OpenLLM-France/wikimedia huggingface dataset:
# Space and Global Health/Science Policy Interface

The United Nations - Office of Outer Space Affairs has a Scientific and Technical Subcommittee STSC of the Committee Of Peaceful Use of Outer Space (COPUOS), that serves as a science policy interface.
Working Group for Space and Global Health consists of two organisational structure:
* (Political/Organisational Level at UNOOSA) the Expert Focus Group with official meetings at the UN COPUOS is the organisational Network Hub between Space and Health domain, i.e. WHO, UNOOSA, ESA, national Public Health Agency...).
* (Implementation Level in a Community of Practice) Community of Practice can be regarded as sensor network in communities, that perform risk mitigation strategies, research and development in the context of Space and Global Health. For the Working Group it can be helpful to identify key requirements and constraints for policy making that improve Risk Mitigation, applications of Space Technology in the health domain and support evidence based implementation and decision making by application of space technology in the Global Health domain.
The Open Community Approach allows user-driven innovation that can be institutionalized in a Living Lab. Capacity Building and learning is a key element for global health risk management. Derived from the results of AT6FUI as a member state activity, the feedback from Community of Practice to the political level
    and vice-versa

## Learning Task

* WHO is responsible for science policy interface on the global scale with interface to national public health agencies. UNOOSA is responsible for the science policy interface. Identify the requirements and constraints of a science policy interface between WHO and UNOOSA and describe how policy making has an impact on science and scientific results have an impact policy making. Find examples for the science policy interface in general and in the health domain.
* Explain if and how is technological innovation and development is dependent on a legal framework. International coordination is relevant with the domain of space technology UNOOSA (e.g. mega constellation, "Is the enough space in space?") and in the health domain e.g. for epidemics and regulation for notifiable diseases (WHO). What areas of international regulations are required for the interoperability between the space and the health domain.
# Space and Global Health/Institution and Organisations
## Organisations link Space and Health Domain

Organisation in alphabetical order. Please add other space agencies with information about health related topic
* ESA Space meets Health
* JAXA
* NASA Life Science
* ROSCOSMOS
* Space Generation Advisory Council . Space Medicine and Life Science
* UNOOSA Space and Global Health

## Support of the Community of Practice

The Community of Practice is a collaboration of people work on Space and Global Health form different angles.
* Institutions do not have an in general an official mandate to work on capacity building within Wikiversity as Open Educational Resources.
* Institution can support development of capacity building resources and the translation for other member states by providing the content elementes like guidelines, images, videos, diagrams, ... with an Creative Commons License (e.g. CC-BY) which allows the adaptation to the requirements and constraints of member states, regions or communities.
* No all content can be opened up to the public as Open Educational Resources, but institutions can facilitate the use of specific content elements by assignment of licencing to specific content elements and media in a granular way (e.g. for an satellite image of Harmful Algae Bloom HAB, that shows how to detect HAB and trigger public health warnings for fishery or cost lines that are affected due to a negative impact on respiratory diseases (see Precision Global Health).
# Space and Global Health/Risk Literacy

In this resource for capacity building Risk Literacy for Global Health is addressed. It can be considered on an organisational level, how institutions and organisations are able to leverage the potential of space technology for Global Health challenges. Furthermore Risk Literacy in the context of Global Health and the Open Community Approach has the objective to improve the ability to perceive the global health risks for individuals, communities and environment and respond with locally appropriate risk mitigation interventions. The capacity building toderive appropriate decisions from the detection of risks and demands on the organisational level induces awarness programmes for exposed communities and tailored delivery of educational resources for specific regions and local requirements and constraints. Organisational analysis of Global Health challenges is dependent on the risk perception as a subjective judgement of people. Improving risk literacy supports capacity building for the assessment of a local severity of a specific health problem. The individual competence to identify risks may vary from person to person and may be different in comparision between organisations. Furthermore requirements and constraints change in time and therefore risk management and decision support must be adapted according to location and time.

## Creating risk literacy materials with space technology

In this framework space technology is used for different tasks. For some risks the spatial distribution can be determined via satellite images. For example the health of plants can be measured indirectly with the help of multispectral images by calculating a index called NDVI, which is a measure about how much chlorophyll a plant has or how healthy a plant is. This data can be for example used to determine in which areas forest dieback occur. With the help of the NDVI it is also possible to detect habitat conditions like available water surfaces for vectors responsible for human health risks like dengue or malaria. Also plastic garbage patches in the ocean can be observed via satellite images.

