Clean Development Mechanism to
reduce the green house gas emissions
and a tremendous potential to earn car-
bon credits. The system is recommended
to establish rural entrepreneurship for the
effective utilization of local resources, for
production of biogas energy in decentral-
ized manner, to earn carbon credits, en-
ergy security, reducing Green House Gas
emissions, sustainable rural development
and employment generation in the study
area.
1. Aurich, A.M., A. Schattauer, H.J. Hel-
lebrand, H. Klauss, M. Plochl, and W.
Berg, (2012). Impact of uncertain-
ties on greenhouse gas mitigation
potential of biogas production from
agricultural resources, Renewable En-
ergy, 37, (1), pp. 277-284.
2. Baban, S.M.J., and T. Parry, (2001).
REFERENCES
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Developing and applying a GIS-
assisted approach to locating wind
farms in the UK, Renewable Energy, 24,
pp. 59–71.
3. Census of India, (2011). Government
of India, Ministry of Human Resourc-
es, New Delhi.
4. Gelegenis, J., D. Georgakakis, I. An-
gelidaki, N. Christopoulou, and M.
Goumenaki, (2007). Optimization of
biogas production from olive-oil mill
wastewater, by co-digesting with di-
luted poultry-manure, Applied Energy -
APPL ENERG , 84, (6), pp. 646-663.
5. Goetz, S.J., A. Baccini, N.T. Laporte,
T. Johns, W. Walker, J. Kellndorfer,
R.A. Houghton and M. Sun, (2009).
Mapping and monitoring carbon
stocks with satellite observations: a
comparison of methods, Carbon Balance
and Management, 4,(2), pp.1-7.
6. Hanandeh, A.E., and A.E. Zein,
(2011). Are the aims of increasing
the share of green electricity genera-
tion and reducing GHG emissions al-
ways compatible? Renewable Energy,
36, (11), pp. 3031-3036.
7. Humbad, A., B.S. Kumar, and V.
Babu, (2009). Carbon credits for en-
ergy self sufficiency in rural India – A
case study, Energy Education Sci-
ence and Technology, Part A: Energy
Science and Research, 22, (2), pp. 187-
197.
8. Kapdi, S.S., V.K. Vijay, S.K. Rajesh,
and R. Prasad, (2005). Biogas scrub-
bing, compression and storage: Per-
spective and prospectus in Indian
context, Renewable Energy, 46, (4), pp.
238.
9. Madhusoodanan, (2010). Copenha-
gen: The way Forward, Energy Manager,
03, (1), pp. 18-20.
10. Oliveira, M.O., R. Somariva, O.H.
Ando Junior, J.M. Neto, A.S. Bretas,
O.E. Perrone, and J.H. Reversat,
(2012). Biomass Electricity Genera-
tion Using Industry Poultry Waste,
European Association for the Devel-
opment of Renewable Energies, En-
vironment and Power Quality, Inter-
national Conference on Renewable
Energies and Power Quality, Spain:
Santiago de Compostela, pp. 1-5.
11. Purohit, P., and A. Michaelowa,
(2008). CDM potential of SPV pumps
in India, Renewable and Sustainable En-
ergy Reviews, 12, pp.181–199.
12. Ramachandra, T.V., (2008). Geo-
graphical Information System Ap-
proach for Regional Biogas Potential
Assessment, Research Journal of Envi-
ronmental Sciences, 2, (3), pp. 170-184.
13. Saenz, R.D., P.B. Zarate Segura, C.
Guerrero-Barajas, and E.I. Garcia
Pena (2009). H2S and volatile fatty
acids elimination by biofiltration:
Clean-up process for biogas poten-
tial use, Journal of Hazardous Materials,
163, pp. 1272–1281.
14. Salminen, E., and J. Rintala, (2002).
Anaerobic digestion of organic solid
poultry slaughterhouse waste – a re-
view, Bioresource Technology, 83, (1), pp.
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13-26.
15. Soil Survey and Land Use Organi-
zation (1998). Soil Atlas, Namakkal
District, Coimbatore: Soil Survey &
Land Use Organization.
16. Westerman, P., M. Veal, J. Cheng
and K. Zering, (2008). Carbon Cred-
its for Methane Collection and Com-
bustion. North Carolina: Published
by North Carolina Cooperative Ex-
tension.
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A VILLAGE MODEL OF
SUSTAINABLE DEVELOPMENT
Malika Pal
Principal, Extol Institute of management, Bhopal
Email : drmalikapal@gmail.com
Ancient villages with reference to
their self-sufficiently and a way of life
which was aimed at sustainable de-
velopment, villages which were self-
dependent and self sufficient. The
quest took me to various places in the
interiors of M.P. The desire to see a
village surviving with minimal govern-
ment aid or government intervention
eluded me. So when I found the op-
portunity to visit Panchmari during the
Christmas holidays I extended and
modified it to a visit to Patalkot. I had
heard so much about it that it seemed
most incredible place on the Earth as
sunrays could reach the villages only
during the noon.
To me this visit was a pleasant surprise.
The name of the first village is Ratherh.
Our contact person at Tamia gave us
two names that would help us to see
the entire Patalkot; they were Bhura, a
jadi buti (local medicinal herb) expert,
and Rajkumar Bharti, the most educat-
ed person of Patalkot, now a teacher
at the local primary school. Two young
adventurous students of class 12th
also
accompanied us.
My quest for energy self sufficient village community took me to Patalkot. Electricity
reached the villages of Patalkot only in the month of October this year. Tamia is about
32 km from Chindwara form there one can reach Patalkot. It includes a cluster of 16
villages namely Raterh, Chimtipur, Jarh, Mandal, Harakachar , Khamarpur, Chotipeer,
Jhiran, Malani, Dokadahar, Sukhabhant, Devripatha, Kareaam, Gujja Dongi and Gel-
Dubba , at the depth of 1200-1500 ft in the Horse shoe shaped valley. The villages as
it seemed to me as self sufficient, producing their own food without the use of fertiliz-
ers and other farm chemicals. They get water from natural sources like the mountain
stream and three rivers –Gai, Dudhi and Cheeta rekha. They never felt any need to visit
a doctor and education imparted by the primary school is irrelevant to them. I person-
ally felt that development or so called betterment of these villages will actually destroy
a culture and store house of ancient wisdom.
INTRODUCTION
Key Words: Ancient Villages, Ethnic Bharia Community, Fertilizers And Other Farm
Chemicals.
32-37
AbstractAbstract
References: 01Pages: 06

