ENGRD 241: Engineering Computation
Curve Fitting by Least Squares:
Given a set of points: experimental data, tabular data, etc.
Fit a curve (surface) to the points so that we can easily evaluate f(x) at any x of
If x within data rang
1 Monday, June 13, 2011
Metallurgical engineering is one of the most interesting
branches of engineering.
Metallic compounds can be found in jewelry, vehicles and
many items we use in our everyday life.
Metallurgical engineering is a branch of engineering
Peoples Small-Scale Mining Areas
From RA 7076
(Peoples Small-Scale Mining Act o f 1991)
areas refer to
areas with naturally occurring
Small-scale mining refers to
UPSTREAM AND DOWNSTREAM
The upstream stage of the production process involves
searching for and extracting raw materials. It does not do
anything with the material itself, such as processing the
The downstream stage in the production
A tax "is not a voluntary payment or donation, but an enforced
contribution, exacted pursuant to legislative authority" and is "any
contribution imposed by government.
Where do taxes go?
the enforcement oflaw andpublic order protection
What is responsible mining?
Responsible miningrefers to advocacy to
Dave Toycen (Pres. and CEO of WVC)
Responsible mining means respecting the
environment by meeting and exceeding national and
international norms, and seek
In the mining industry, we encounter terms such as upstream and downstream processing.
These two processes generally make up the mining process and are related to each other. That is
why one must be able to understand the upstream process to comprehend wi
1) Section 19 of RA No. 7942
2) National Integrated Protected
Areas System (NIPAS) under RA
3) RA No. 6657, or the
Comprehensive Agrarian Reform
Law of 1988
Mining ban expanded
4) 78 tourism Dev
CHILD ABUSE AND NEGLECT
USER MANUAL SERIES
The Role of E ducators in
Preventing and Responding to
Child Abuse a nd N eglect
U.S. Department of Health and Human Services
Administration for Children and Families
Administration on Children, Youth and Familie
Illustrates the stable phase/s present in a system
at a given condition (pressure, temperature and
Provides a correlation between the
microstructure of materials and its mechanical
Used in the design and control o
Interpolation & Extrapolation
Interpolation: data to be found are within the range of
Extrapolation: data to be found are beyond the range of
observation data. (not reliable*)
Interpolation vs. Regress
f ( x)dx = f ( x)dx + f ( x)dx
where A is sufficiently large so the function is approaching zero at least as fast as 1/x .
To avoid evaluating a function at one of the limits, use one of the open forms of the Newton-Cotes
formulas given in the
Newton-Cotes Integration (C&C Chap. 21, p. 582):
Section 6 - Numerical Integration and Differentiation
Two general types of integrations are solved numerically, ones where the function is presented as
tabulated data or as a complicated function.
6.1 Newton-Cotes Formulas
The Newton-Cotes formulas are ba
Without going into too much detail, computers (and calculators) retain only a fixed number of
significant figures during calculations. This leads to what is known as round-off error. The
following aspects are always important to keep in mind when performi
mathematical model with measured data.
Trend analysis. Predicting values of dependent
variable, may include extrapolation beyond data
points or interpolation between data points.
In engineering, two types of applic
The above stands for integral of function f(x)
with respect to the independent variable x
between the limits x = a to x = b.
I f ( x ).dx
I f ( x ).dx A
Graphically integration is simply to find the
area under a certain curve between the 2
f ( xi )
f ( xi )
f ( xi 3 ) 3 f ( xi 2 ) 3 f ( xi 1 ) f ( xi )
f ( xi 2 ) 2 f ( xi 1 ) 2 f ( xi 1 ) f ( xi 2 )
f ( xi 1 ) 2 f ( xi ) f ( xi 1 )
f / ( xi )
f / ( xi )
f ( xi 1 ) f ( xi 1 )
f / ( x
What is responsible
Holcim Philippines, Inc.
Established in 1974
One of the world's leading
suppliers of cement and
Occupational Health and
Holcim 'galing Mason