## Applications

* Normalized Difference Vegetation Index
* Garbage Patches, especially Great Pacific Garbage Patch

## Learning Task

* Explore the concept of Risk Literacy
* Explore the concept of Global Health
* Explore Risk Management
* Analyze additional possibilities for applications of Space Technology
# Space and Global Health/History

The Expert Focus Group on Space & Global Health has been established by the Scientific and Technical Subcommittee (STSC) of the United Nations Committee for the Peaceful Uses of Outer Space (UN COPUOS) The first meeting of the group was held on 5 February 2015 in Vienna. This focus group evolved from the earlier Action Team 6 established in 2001, and the subsequent AT 6 Follow-up Initiative (2012-15). The focused expert group reviews and analyses current uses of space (technology, applications, practices and initiatives) in support of globalhealth needs in order to: identify gaps; propose recommendations; and provide orientation for the future work of the STSC.
In February 14th, 2019 the proposal was accepted to request an official working group status for the former Expert Focus Group for Space and Global Health.
| Status | Year | Description |
| Action Team 6 (AT6) | 2001-2011 | Based on UNISPACE III Recommendation 6 - Improve Health by Application of Space Technology |
| Action Team 6 Follow-Up Initiative (AT6) | 2012-2015 | Member State Activity without official status - transition period based on the Open Community Approach - |
| Expert Focus Group for Space and Global Health | 2015-2019 | Expert Focus Group Status established in 2015 - |
| Working Group for Space and Global Health | 2019-2022 | Working group status announces in Vienna COPUOS Scientific and Technical Subcommittee on February 14th, 2019 - Multiyear |
Health was addressed in the context of space technology in different organisational forms (see official UN documents on Space and Global Health:
* Action Team 6 (AT6): Improve Health by Application of Space Technology (UNISPACE III Recommendation 6), Chair: Canada
* Action Team 6 Follow-Up Initiative (AT6FUI): As member state activity with side events at annual COPUOS meeting in February, Chair: Canada
* Expert Focus Group for Space and Global Health (EFG-SGH): Topic organized as expert focus group in UNOOSA, Chair: Canada, Switzerland
* Working Group for Space and Global Health (WG-SGH): Expert Focus Group became working group status Chair: Switzerland
"An important aspect of global health is the transnational impact that globalization exerts on the social, economic and cultural factors that determine good or bad health (known as health determinants) and health problems, something that is beyond the control of individual States. Global health emergencies, epidemics and early warning events can become threats to the stability of the international community. Issues related to environmental and climate change, such as air pollution and water quality, which are essential for human health and well -being, are also intrinsically transboundary. Space technology, supported by in situ observations, can provide important data for environmental, epidemiological and molecular models for disease risk forecasting and the formulation of policies to monitor environment, prevent outbreaks or contain epidemics. It is therefore important to promote enhanced cooperation and the exchange of information in this area."
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg29
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 29: Tue, 26Oct10
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg31
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 31: Thur, 28Oct10
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg1
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 1: Tue, 24 Aug 10

### Page 1-1

- course website, wiki
- high-speed trains
German transrapid (electromagentic attraction)
Japanese MAglev (electrodynamic repulsion)
Grench TGV (wheel on rail)
Vu Quoc and Olsson 1989 CMAME
vehicle/structure interaction, where vehicle is the high speed maglev and the structure is the the flexible guideway

### Page 1-2

$Y^{1}(t)=\$ nominal position of wheel (w/o guideway definition)
$S=x^{1}\$, horizontal coordinate
$u^{1}(S,t)=\$ axial deformation (displacement) of guideway, where $t\$ is the time parameter
$u^{2}(S,t)=\$ transverse deformation (displacement) of guideway
$u_{,s}^{2}:={\frac {\partial u^{2}(s,t)}{\partial S}}\$, where := means equal by definition (non symmetric)
NOTE: $\Delta \$ and def are symbols (no direction)
$A:=B\$ means A is defined by B

