This word file contains history, applications, pros and cons of numerical integration methods, to be precies (Open Newton cotes and Closed Newton Cotes Methods) along with a flowchart and algorithm explaning the structure and flow of a MATLAB program working on Numerical Integration Methods.
The refernces are also linked in the end.
A short presentation on the topic Numerical Integration for Civil Engineering students.
This presentation consist of small introduction about Simpson's Rule, Trapezoidal Rule, Gaussian Quadrature and some basic Civil Engineering problems based of above methods of Numerical Integration.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
Regula Falsi or False Position Method is one of the iterative (bracketing) Method for solving root(s) of nonlinear equation under Numerical Methods or Analysis.
A short presentation on the topic Numerical Integration for Civil Engineering students.
This presentation consist of small introduction about Simpson's Rule, Trapezoidal Rule, Gaussian Quadrature and some basic Civil Engineering problems based of above methods of Numerical Integration.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
Regula Falsi or False Position Method is one of the iterative (bracketing) Method for solving root(s) of nonlinear equation under Numerical Methods or Analysis.
This ppt covers following topics of Unit - 2 of B.Sc. 2 Mathematics Rolle's Theorem , Lagrange's mean value theorem , Mean value theorem & its example .
This lecture contains Newton Raphson Method working rule, Graphical representation, Example, Pros and cons of this method and a Matlab Code.
Explanation is available here: https://www.youtube.com/watch?v=NmwwcfyvHVg&lc=UgwqFcZZrXScgYBZPcV4AaABAg
Applied Mathematics and Sciences: An International Journal (MathSJ)mathsjournal
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
Efficient Accuracy: A Study on Numerical Integration. ShaifulIslam56
Efficient Accuracy: A Study on Numerical Integration. Numerical Integration: Trapezoidal rule. Simpson's 1/3 rule. Simpson's3/8 rule. Weddle's rule etc.
This ppt covers following topics of Unit - 2 of B.Sc. 2 Mathematics Rolle's Theorem , Lagrange's mean value theorem , Mean value theorem & its example .
This lecture contains Newton Raphson Method working rule, Graphical representation, Example, Pros and cons of this method and a Matlab Code.
Explanation is available here: https://www.youtube.com/watch?v=NmwwcfyvHVg&lc=UgwqFcZZrXScgYBZPcV4AaABAg
Applied Mathematics and Sciences: An International Journal (MathSJ)mathsjournal
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
Efficient Accuracy: A Study on Numerical Integration. ShaifulIslam56
Efficient Accuracy: A Study on Numerical Integration. Numerical Integration: Trapezoidal rule. Simpson's 1/3 rule. Simpson's3/8 rule. Weddle's rule etc.
NUMERICA METHODS 1 final touch summary for test 1musadoto
MY FINAL TOUCH SUMMARY FOR TEST 1
ON 6TH MAY 2018
TOPICS AND MATERIALS COVERED
1. Class lecture notes (Basic concepts, errors and roots of function).
2. Lecture’s examples.
3. Past Years Examples.
4. Past Years examination papers.
5. Tutorial Questions.
6. Reference Books + web.
Symbolic Computation via Gröbner BasisIJERA Editor
The purpose of this paper is to find the orthogonal projection of a rational parametric curve onto a rational parametric surface in 3-space. We show that the orthogonal projection problem can be reduced to the problem of finding elimination ideals via Gröbnerbasis. We provide a computational algorithm to find the orthogonal projection, and include a few illustrative examples. The presented method is effective and potentially useful for many applications related to the design of surfaces and other industrial and research fields.
A NEW STUDY OF TRAPEZOIDAL, SIMPSON’S1/3 AND SIMPSON’S 3/8 RULES OF NUMERICAL...mathsjournal
The main goal of this research is to give the complete conception about numerical integration including Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to determine the best method, as well as the results, are compared. It includes graphical comparisons mentioning these methods graphically. After all, it is then emphasized that the among methods considered, Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving a definite integral.
NP Complete problems in the field of graph theory have been selected and have been tested for a polynomial solution. Successfully studied and implemented a few solutions to various NP-Complete Problems. Various polynomial time reductions are also been studied between these problems and and methods have been worked on. I have secured a letter of appreciation from the Guide for my performance during the course of the Internship.
Overviewing the techniques of Numerical Integration.pdfArijitDhali
In this presentation we discuss the ways of integrating a function using trapezoidal, simpsons 1/3,3/8 and boole's method. We also discussed its error and analysised other ways to solve it than mention.