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32-37
THE LOCATION
Tamia is approximately 35 km from Chind-
wara on the way to Panchmari. Patalkot is
a small cluster of 16 villages which are sur-
rounded by hills of Sahydri ranges from all
sides, forming huge walls of (1200-1500 ft)
sedimentary rocks. Earlier due to the pres-
ence of dense forest and steep descent,
sunlight rarely reached the ground. Now
due to deforestation day light reaches
the villages but the sun starts setting at
Patalkot by 3 pm. There was minimal in-
teraction with persons living on both sides
.It takes 30 minutes to climb down to the
first village Ratherh Plate I. Other villages
at the depth of 1200-1500 ft in the Horse
shoe shaped valley are Chimtipur, Jarh,
Mandal, Harakachar , Khamarpur, Choti-
peer, Jhiran, Malani, Dokadahar, Sukhab-
hant, Devripatha, Kareaam, Gujja Dongi
and Gel-Dubba ,. Though very few original
forest trees are left, still their remains are
obviously visible. We came across many
villagers climbing up with their head load
of fire woods and a bag full of ‘Jadi Buties’
for markets of Chindi Plate II. They were
neither annoyed nor surprised to see us
because this area is being opened up for
adventure sports activities and tourists
are constantly visit this place.
THE VILLAGE
The villages are simple with widely
spaced clusters of hut. The population
of the total _ villages is 350 people. Each
hut was surrounded by small farms of
beans Plate III and tooar dal Plate IV. They
do not use any kind of fertilizers or other
agro-chemical products, a walk through
the farms revealed that indeed the crop
was healthy with no signs of chronic dis-
ease or pests. They grew corns, paddy,
barbate, kutki, kondo, etc. Most of these
are for their personal use only. They only
sell tooar dal to the markets of Chindi.
But the main exports from the area are
various jadi buties which men folk collect
from the surrounding hill and forests. The
animals like cows, goats and hens are
there for their personal use. Wheat and
salt are the two main things which they
purchase from markets. The villages are
well supplied with water as three rivers,
Doodhi, Gaye, Cheetah Rewa cris-cross
the villages and apart from that various
natural jhirries immerge on rock side from
time to time. We have also seen tube-
well and a well in Ratherh village. It has
a small school. Several stop dams have
been built with Government aid to further
ease the problem of water. We met many
children- Sukhan Singh, Sundaria, and
Sunita, who happily told their classes. The
children here as seemed to me as healthy
and happy as anywhere else.
SOCIAL LIFE
The family of parent and siblings live in
small huts. Majority of their activities are
out door so hut are small with 2-3 rooms,
which have space for hens to brood and
for very young calf as they are treated as
family members Plate V. The belongings
included some vessels for the storage
of water, for cooking, for eating and few
clothes. Stone grinders to grind cereals
are built within the huts. The average age
of marriage is 22-yrs or more for both girls
and boys. The marriages are arranged
within Bharia community. They have cus-
tom of giving valuables to girl during mar-
riage. The festivals they celebrate are Holi,
Diwali and Pola. They do no have any tra-