### Page 1-3

$A=:B\$ means B is defined by A
Axial displacement under moving wheel/magnet $=u^{1}(Y^{1}(t),t)\$
| $\displaystyle {\begin{aligned}u^{1}(S,t)\end{aligned}}$ | (1) |
Where $s=y^{1}(t)\$
General setting: $f(S,t)\$, where $S=Y^{1}(t)\$
| $\displaystyle {\begin{aligned}=f(Y^{1}(t),t)\end{aligned}}$ | (2) |
| $\displaystyle {\begin{aligned}{\frac {d}{dt}}f(Y^{1}(t),t)={\frac {\partial f(Y^{1}(t),t){\dot {y}}^{1}}{\partial S}}+{\frac {\partial f(Y^{1}(t),t)}{\partial t}}\end{aligned}}$ | (3) |
where ${\dot {y}}^{1}={\frac {dY^{1}}{dt}}$
| $\displaystyle {\begin{aligned}{\frac {d^{2}f}{dt^{2}}}=f_{,s}(Y^{1},t){\ddot {y}}^{1}+f_{,ss}({\dot {y}}^{1})^{2}+2f_{,st}{\dot {y}}^{1}+f_{,tt}\end{aligned}}$ | (4) |
Where $f_{,s}(Y^{1},t)={\frac {\partial f}{\partial S}}\$
and $f_{,ss}(Y^{1},t)={\frac {\partial ^{2}f}{\partial S^{2}}}\$
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg11
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 1: Thur,24Aug10

### Page 11-1

HW P.10-4 (continued)
2) Assume $a_{1}(x)\neq 0\forall \ x\$ , Eq(8) P.10-3 becomes $y'+{\frac {a_{0}(x)}{a_{1}(x)}}y={\frac {b(x)}{a_{1}(x)}}\$
Where ${\frac {a_{0}(x)}{a_{1}(x)}}=P(x)\$ and ${\frac {b(x)}{a_{1}(x)}}=Q(x)\$ from K.p.512
Find expression for $y(x)\$ in terms of $a_{0},a_{1},b\$.
3) $a_{1}(x)=x^{2}+1\$
$b(x)=2x\$
$a_{0}(x)=x\$
NOTE: cf. to K.p.512
1) K. etal. did not derive expression Eq.(1)p.10-3 $h(x)=e^{\left[\int _^{x}a_{0}(s)\,ds\right]}\$
"pulling rabbit out of hat"
2) $\oint _^{x}f(s)\,ds:=\int _^{x}f(s)\,ds\ \equiv \int f(x)\,dx$ without constant in K.2003

### Page 11-2

Lecture: $\int _^{x}f(s)\,ds=\int f(x)\,dx+k=\oint _^{x}f(s)\,ds+k\$
Eq.(6)p.10-3 :2 constants $k_{1}\$ and $k_{2}\$
Eq.(1)p.10-3 : $h(x)\rightarrow \ k_{1}\$
Eq.(6)p.10-3 : $\int _^{x}h(s)b(s)\,ds\rightarrow \ k_{2}\$
But Eq.(5)p.10-2 is L1_ODE_VC
HW: $\alpha \ \$ Show that $k_{1}\$ is not necessary.
HW: $\beta \ \$ Show Eq.(6)p.10-3 agrees with K.p.512, i.e. $y(x)=Ay_{H}(x)+y_{P}(x)\$
HW: $\gamma \ \$ Find $y_{H}(x)\$ independant, i.e. solve $y'+a_{0}y=0\$
$\delta \ \$ How about $y_{P}(x)\$ ? $\Rightarrow \ \$ Variation fo parameters (later)

### Page 11-3

A class of exact N1_ODE:
Recall Eq.(7)p.10-1 (Case 1)
One possibility to satisfy this condition: Consider:
| $\displaystyle {\begin{aligned}N(x,y)=N(x)\end{aligned}}$ | (1) |
| $\displaystyle {\begin{aligned}N_{x}(x,y)=b(x)\end{aligned}}$ | (2) |
| $\displaystyle {\begin{aligned}M_{y}(x,y)=a(x)\end{aligned}}$ | (3) |
| $\displaystyle {\begin{aligned}\Rightarrow \ M(x,y)=a(x)y+k(x)\end{aligned}}$ | (4) |
| $\displaystyle {\begin{aligned}N(x,y)=\int _^{x}b(s)\,ds=:{\bar {b}}\ (x)\end{aligned}}$ | (5) |
| $\displaystyle {\begin{aligned}M+Ny'=\left[a(x)y+k(x)+{\bar {b}}\ (x)y'=0\right]\end{aligned}}$ | (6) |
Where Eq(6) is a L1_ODE_VC (not necessarily exact, but can be made exact: integrating factor method)
Application: Consider $a(x)=x^{4}\neq \ b(x)=x\Rightarrow \ {\bar {b}}\ (x)={\frac {1}{2}}x^{2}\$
$k=10\$
| $\displaystyle {\begin{aligned}\left[x^{4}y+10\right]+\left({\frac {1}{2}}x^{2}\right)y'=0\end{aligned}}$ | (7) |
F09: Find $h(x)\$ such that Eq.(7) is exact