AN ALTERNATIVE APPROACH FOR SELECTION OF PSEUDO RANDOM NUMBERS FOR ONLINE EXA...cscpconf
Fast and accurate selection of random pattern is needed for many scientific and commercial applications. One of the major applications is Online Examination system. In this paper, a sophisticated approach has been developed for the selection of uniform pseudo random pattern for Online Examination System. Three random integer generators have been compared for this
purpose. Most commonly used procedural language based pseudo random number; PHP random generator and atmospheric noise based true random number generator have been considered for easy generation of random patterns. The test result shows a varying degree of improvement in the quality of randomness of the generated patterns. The randomness quality of the generated pseudo random pattern has been assured by diehard test suite. An experimental
outcome for our recommended approach signifies that our approach selects a quality set of random pattern for Online Examination System
This Presentation Is Specially Made For Those Engineering Students Who are In Gujarat Technological University. This Presentation Clears Your All Doubts About Basics Fundamentals of Numerical Integration. Also You Will Learn Different Types Of Error Formula To Solve the Numerical Integration Sum.
Similar to Numerical Integration Project Report (20)
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
2. CONTENTS:
History and background of Numerical
Integration
Flowchart, Algorithms and Programs
Pros & Cons of Numerical Integration
Summary
References
3. HISTORY OF
NUMERICAL
INTEGRATION
The term "numerical integration" first appears in 1915 in the publication A Course in Interpolation
and Numeric Integration for the Mathematical Laboratory by David Gibb.
The beginnings of numerical integration have its roots in antiquity. A prime example of
how ancient these methods are, is the Greek quadrature of the circle by means of inscribed and
circumscribed regular polygons. This process led Archimedes to an upper bound and lower bound for the value Pi.
These methods were used widely due to the lack of formal calculus. The method
of the sum of an infinitesimal area over a finite range was unknown until the sixteenth century
when Newton formalized the concepts of what we know now know as calculus. The earliest forms
of numerical integration are similar to that of the Greek method of inscribing regular polygons
into curved functions. This process broken down was taking a known area and overlapping it with
an unknown area to approximate the area of the unknown shape. One could improve accuracy by
choosing a better fitting shape. Later methods decided to improve upon estimating area under a
curve decided to use more polygons but smaller in area. Such an example is the use of rectangles
evenly spaced under a curve to estimate the area. Even further improvements saw the use of
trapezoids instead of rectangles to better fit the curvature of the function being analyzed. Today
the best methods for numerical integration are known as quadrature methods that have a very
small error.
4. Start
Input ‘eq’
equation, limits
‘x0, x1’ & ‘N’
If N == 1
Formulate
Trapezoid
Equation
Formulate
Simpson’s
1/3 Equation
Formulate
Simpson’s
3/8 Equation
If N == 2
If N == 3
A
N
Yes
Yes
Yes
No
No
No
CLOSED
NEWTON
CROOTES
5. A
N
=
=
1
If N == 4
Formulate
Boole’s
Equation
Default
Invalid
Input
Show ‘ans’
Answer
End
End
Yes
Yes
No
6. Start
Input ‘eq’
equation, limits
‘x0, x1’ & ‘N’
If N == 1
Formulate
using
Formula 1
Formulate
using
Formula 2
Formulate
using
Formula 3
If N == 2
If N == 3
A
N
=
Yes
Yes
Yes
No
No
No
OPEN
NEWTON
CROOTES
7. A
N
=
=
1
If N == 4
Formulate
using
Formula 4
Default
Invalid
Input
Show ‘ans’
Answer
End
End
Yes
Yes
No
10. Reasons for numerical integration
There are several reasons for carrying out numerical integration.
1. The integrand f(x) may be known only at certain points, such as obtained by sampling. Some
embedded system and other computer applications may need numerical integration for this reason.
2. A formula for the integrand may be known, but it may be difficult or impossible to find an
antiderivative that is an elementary function. An example of such an integrand is f(x) = exp (−x2),
the antiderivative of which (the error function, times a constant) cannot be written in elementary
form.
3. It may be possible to find an antiderivative symbolically, but it may be easier to compute a
numerical approximation than to compute the antiderivative. That may be the case if the
antiderivative is given as an infinite series or product, or if its evaluation requires a special function
that is not available.
Applications:
it helps to
Find the area
Locate the centroid
Find the arc length of graph
Find the surface area of solid
Find the volume of a solid figure
Solve for the work done
Solve the moment of inertia
It is also used to find
Water plane area
Sectional area
Submerged volume
Longitudinal center of floatation
Pros
PROS & CONS
FOR NUMERICAL
INTEGRATION
11. Possible to integrate any function
Multidimensional integrals are straightforward
Ability to solve integrals along irregular domains in multidimensional spaces (any shape).
Numerical integration gives you an answer to some problems that analytic techniques don’t.
Cons
There is an intrinsic error in calculation
Numerical integrals are, always, computationally expensive.
12. SUMMARY AND
REFRENCES
Wikipedia
Quora
California University papers
MATLAB Documentation
In numerical analysis, numerical integration constitutes a broad family of
algorithms for calculating the numerical value of a definite integral, and by
extension, the term is also sometimes used to describe the numerical solution of
differential equations. This article focuses on calculation of definite integrals. The term
numerical quadrature (often abbreviated to quadrature) is more or less a synonym
for numerical integration, especially as applied to one-dimensional integrals.
Integration has been there since even before the proper use of calculus. In modern
day integration has led to some great creations including the petronas towers and
the Sydney opera house.