This document provides an introduction and overview of numerical analysis. It begins by stating that numerical analysis aims to find approximate solutions to complex mathematical problems through repeated computational steps when analytical solutions are not available or practical. It then discusses that numerical analysis is important because it allows for the conversion of physical phenomena into mathematical models that can be solved through basic arithmetic operations. Finally, it explains that numerical analysis involves developing algorithms and numerical techniques to solve problems, implementing those techniques using computers, and analyzing errors in approximate solutions.
Numerical Analysis And Linear Algebra..
these slides Are very Informative.. In Short Time you Can Get Enough Knowledge of Linear Algebra As well As Numericals
Numerical Analysis And Linear Algebra..
these slides Are very Informative.. In Short Time you Can Get Enough Knowledge of Linear Algebra As well As Numericals
c++ computer programming language datatypes ,operators,Lecture 03 04jabirMemon
Data types
Data literals
Variables
Constants
Rules for naming variable and constant
Operators ,Problem solving
Six steps towards problem solution
Basic problem solving concepts
A brief study on linear programming solving methodsMayurjyotiNeog
This small presentation includes a brief study on various linear programming solving methods. These methods (graphical & simplex) are used to solve industrial engineering related problems in practical use.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
2. Aims and ObjectivesAims and Objectives
After completing this course you should be able
to:
1.Understand the importance of numerical
analysis;
2.Learn the development of Mathematical
Models related to Engineering and Science
problems;
3.Apply various methods in different fields of
Engineering.
3. IntroductionIntroduction
In real world how the solutions of any physical
problems can be obtained?
Two ways to find the solution of physical
problems in real world:
1.Experimental:
•Laboratory experiments;
•Field observations / Study;
4. IntroductionIntroduction
Experimental studies (both Laboratory and
Field Observations) are very expensive, time
consuming and specific (parameter dependent);
2.The alternate way is mathematical solution.
Mathematical solution can be obtained in two
ways, i.e., Analytical methods and numerical
Methods.
19. Zero order approximation First-order Second-order
Based on the strategy of replacing a complicated function or
tabulated data with an approximating function that is easy to
integrate:
∫∫ ≅=
b
a
n
b
a
dxxfdxxfI )()(
)( 10
n
nn xaxaaxf +++=
20. a b
To find the area in between a
and b where
A = 0 and b = 125 cm and
space of each line is h = 1 or
0.5 or 0.1
22. There are two ways
•Either use Laboratory instruments to
the area of whole length of the geometry
•Either use numerical methods to find
the area of small rectangles/squares
then sum of all rectangle or squares
25. IntroductionIntroduction
In real world many physical problems are
complex for which analytical solution may not
be available or may be so complex that they
are quite unsuitable for practical purposes. In
this situation, the only alternate way is to
approximate the problem. The approximate
solution can be obtained through automatic
computation to a repetition process of series of
steps. Such process is known as numerical
methods and the analysis of such methods is
called Numerical Analysis.
26. IntroductionIntroduction
The subject of numerical analysis is concerned
with the derivation, construction of algorithm,
implementation and analysis of method for
finding optimal approximate / numerical
solution to complex mathematical problems up
to desire (given) degree of numerical accuracy.
28. IntroductionIntroduction
What is numerical analysis?
• Branch of science which deal with numbers
and algebraic operations, and repeated
steps;
• Art to design algorithm;
• Involves engineering and physics.
29. IntroductionIntroduction
Why numerical analysis?
• Converting a physical phenomenon into
mathematical model;
• When exact/analytical solution or close form
is not available;
• Complex problems can be solved with simple
arithmetic operations;
30. Why numerical analysis?Why numerical analysis?
• Numerical analysis involves mathematics in
developing techniques for the approximate
solution of the mathematical equations
describing the model and involves basic
arithmetic operations.
• Finally, numerical analysis involves
computer science for the implementation of
these techniques in a optimal fashion for the
particular computer.
31. Numerical MethodsNumerical Methods
Main aim / objective of numerical methods is to
provide practical procedure for calculating the
approximate solution of problems in applied
mathematics to a specified degree of accuracy.
It is study of relations that exist between the
values assumed by the function when ever the
independent variable changes by finite jumps
whether equal or unequal.
32. Numerical MethodsNumerical Methods
Main aim / objective of numerical methods is to
provide practical procedure for calculating the
approximate solution of problems in applied
mathematics to a specified degree of accuracy.
It is study of relations that exist between the
values assumed by the function when ever the
independent variable changes by finite jumps
whether equal or unequal.