### Page 11-4

Question: But Eq.(6)p.11-3 is linear!
Find N1_ODEs that are exact or can be made exact by integrating factor method.
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg23
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 23: Tue,12Oct10
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg3
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 3: Thur, 26 Aug 10

### Page 3-1

NOTE: - page numbering 3-1 defined as meeting number 3, page 1
- T = torque Fig.p.1-1
- HW*
Eq.(3)P.2-1 : "Ordinary" Differential Equation (ODE)
order = highest order of derivative
Nonlinearity = What is linearity? ; use intuition for now, formal definition soon.
System has 3 unknowns:
$y^{1}(t)\$
$u^{1}(s,t)\$
$u^{2}(s,t)\$
$\equiv \$ Partial Differential Equations (PDE)
3 equations are coupled $\Rightarrow \ \$ Numerical Methods
Simplify for analytical solution Ref:VQ&O 1989
2nd Order $\rightarrow \ \$ 2nd Order
nonlinear $\rightarrow \ \$ linear
unknown varying coefficient $\rightarrow \ \$ known varying coefficient

### Page 3-2

Note: Math structure of coefficient $c_{i}(Y',t)\$ for $i=0,1,...3\$ is known, but not their values until $u^{1}\$ and $u^{2}\$ are known (solved for)
General structure of Linear 2nd order ODEs with varying coefficients (L2_ODE_VC)
| $\displaystyle {\begin{aligned}P(x)y''+Q(x)y'+R(x)y=F(x)\end{aligned}}$ | (1) |
where $y''={\frac {d^{2}y}{dx^{2}}}\$
$x=\$ independant variable
$y(x)=\$ dependant variable (unknown function to solve for)
Many applications in engineering are a result of solving PDEs by separation of variables. Some examples include, but are not limited to: Heat, Solids, Fluids, Acoustics and electrmagnetics.
Examples of these types equations are:
the Helmholz equation: $\Delta \ X+k^{2}X=0\$
and the Laplace Equation: $\Delta \ X=0\$
Ref F09 Mtg.28, Ref F09 Mtg.29 , Ref F09 Mtg.30

### Page 3-3

In 3_D, $x=(x_{1},x_{2},x_{3})\$
| $\displaystyle {\begin{aligned}X(x)=X_{1}(x_{1})X_{2}(x_{2})X_{3}(x_{3})\end{aligned}}$ | (1) |
Where the lowercase $x\$ in the first term $X(x)\$ is defined as $x=(x_{1},x_{2},x_{3})\$
and $X_{1}(x_{1})X_{2}(x_{2})X_{3}(x_{3})\$ is the separation of variables
| $\displaystyle {\begin{aligned}X(\xi \ )=X_{1}(\xi \ _{1})X_{2}(\xi \ _{2})X_{3}(\xi \ _{3})\end{aligned}}$ | (2) |
Where $\xi \ \$ in the first term $X(\xi \ )\$ is defined as $\xi \ =(\xi \ _{1},\xi \ _{2},\xi \ _{3})\$
and $X_{1}(\xi \ _{1})X_{2}(\xi \ _{2})X_{3}(\xi \ _{3})\$ is the separation of variables
Separated equations for $i=1,2,3\$
| $\displaystyle {\begin{aligned}{\frac {1}{g_{i}(\xi \ _{i})}}{\frac {d}{d\xi \ _{i}}}\left[g_{i}(\xi \ _{i}){\frac {dX_{i}(\xi \ _{i})}{d\xi \ _{i}}}\right]+f_{i}(\xi \ _{i})X_{i}(\xi \ _{i})=0\end{aligned}}$ | (3) |