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ACKNOWLEDGEMENTS
Author wish to thank the managerial
board of Extol Institute of management,
Bhopal, for their co-operation and sup-
port.
32-37
dition of bhagoria. The festival of Pola is
celebrated in savan or rainy season. In this
festival they worship Nag deity and Guari-
made up of bamboo, make savethatera
and dance with beat of ramdhol.
All the ailments are treated personally by
the use of local herbs and never felt the
need to visit doctors. They burry the dead
body as it costs nothing. They generally
avoid burning due to the cost involved in
the Vedic method of cremation.
All the cattle of a village are taken to pas-
ture by one person only. All the disputes
what so ever were mitigated by village
elders. There were no signs of police sta-
tion or weapons of any kind in their hous-
es. Any kind of lock or bolt system on the
doors of those huts was not seen.
GOVERNMENT AID
This ethnic Bharia community is living in
this area from ages. Distribution of ration
started about a decade ago or so. The
village school is up to class 5th
only and
for further studies students have to go to
schools located at Bijar and Tamia which
are 20-25km away from the village.
Distribution of ration, wheat, rice, sugar,
kerosene is or for them, because these
things are not main part of their diet. They
normally relish maize flour, baller ki dal,
tooar ki dal and kodo ki chutney. This dis-
tribution began a decade or so. Electricity
reached the village only in October 2010.
CONCLUSION
What I personally felt that these people
are fairly self sufficient. It is not justified to
compare them with urban poor people.
Earning money and stuffing big houses
with energy consuming gadgets is not
their way of life and thinking. The little
money they need they acquire by work-
ing as labor, generally to bring clothes
and salt. Clothes again are not needed as
style statement; it is needed only to save
them from wrath of seasons. Little furni-
ture which they need they make them-
selves from bamboo (purchased from
Tamia) and wood. Their energy require-
ment is low. They do not need any kind
of transportation so not pollution due to
burning of fossil fuel. They use local pro-
duce and generate little waste, which is
biodegradable. They know how to man-
age their recourses. It will be better if we
learn from them instead of teaching them
our exploitive way of life. This cluster of a
few hutments can be safely dubbed as a
model of sustainable development. We
should learn to minimize needs. This will
also lead to the conservation of biodiver-
sity.

35 ••
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Plate I. Ratherh
Plate II- Bhurias selling‘Jadi Buties’
Plate III small farms of beans
Plate IV tooar dal (.lenticels )
32-37

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Plate V Hut from in side.
Plate VI-The rich biodiversity of the
area
Plate VII- Origin of river Gai
Plate VIII – Drying maize cobs
32-37

