The document discusses the Gauss Divergence Theorem, which states that the volume integral of the divergence of a vector field over a volume is equal to the surface integral of that vector field over the bounding surface of the volume. The divergence of a vector field at a point represents the flux of that vector field diverging out per unit volume at that point. The divergence can be positive, negative, or zero, indicating whether there are sources, sinks, or neither of the vector field at that point.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
Gauss's divergence theorem, the last of the big three theorems in multivariable calculus, links the integral of the divergence of a vector field over a region with the flux integral of the vector field over the boundary surface.
This talk argues that the future of data query/analytic languages will be all about embedding the language into the native programming language of the developer. As an example of this style, the Gremlin graph traversal language is presented. Gremlin can be represented in any programming language that supports function composition and function nesting. The language representation is then compiled to Gremlin bytecode to ultimately be executed by the/a Gremlin graph traversal machine. This enables both the Gremlin language and machine to be agnostic to the execution language.
Apache TinkerPop serves as an Apache governed, vendor-agnostic, open source initiative providing a standard interface and query language for both OLTP- and OLAP-based graph systems. This presentation will outline the means by which vendors implement TinkerPop and then, in turn, how the Gremlin graph traversal language is able to process the vendor's underlying graph structure. The material will be presented from the perspective of the DSEGraph team's use of Apache TinkerPop in enabling graph computing features for DataStax Enterprise customers.
About the Speaker
Marko Rodriguez Director of Engineering, DataStax
Dr. Marko A. Rodriguez is the co-founder of Apache TinkerPop and creator of the Gremlin graph traversal language. Gremlin is leveraged by numerous graph system vendors including DataStax's DSEGraph. Currently, Marko is a Director of Engineering at DataStax focusing his time and effort on graphs in general and Apache TinkerPop in particular.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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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?
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
A Strategic Approach: GenAI in EducationPeter 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.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
2. The Divergence Theorem
In this section, we will learn about:
The Divergence Theorem & Gauss Divergence Theorem.
3. Divergence of a vector Field
The divergence of a vector field ar a point is a scalar
quantity of magnitude equal to flux of that vector field
diverging out per unit volume through that point in
mathematical from, the dot product of del operator and
the vector field A(x,y,z,) gives the divergence of a vector field
A. i.e. ,
div A. = .. A
4. But = Î ∂∕∂x + ĵ ∂∕∂y + k∂∕∂z and A = ÎAX + ĵ AY +
AZ k
. A = (Î ∂∕∂x + ĵ ∂∕∂y + k∂∕∂z).(ÎAX + ĵ AY + AZ k)
. A = ( ∂AX∕∂x + ∂ AY ∕∂y + ∂ AZ ∕∂z)
div A = ∂AX∕∂x + ∂ AY ∕∂y + ∂ AZ ∕∂z
5. The divergence of a vector field can bev
positive nigetive or zero.
(1) if the divergance of a vector field at a point is
positive (div A = +ve) it means that the flux
entering through the surface is less then the flux
comeing out through that surface. In other words ,
there is a source of that vector field in the region.
6. (2) if the divergance of a vector field at a
point is nigetive (div A = -ve) it means
that the flux entering through the surface
is more then the flux comeing out
through that surface. In other words ,
there is sink of that vector field in the
region.
7. if the divergance of a vector field is
zero. it implies that the flux entering
through the surface is equal to the flux
leaving that surface. In other words ,
there is neither the source nor sink in
that region.
8. According to this theorem the volume intrigle of
divergence of a vector field A over a volume V is
equal to the surface integral of that vector field A
taken over the surface S which encloses that
volume V. I,.e.
∫∫∫(divA)dV = ∫∫A. da
thus this theorem is used to convert the volume
integral into the surface integral or to convert
surface integral into the volume intrgral.
9. Proof : In cortesian coordinates,
div A = .A = (Î ∂∕∂x + ĵ ∂∕∂y + k∂∕∂z).(ÎAX + ĵ AY + AZ
k)
= ( ∂AX∕∂x + ∂ AY ∕∂y + ∂ AZ ∕∂z)
And dV = dxdydz
While A.da = (ÎAX + ĵ AY + AZ k).(Îdax + ĵday + kdaz)
= Axdax + Ayday + Azdaz
= Axdax + Ayday + Azdxdy
y
10. According to Gauss Theorem,
∫∫∫ (∂AX∕∂x + ∂ AY ∕∂y + ∂ AZ ∕∂z)dxdydz = ∫∫ (Axdydz + Aydxdz + Azdxdy)