### Page 3-4

Simplify:
$\xi \ _{i}\rightarrow \ x\$
$X_{i}(\xi \ _{i})\rightarrow \ y(x)\$
$g_{i}(\xi \ _{i})\rightarrow \ g(x)\$
$f_{i}(\xi \ _{i})\rightarrow \ a_{0}(x)\$
Eq.(3)p.3-3:
| $\displaystyle {\begin{aligned}y''+{\frac {g'(x)}{g(x)}}y'+a_{0}(x)y=0\end{aligned}}$ | (1) |
Where ${\frac {g'(x)}{g(x)}}=a_{1}(x)\$
Particular case of Eq.(1)p.3-2
Linearity: Let $F(.)\$ be an operator.
$u\$ and $v\$ are 2 possible arguments (could be functions) of $F(.)\$
$F(\alpha \ u+\beta \ v=\alpha \ F(u)+\beta \ F(v)\$
Where $\alpha \ \$ and $\beta \ \$ are any arbitrary number.
# University of Florida/Egm6341/s10.team3.aks/HW6
## (3) Evaluate the rest of the coefficient of matrix

Ref Lecture Notes p.35-3

### Problem Statement

Evaluate the remaining coefficient of Matrix by using degrees of Freedom

### Solution

We have
$Z(s)=\sum _{i=0}^{3}c_{i}s^{i}=\sum _{i=0}^{3}N_{i}(s)d_{i}$
such that
$d_{1}=Z_{i}$
$d_{2}={\dot {Z_{i}}}$
$d_{3}=Z_{i+1}$
$d_{4}={{\dot {Z}}_{i+1}}$
where
${\dot {Z}}={\frac {dZ}{dt}}={\frac {dZ}{ds}}{\frac {ds}{dt}}$
such that ${\frac {ds}{dt}}={\frac {1}{h}}$
We know the coefficient of matrix for first two rows from lecture notes p.35-3
${\begin{bmatrix}1&0&0&0\\0&1&0&0\end{bmatrix}}$
Using the equations above we have
$d_{3}=Z_{i+1}=Z(s=1)=c_{0}+c_{1}+c_{2}+c_{3}$
$d_{4}={\dot {Z}}_{i+1}={\frac {1}{h}}Z'(s=1)=c_{1}+2c_{2}+3c_{3}$
Putting the results in matrix form we obtain
${\begin{bmatrix}1&0&0&0\\0&1&0&0\\1&1&1&1\\0&1&2&3\end{bmatrix}}{\begin{Bmatrix}c_{0}\\c_{1}\\c_{2}\\c_{3}\end{Bmatrix}}={\begin{Bmatrix}Z_{i}\\Z'_{i}\\Z_{i+1}\\Z'_{i+1}\end{Bmatrix}}$

## (4) Verify the inverse of matrix using Matlab

Ref Lecture Notes p.35-4

### Problem Statement

Find the inverse of given Matrix
A =

### Solution

which is same as the one given on p.35-4
Hence Verified

## (5) Identify basis functions and plot them

Ref Lecture Notes p.35-4

### Problem Statement

Identify the basis functions
$N_{i}(s)$
where $i=1,2,3,4$

### Solution

We have
$z(s)=\sum _{i=0}^{3}c^{i}s^{i}=\sum _{i=1}^{4}N_{i}(s)d_{i}$
Expanding above we obtain
$N_{1}d_{1}+N_{2}d_{2}+N_{3}d_{3}+N_{4}d_{4}=C_{0}s^{0}+C_{1}s^{1}+C_{2}s^{2}+C_{3}s^{3}$
$=C_{0}+C_{1}s^{1}+C_{2}s^{2}+C_{3}s^{3}$
$d_{1}=z_{i}=z(s=0)=C_{0}$
$d_{2}={\dot {z}}_{i}={\dot {z}}_{i}(s=0)=C_{1}$
$d_{3}=z_{i+1}=z_{i+1}(s=1)=C_{0}+C_{1}+C_{2}+C_{3}$
$d_{4}={\dot {z}}_{i+1}=C_{1}+2C_{2}+3C_{3}$
Inserting above values in first eq we obtain
$(N_{1}+N_{3})C_{0}+(N_{2}+N_{3}+N_{4})C_{1}+(N_{3}+2N_{4})C_{2}+(N_{3}+3N_{4})C_{3}=C_{0}+C_{1}s+C_{2}s^{2}+C_{3}s^{3}$
Comparing both LHS and RHS we obtain
$N_{1}+N_{3}=1$
$N_{2}+N_{3}+N_{4}=s$
$N_{3}+2N_{4}=s^{2}$
$N_{3}+3N_{4}=s^{3}$
Solving above we obtain basis functions
$N_{1}=1-3s^{2}+2s^{3}$
$N_{2}=s^{3}-2s^{2}+s$
$N_{3}=3s^{2}-2s^{3}$
Below is the plot of above basis functions
$N_{4}=s^{3}-s^{2}$