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REFERENCES
1. Retrieved July 24, 2010
from http://iweoxplore.
ieee.org/stanp/platevii.jsp?arnusber.04141663.
1141.
32-37
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TECHNOLOGY IN MATHEMATICS EDUCATION
Presentation of Material Developed for First year calculus
Topics – Formal-Definition of Limit
Barun Maity
Department of mathematics
Pingla Thana Mahavidyalaya, Maligram, Paschim Medinipur, West Bengal-721140
Email : barunmaity1986@gmail.com
This chapter presents interactive class
notes and various demonstrations de-
signed for use in a first year calculus
course. For more in depth information
on the tropics, see Stewart [24]. The
class materials are all developed in Ma-
ple and available on the CD provided. A
sample class from the interactive notes
is available in Appendix C. Printed code
for one demonstration is available in
Appendix D. The interacti9ve notes were
developed fro a first semester calculus
course at the University of Guelph. The
notes were designed to be used during
34 one-hour classes. The notes com-
prised the body of the course manual
students were required to purchase.
The notes were 60%-80% complete with
the remaining to be filled in by students
in class. The notes were fully executa-
ble meaning that every problem could
À set of interactive class notes and a library of computer demonstration designed to be
used in and out of material developed for first year calculus classroom are presented.
The maximum area of this are explained by the modern technology. The demonstra-
tion are coded in Maple and designed to give geometric understanding to challeng-
ing calculus concepts. The interactive notes were first implemented in the fall 2010
semester, in a class of approximately 600 students were designed to be used during
34 one hour classes. Also the notes were 60%-80% complete with the remaining to
be filled in by students in class and were fully executable,meaning that every problem
could be answered using the software. The class materials are all developed in Ma-
ple and available on the CD provided.It is important to note that the discussion in this
paper only give some suggestions on the use of these programs and that if instruc-
tors choose to utilize these tools, they will likely find other uses the better fit their own
teaching style and course to maximize the potential benefit. This Paper will give insight
info the uses and benefits of computer – aided instruction (CAT) in a mathematics
classroom.
INTRODUCTION
Key Words: Interaction Notes, Learning Tools, Formal Limit, Potential Benefit.
38-44
Pages:7 References: 16
AbstractAbstract

39 ••
www.manishanpp.com
be answered using the software. This
could be used by the instructor as an
opportunity to discuss why the answer
found on paper may differ .
38-44
The formal mathematical definition of a
limit is typically presented after students
have experience calculating limits. This
topic is notoriously difficult for first-year
students to grasp. There are two common
issues that lead to trouble understanding
this topic. The first is the fact that there are
various forms of the definition depending
on if the point of interest is finite or wheth-
er the limiting value tends to infinity. The
secondisthatthedefinitionsaredensewith
mathematical notation making it difficult
tofindageometricunderstanding.Wenow
introduce some of these limit definitions.
Definition 4.1 Assume that f(x) is a real-
valued function defined in some open
neighbourhood of a real number a. The
limit of the function f(x) as x approaches
a is the finite number L, written
limf(x) (x→a)
= L, if ε > 0 Ǝ δ > 0 such
THE FORMAL DEFINITION OF A
LIMIT
Description of the Lesson
showing the function, horizontal bars in-
dicating the range ly — Ll < ε, and vertical
bars outlining the range Ix = al <δ. The ani-
mation shows delta increasing from zero
tothemaximumδvalue.Aseriesofframes
from a typical animation Can be found
inFigure4.1.Theprogramalsoshowssmall
dashed horizontal lines indicating the
bounds of where the function val-
ues lie, showing that small-
er values of δ often result
in the function being closer than ε to the
limit value. This procedure can also be
used to animate one-sided limits. de-
fined in Definition 4.2.
that if 0<| x-a |<δ then | f(x)-L |<ε.
Definition 4.2 Assume that f(x) is a real-
valued function defined on some open
interval (a,b), b>a. The one-sided limit
of the function f(x) as x approaches a
from the right is the finite number L, writ-
ten limf(x) (x→a)
= L, if ε>0 Ǝ δ>0 such
that if 0< x-a < δ then | f(x)-L | < ε.
A
A
The program then calculates the limit Of
the function at the given point and the
maximum value for the given E. Using this
information, an animation is displayed.

40 ••
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38-44
The procedure for limits taken at infin-
ity, defined in Definition 4.3, is called
FormalLimitAtInfinity. The user enters a
function, specifies positive or negative
infinityandavalueforε.Theprogramthen
calculates the limit specified and the
minimum N value for the given
ε. An animation displaying
the function, horizontal
lines showing the range
ly— Ll <ε and a vertical line
showing the minimum N value.
A second vertical line from the mini-
mum N to infinity showing that for any
values larger than the minimum N, the
function is Still within ε of the limit value
(in the case that the lim-
it is taken as x→+∞). A se-
ries of frames from an example
animation can be found in Figure 4.2.
The final procedure discussed in this sec-
tion illustrates limits that tend to infinity,
defined in Definition 4.4, and is called For-
malLimitToInfinity. The user must enter
a function, a point to take the limit and a
value for N. The procedure then calculates
the limit (which must be positive or nega-
tive infinity) and maximum δ value for the
given N. An animation showing the func-
tion, a horizontal line showing the given N
and vertical bars showing the current δ
range is displayed. The animation shows δ
Starting at zero and increasing until the
maximum δ value is reached. The students
will that for any δ smaller than the maxi-
mum δ.

