How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
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.
Extraction Of Natural Dye From Beetroot (Beta Vulgaris) And Preparation Of He...SachinKumar945617
If you want to make , ppt, dissertation/research, project or any document edit service
DM me on what's app 8434381558
E-mail sachingone220@gmail.com
I will take charge depend upon how much pages u want
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Power-sharing Class 10 is a vital aspect of democratic governance. It refers to the distribution of power among different organs of government, levels of government, and social groups. This ensures that no single entity can control all aspects of governance, promoting stability and unity in a diverse society.
For more information, visit-www.vavaclasses.com
1. TAYLOR AND MACLAURIN
how to represent certain types of functions as sums of power series
You might wonder why we would ever want to express a known function
as a sum of infinitely many terms.
Integration. (Easy to integrate polynomials)
Finding limit
Finding a sum of a series (not only geometric, telescoping)
dx
ex2
2
0
1
lim
x
x
ex
x
2. TAYLOR AND MACLAURIN
Example: x
e
x
f
)
(
0
n
n
n
x
x
c
e
5
5
4
4
3
3
2
2
1
0 x
c
x
c
x
c
x
c
x
c
c
Maclaurin series ( center is 0 )
Example:
x
x
f cos
)
(
Find Maclaurin series
14. TAYLOR AND MACLAURIN
Leibniz’s formula:
Example: Find the sum
0
1
2
1
1
2
)
1
(
)
(
tan
n
n
n
n
x
x
7
5
3
)
(
tan
7
5
3
1 x
x
x
x
x
0 1
2
)
1
(
n
n
n
7
1
5
1
3
1
1
34. TAYLOR AND MACLAURIN
Taylor series ( center is a )
0
)
(
)
(
!
)
(
)
(
k
k
k
a
x
k
a
f
x
f
Taylor polynomial of order n
n
k
k
k
n a
x
k
a
f
x
P
0
)
(
)
(
!
)
(
)
(
Remainder
1
)
(
)
(
!
)
(
)
(
n
k
k
k
n a
x
k
a
f
x
R
Taylor Series
)
(
)
(
)
( x
R
x
P
x
f n
n
Remainder consist of infinite terms
k
n
n a
x
n
c
f
x
R )
(
)!
1
(
)
(
)
(
)
1
(
for some c between a and x.
Taylor’s Formula
REMARK: )
(
not
)
( )
1
(
)
1
(
a
f
c
f n
n
Observe that :
35. TAYLOR AND MACLAURIN
k
n
n a
x
n
c
f
x
R )
(
)!
1
(
)
(
)
(
)
1
(
for some c between a and x.
Taylor’s Formula
k
n
n x
n
c
f
x
R
)!
1
(
)
(
)
(
)
1
(
for some c between 0 and x.
Taylor’s Formula
36. TAYLOR AND MACLAURIN
Taylor series ( center is a )
nth-degree Taylor polynomial of f at a.
DEF:
Remainder
DEF:
)
(
)
(
)
( x
T
x
f
x
R n
n
Example:
0
1
1
)
(
n
n
x
x
x
f 3
2
3
0
3 1
)
( x
x
x
x
x
T
n
n
6
5
4
4
3 )
( x
x
x
x
x
R
n
n