# (6) Show that s = s(t)

Ref Lecture Notes p.36-1

### Problem Statement

We have to show that s is the function of t (s = s(t) )

### Solution

We have (from p.35-1 eq (1))
$t(s)=(1-s)t_{i}+st_{i+1}$
$=t_{i}+s(t_{i+1}-t_{i})$
$but{\frac {ds}{dt}}={\frac {1}{h}}$
$or{\frac {dt}{ds}}=h$
so $t_{i+1}-t_{i}={\frac {t_{i+1}-t_{i}}{1-0}}=h$
$t(s)=t_{i}+hs$ $hs=t-t_{i}$ $s={\frac {(t-t_{i})}{h}}$ $s=s(t)$
Hence Proved
# University of Florida/Egm6341/s10.team3.aks/HW7

(5)Use the code of HS algorithm and run the code for $h=2^{k}h$ and also develop and run the code for Forward and backward Eular methods for the same step size
Ref Lecture p.40.2

## Problem Statement

Integrate the logistic equation and use the code of question 3 for HS and run the code for $h=2^{k}h$ and also develop Forward Eular and Back Eular methods for the same step sizes.

## Solution

Matlab code with change in step size is given below.
MATLAB CODE:
For k = 1
For k = 2
For k=3
We can see that as we increase the value of k due to decrease in step size our curve shifted to the left side.
Below is the code for Forward Eular method
MATLAB CODE:
Forward Eular breaks down at higher values of step size h .This shows that it is unstable in nature. Below is the code for Backword Eular Method
MATLAB CODE:
For k = 1
For k=2

## (12)Convert circumference of ellipse formula from t to α variable

Ref Lecture 42.2

### Problem Statement

Prove that $a\int \limits _{t=0}^{2\pi }[1-e^{2}cos^{2}t]^{1/2}dt=4a\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}d\alpha$

### Solution

$a\int \limits _{t=0}^{2\pi }[1-e^{2}cos^{2}t]^{1/2}dt$
$=4a\int \limits _{t=0}^{\pi /2}[1-e^{2}cos^{2}t]^{1/2}dt$
Let $cost=Sin\alpha$
$-sintdt=cos\alpha d\alpha$
Using above values we obtain
$=4a(-)\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}(-){\frac {cos\alpha }{sint}}d\alpha$
$=4a(-)\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}(-){\frac {cos\alpha }{sint}}d\alpha$
$=4a\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}{\frac {cos\alpha }{(1-sin^{2}\alpha )^{1/2)}}d\alpha$
$=4a\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}{\frac {cos\alpha }{cos\alpha }}d\alpha$
$=4a\int \limits _{\alpha =0}^{\pi /2}[1-e^{2}sin^{2}\alpha ]^{1/2}d\alpha$
Hence Proved
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg25
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 25: Thur,14Oct10
# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg33
## EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 33: Thur, 4Nov10
# Multicultural Perspectives on Health and Wellbeing/Quizzes

There will be a total of seven quizzes conducted over the semester. Quizzes will be held during weeks 3,4,5,6,8,9 and 12. Each quiz will consist of five multiple choice questions, covering the lecture topics from the previous weeks. For example, questions for the Week 12 quiz will be on topics from Weeks 10,11 and 12.
Each quiz is the equivalent of 5% of your overall mark (35% for seven quizzes).
# Multigrade operator

☞ This page belongs to resource collections on Logic and Inquiry.
A multigrade operator $\Omega \!$ is a parametric operator with parameter $k\!$ in the set $\mathbb {N} \!$ of non-negative integers.
The application of a multigrade operator $\Omega \!$ to a finite sequence of operands $(x_{1},\ldots ,x_{k})\!$ is typically denoted with the parameter $k\!$ left tacit, as the appropriate application is implicit in the number of operands listed. Thus $\Omega (x_{1},\ldots ,x_{k})\!$ may be taken for $\Omega _{k}(x_{1},\ldots ,x_{k}).\!$

## Syllabus
### Focal nodes

* Inquiry Live
* Logic Live

### Peer nodes

* Multigrade Operator @ InterSciWiki
* Multigrade Operator @ Subject Wikis
* Multigrade Operator @ Wikiversity
* Multigrade Operator @ Wikiversity Beta