41 ••
www.manishanpp.com
38-44
x tends to infinity shows the optimal (mini-
mum) N value and then shows larger N
values. Going from the optimal to larger N
seemed to better illustrate a limit at infinity.
It is important to not let these demonstra-
tions stand on their own, but rather as
a tool to bring life to the in-class explana-
tions. For instance, these animations can
also lead to conversations with the class
as to why a particular definition works to
describe a certain limit. For instance con-
sider a limit taken at infinity, as defined
in Definition 4.3 and illustrated in Figure
4.2. The instructor may focus on just the
first frame and point out that long as x
is to the right of the vertical blue line,
the function is always within E of the lim-
it value. The instructor could then stress
that this is exactly what “ if x > N then
I f(x) — Ll < ε means. Similar observations
could help reinforce why Oth-
er limit definitions are used.
These tools have great potential to give
students a geometric understanding of
the formal definition Of a limit. In order to
stress that the definition of a limit changes
when infinity is involved, the choice was
made to create programs to illustrate the
different limits. It would have been pcxsi-
ble to have the user enter a function and a
point and hawe the program decide which
definition needed to be used, but we want-
ed the students to make this decision if
they are using the programs on their own.
The animation to demonstrate limits
where x tends to infinity is qualitatively
different from the other demonstrations.
The limits taken at a finite point show the
smaller δ values first, then stop at the
optimal δ value. The animation for limits
where
DISCUSSION AND SUGGESTED
USE

42 ••
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38-44
A typical problem students may be asked
to complete, along with a common error
students may make, is presented below
in Figure 4.4. The student has outlined the
largest possible interval around x = a
that satisfies the condition | If(x) — L | < ε.
The issue with this solution is obvious:
the region the student has outlined is not
symmetric about the point x = a, but any
region of the form Ix — al< δ must be.
The Formal Limit procedure may be used
to help students understand this particular
error. The student will see that the val-
ue increases, the interval | x-a | < δ al
grows, but remains centered at x = a. The
student will also observe that once the
function crosses one of the horizontal
lines representing L + ε or L — ε, both sets.
Figure 4.4: A common sample problem in a first-year formal limit
definition unit, along with a Common error students may make.
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ner, R., “Comparison ofstudents
performance using web and paper-
based homework incollege-level
physics”, Journal of Research in Sci-
ence Teaching, Vol30, No 10, 2003, pp.
1050-1071.

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4. Brown, B. and Liedholm, C., “Can
web course replace theClassroom in
principles of microeconomics? :, The
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761-768.
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Prof. T.R.C Sinha a true lover of science
and always concerned about the environment.
It was his dream to publish scientific jour-
nals and he started this project with the same
enthusiasm as he had done for every project
he undertook.We are guided by the vision of
Prof. Sinha and endeavour to make his dream
of promoting science and help young scientists,
publish their articles and encourage them in
their research.
Manisha Verma

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York. p. 12.
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isotope ratios of some mangroves in North Queensland. In: H.J. Teas (Ed.), Physiology and Management of Mangroves. W. Junk.
The Hague. pp. 15-23.
From website:-National Oceans and Atmospheric Administration (NOAA). 1995. Regional Perspectives: Indian
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Volume No. 2, Issue No. 2, 2014
C o n t e n t s
Reviewed Articles
1.
2.
3.
4.
1
17
32
38
December, 2014
ACADEMIC AND RESEARCH
PUBLICATIONS
H.Office: EC 41, Maya Enclave,
New Delhi -110064
Email : manik.sinha2@gmail.com
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Delineation Of Groundwater Potential Zones
In Coimbatore District, Tamil Nadu,
Using Remote Sensing And Gis Techniques
P. Meenakshi, K. Kannadasan and A. Ganesh
Green Energy Production Technology For Clean Environment
And Carbon Trading Potential From Poultry Litter In Namak-
kal Taluk, Tamil Nadu, India Using Gis
Dr. P. Gunasekaran and Dr. A. Ganesh
A Village Model Of Sustainable Development
M.Pal
Technology In Mathematics Education
Presentation Of Material Developed For First Year
Calculus Topics – Formal-Definition Of Limit
Barun Maity
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