33. Error AnalysisError Analysis
What is error?
Definition: An error is basically the deflection
of computed/estimated/observed values from
actual/computed/targeted values .
In other words error is a difference between
actual and computed values.
34. Error AnalysisError Analysis
Errors analysis is the study of estimation of
accuracy of the approximate solution with
exact solution and suggest the ways to
eliminate or minimise difference or
enhancement of the accuracy. Estimation of
error is used to find the optimal numerical
solution.
35. Error AnalysisError Analysis
Here various types of errors are discussed,
there source and the nature of their
propagation.
Sources of errors:
In many computational techniques there is the
requirement of precision of significant figures.
The significant figure is a number that carries
real information about the magnitude of
number.
36. Error AnalysisError Analysis
Some times in calculations we approximate
values, so as to make the values smaller than
their original size thus making calculations
much more simplified.
This process may be very useful, but it causes
the errors to occur. Errors in computational
field are surplus to requirements. Because of
this first of all we analyse the errors and than
seek to avoid them in the best possible manner.
36
37. Error AnalysisError Analysis
Types of error:
Errors are classified as follows:
•Gross errors;
•Round off error;
•Truncation error;
•Inherent error;
•Absolute error;
•Relative absolute percentage error;
•Root mean square error;
38. Error AnalysisError Analysis
GROSS ERRORS:
Not directly related with most of the numerical
methods, may have great impact on the success
of modelling efforts. Examples of this type of
error are: use of inaccurate data, mathematical
formulae, algorithm and mishandling of in the
interchanging of neighbouring digits.
39. Error AnalysisError Analysis
ROUND OFF ERRORS:
These errors are unavoidable in most of the
calculations since some of the quantities in the
calculations will be non-terminating decimal
places and for practical reasons only certain
number of will be carried in calculations. These
are due to the fact that in computational work
we have to deal with approximations.
40. Error AnalysisError Analysis
TRUNCATION ERRORS:
These are caused by the use of a closed form,
such as the first few terms of an infinite series
to express a quantity defined by the limiting
process. For example, such errors occur when
a definite integral is computed by Simpson’s
rule or when a differential equation is solved
by some difference method.
41. Error AnalysisError Analysis
PROPAGATION OR INHERENT ERRORS:
These errors are due to the approximate
nature of the applied formulae used in the
solution. It is caused by the use of previous
points calculated by the computer which
already has errors owing to the two errors
above since we are already off the solution
curve, we cannot expect any new points we
compute it to be the correct solution curve.
42. Error AnalysisError Analysis
Some definitions: Before proceeding further, it
would be constructive to have knowledge about
some following terms
•Significant digits;
•Precision and accuracy;
•Absolute, relative and percentage;
43. Significant digitsSignificant digits
A significant digits in an approximate number
is a digit, which provides reliable information
regarding the magnitude of number.
Alternatively, a significant digit is used to
express accuracy, i.e., how many digits are
meaningful in the number.
44. Significant digitsSignificant digits
Rules for significant digits:
•Leading zeros are not significant; The no.
0.0002025 has four significant digits.
•Following zeros that appear after the decimal
point are significant; The no. 0.00202570 has
six significant digits.
45. Significant digitsSignificant digits
• Following zeros that appear before the
decimal point may or may not be
significant, as more information is
required for decision; 202570 has four,
five, six or seven significant digits
depending upon the situation.
• The significant digit in a number do not
depend on the position of the decimal point
in the number; The no. 12456 and .12456
both contain five significant digits.
46. Precision and AccuracyPrecision and Accuracy
Precision and Accuracy are often confusing !!
Precision is the number of digits in which a
number is expressed.
Accuracy is the number of digits to which
solution is correct: to a given number of
decimal places or significant figures.
47. Numerical AnalysisNumerical Analysis
In numerical analysis the robustness of the
numerical algorithm depends on the accuracy
of the approximate numerical solution,
convergence and stability of the numerical
method has always of great importance.
48. Error AnalysisError Analysis
ABSOLUTE ERRORS:
The absolute error of number, measurement,
or calculation is the numerical difference
between the true value of the quantity and its
approximate value as given or obtained by
measurement or calculation. If Xa and Xc are
respectively the actual and computed solution
of a quantity, then the absolute error (AE) is
define by, a cAE X X= −
49. Error AnalysisError Analysis
RELATIVE ERRORS:
The relative error is the absolute error divided
by the true value of the quantity or ration of
absolute error and actual solution. Then the
relative error (RE) is define by,
; 0.
a
AE
aX
RE X= ≠