Introduction to basic differential calculus for algebra students familiar with the concept of the slope of a line. See my blog at http://roundyeducationblog.blogspot.com/2015_11_01_archive.html
Introduction to basic differential calculus for algebra students familiar with the concept of the slope of a line. See my blog at http://roundyeducationblog.blogspot.com/2015_11_01_archive.html
Materi kuliah tentang Aplikasi Integral. Cari lebih banyak mata kuliah Semester 1 di: http://muhammadhabibielecture.blogspot.com/2014/12/kuliah-semester-1-thp-ftp-ub.html
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
Application of partial derivatives with two variablesSagar Patel
Application of Partial Derivatives with Two Variables
Maxima And Minima Values.
Maximum And Minimum Values.
Tangent and Normal.
Error And Approximation.
3 examples of PDE, for Laplace, Diffusion of Heat and Wave function. A brief definition of Fouriers Series. Slides created and compiled using LaTeX, beamer package.
This is my leader I admire speech for Tim Hudson. He has an organization called Hudson Family Foundation who help children who are sick in Alabama and Georgia.
Materi kuliah tentang Aplikasi Integral. Cari lebih banyak mata kuliah Semester 1 di: http://muhammadhabibielecture.blogspot.com/2014/12/kuliah-semester-1-thp-ftp-ub.html
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
Application of partial derivatives with two variablesSagar Patel
Application of Partial Derivatives with Two Variables
Maxima And Minima Values.
Maximum And Minimum Values.
Tangent and Normal.
Error And Approximation.
3 examples of PDE, for Laplace, Diffusion of Heat and Wave function. A brief definition of Fouriers Series. Slides created and compiled using LaTeX, beamer package.
This is my leader I admire speech for Tim Hudson. He has an organization called Hudson Family Foundation who help children who are sick in Alabama and Georgia.
A tutorial on the Frobenious Theorem, one of the most important results in differential geometry, with emphasis in its use in nonlinear control theory. All results are accompanied by proofs, but for a more thorough and detailed presentation refer to the book of A. Isidori.
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.
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.
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”.
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!
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.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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.
2. Consider a function defined by y=f(x) where x is
the independent variable. In the four-step rule we
introduced the symbol Δx to the denote the
increment of x. Now we introduce the symbol dx
which we call the differential of x. Similarly, we shall
call the symbol dy as the differential of y. To give
separate meanings to dx and dy, we shall adopt the
following definitions of a function defined by the
equation y=f(x).
DEFINITION 1: dx = Δx
In words, the differential of the independent
variable is equal to the increment of the variable.
3. DEFINITION 2: dy = f’ (x) dx
In words, the differential of a function is equal to
its derivative multiplied by the differential of its
independent variable.
We emphasize that the differential dx is also an
independent variable, it may be assigned any value
whatsoever. Therefore, from DEFINITION 2, we see
that the differential dy is a function of two
independent variables x and dx. It should also be
noted that while dx=Δx, dy≠Δy in general.
Suppose dx≠0 and we divide both sides of the
equation
dy = f’ (x) dx
4. by dx. Then we get
( )x'f
dx
dy
=
Note that this time dy/dx denotes the quotient of
two differentials, dy and dx . Thus the definition of
the differential makes it possible to define the
derivative of the function as the ratio of two
differentials. That is,
( )
xofaldifferentithe
yofaldifferentithe
dx
dy
x'f ==
The differential may be given a geometric
interpretation. Consider again the equation y=f(x)
and let its graph be as shown below. Let P(x,y) and
Q(x+Δx,f(x)+Δx) be two points on the curve. Draw the
5. tangent to the curve at P. Through Q, draw a
perpendicular to the x-axis and intersecting the
tangent at T. Then draw a line through P, parallel to
the x-axis and intersecting the perpendicular through
Q at R. Let θ be the inclination of the tangent PT.
P
Q
T
R
θ
6. From Analytic Geometry, we know that
slope of PT = tan θ
But triangle PRT, we see that
x
RT
PR
RT
tan
∆
θ ==
However, Δx=dx by DEFINITION 1 . Hence
dx
RT
tan =θ
But the derivative of y=f(x) at point P is equal to the
slope of the tangent line at that same point P.
slope of PT = f’(x)
Hence,
( )
dx
RT
x'f =
7. And , RT = f’(x) dx
But, dy = f’ (x) dx
Hence, RT = dy
We see that dy is the increment of the ordinate of
the tangent line corresponding to an increment in Δx
in x whereas Δy is the corresponding increment of
the curve for the same increment in x. We also note
that the derivative dy/dx or f’(x) gives the slope of
the tangent while the differential dy gives the rise of
the tangent line.
8. DIFFERENTIAL FORMULAS
Since we have already considered dy/dx as the
ratio of two differentials, then the differentiation
formulas may now be expressed in terms of
differentials by multiplying both sides of the
equation by dx. Thus
d(c) = 0
d(x) =dx
d(cu) = cdu
d(u + v) = du + dv
d(uv) = udv + vdu
d(u/v) = (vdu – udv)/v2
d(un
) = nun-1
du
( ) u2duud =
9. EXAMPLE 1: Find dy for y = x3
+ 5 x −1.
( )
( )dx53xdy
dx5dxx3
1x5xddy
2
2
3
+=
+=
−+=
EXAMPLE 2: Find dy for .
1x3
x2
y
−
=
( )( ) ( )( )
( )
( ) ( )22
2
1x3
2dx
dy
1x3
x62x6
dy
1x3
3x221x3
1x3
x2
ddy
−
−
=∴⇒
−
−−
=
−
−−
=
−
=
dx.byitmultiply
andequationtheofmemberrighttheof
derivativethegetsimplywepractice,In:Note
10. EXAMPLE 3: Find dy / dx by means of differentials
if xy + sin x = ln y .
( )
( )
( ) ( )
( )
1xy
xcosyy
dx
dy
xcosyy
dx
dy
1xy
xcosyy
dx
dy
dx
dy
xy
dx
dy
xcosyy
dx
dy
xy
dx
1
dydxxcosydxydyxy
dydxxcosydxydyxy
ydy
y
1
dxxcosdxydyx
dy
y
1
dxxcosdxydyx
2
2
2
2
−
+−
=∴
+−=−
−−=−
=++
=++
=++
=++
=++
11. ( ) ( ).tgy,tfxequations
cparametrifor,
dx
yd
and
dx
dy
assuchs,derivative
thefindtoeprocedurtheesinvestigatlessonThis
2
2
==
CHAIN RULE FOR PARAMETRIC EQUATIONS
12. ( ) ( )
dt
dx
dx
dy
dt
d
dx
yd
and
dt
dx
dt
dy
dx
dy
symbols,In
manner.similarain
foundaresderivativeHigher.
dt
dx
to
dt
dy
ofratiotheiscurve
cparametritheon
dx
dy
derivativethethatstatesRuleChainThe
tgyandtfx
equationscparametrithebydefinediscurveaSuppose
RULECHAINHET
2
2
==
==
13. Find the derivatives of the following parametric
equations :
tcot
2sint-
2cost
dt
dx
dt
dy
dx
dy
tcos2
dt
dy
andtsin2
dt
dx
:Solution
sint2yt,2cosx.1
−===
=−=
==
3tcot
3sin3t-
3cos3t
dt
dx
dt
dy
dx
dy
t3cos3
dt
dy
andt3sin3
dt
dx
:Solution
3tsiny3t,cosx.2
−===
=−=
==
EXAMPLE :
