Vector spaces over a general field are treated and used to create interesting and practical algebras and geometries. Quotient spaces and dual spaces are emphasized. Algebras and geometries based on vector spaces are introduced. In particular, the exterior algebra of a vector space is constructed and given geometric interpretation. Scalar product spaces are introduced for scalar products of general type, and the Hodge star is treated two different ways for scalar product spaces. The topics are presented in a manner that facilitates self-study through inline exercises interspersed throughout. A basic algebra background is required for successful study of the material; readers should know what an Abelian group is and be able to do basic matrix algebra.
Vector spaces over a general field are treated and used to create interesting and practical algebras and geometries. Quotient spaces and dual spaces are emphasized. Algebras and geometries based on vector spaces are introduced. In particular, the exterior algebra of a vector space is constructed and given geometric interpretation. Scalar product spaces are introduced for scalar products of general type, and the Hodge star is treated two different ways for scalar product spaces. The topics are presented in a manner that facilitates self-study through inline exercises interspersed throughout. A basic algebra background is required for successful study of the material; readers should know what an Abelian group is and be able to do basic matrix algebra.
Think Like Scilab and Become a Numerical Programming Expert- Notes for Beginn...ssuserd6b1fd
Notes for Scilab Programming. This notes includes the mathematics used behind scilab numerical programming. Illustrated with suitable graphics and examples. Each function is explained well with complete example. Helpful to beginners. GUI programming is also explained.
Java Programming Notes for Beginners by Arun Umraossuserd6b1fd
Shot notes for quick revision. Not explained extensively but suitable for last night preparation. Fit for CBSE Class XII board students for their last minute preparation.
Think Like Scilab and Become a Numerical Programming Expert- Notes for Beginn...ssuserd6b1fd
Notes for Scilab Programming. This notes includes the mathematics used behind scilab numerical programming. Illustrated with suitable graphics and examples. Each function is explained well with complete example. Helpful to beginners. GUI programming is also explained.
Java Programming Notes for Beginners by Arun Umraossuserd6b1fd
Shot notes for quick revision. Not explained extensively but suitable for last night preparation. Fit for CBSE Class XII board students for their last minute preparation.
System shear connector digunakan sebagai aplikasi dalam konstruksi bangunan untuk menghasilkan kekuatan coran beton lebih kuat dan stabil sesuai dengan perhitungan engineering civil. Dalam hal ini ada 2 hal perhitungan kekuatan secara umum yaitu kekuatan kelengketan stud pada batang baja sesudah dilas. Dan yang kedua adalah kekuatan stud bolt yang digunakan.
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
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”.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
2. 2 Grade 9 5090 / 62/O/N/2012/GAAS
1. Fig 1.1 is a photomicrograph of a section across an artery and a vein.
a) (i) Make a large, labelled drawing of the artery and the vein as shown in Fig. 1.1.
[5]
Fig. 1.1
3. 3 Grade 9 5090 / 62/O/N/2012/GAAS
(ii) Fig 1.2 shows an image of the actual slide from which the photograph in Fig 1.1 is
taken.
Calculate the magnification of your drawing.
Width of actual specimen ………………………….…………………………………………….
Width of your drawing in (a) (i) ………………………………………………………………….
Show your working.
Magnification ……………………………………………………………………………………[3]
Fig. 1.2
4. 4 Grade 9 5090 / 62/O/N/2012/GAAS
(iii) Complete Table 1.1 to describe three differences that you can see between the artery
and the vein.
Table 1.1
2. Fig.2.1 is a photograph of an eye for an investigation.
a) Use your ruler to draw straight label lines and label both the pupil and the iris.
[2]
Fig 2.1
Artery Vein
5. 5 Grade 9 5090 / 62/O/N/2012/GAAS
b) (i) A student in a brightly lit room covered both of her eyes with her left hand while
holding a mirror in the other hand. The student closed her eyes. She counted slowly
to 60. Then she quickly removed her hand from her eyes, opened them and looked in
the mirror. Make drawings of what her iris and pupil would look like, as they appeared
when the eye was first uncovered and about one minute later.
(ii)Explain how the changes shown between your drawings in (a) (ii) occurred and how
these changes help the functioning of the eye.
..................................................................................................................................................................................
..................................................................................................................................................................................
..................................................................................................................................................................................
..................................................................................................................................................................................
..................................................................................................................................................................................
..................................................................................................................................................................................
.............................................................................................................................................................................[6]
[Total: 10]
6. 6 Grade 9 5090 / 62/O/N/2012/GAAS
3. Fig.3.1 is a diagram of a section through human skin.
Fig. 3.1
(a) Identify structures C, D and E.
[3]
(b) Describe how structure C might be involved in maintaining a constant body
temperature.
[Total : 6]
7. 7 Grade 9 5090 / 62/O/N/2012/GAAS
4. Fig.4.1 shows sections through two different types of flower that may develop on the
same marrow plant.
(a) Complete Table 4.1 by describing two visible differences between flower F and
flower G.
Fig 4.1
Table: 4.1
8. 8 Grade 9 5090 / 62/O/N/2012/GAAS
Fig.4.2 shows a photomicrograph of a pollen grain from a marrow flower.
(i) Suggest, with reasons, how pollination occurs in marrow.
......................................................................................................................
......................................................................................................................
......................................................................................................................
..................................................................................................................[3]
Fig. 4.2
9. 9 Grade 9 5090 / 62/O/N/2012/GAAS
b) Melons are closely related to marrow but the fruits of melons are sweeter than those of
marrows.
The sugar content of some other fruits is shown in Table 4.2.
(i) Draw a bar chart to show the sugar content of these fruits.
(ii) Calculate how many times greater the sugar content of 100g of a ripe banana is than
that of 100g of a melon. Show your working.
[Total: 10]
GOOD LUCK
Table 4.2
![2 Grade 9 5090 / 62/O/N/2012/GAAS
1. Fig 1.1 is a photomicrograph of a section across an artery and a vein.
a) (i) Make a large, labelled drawing of the artery and the vein as shown in Fig. 1.1.
[5]
Fig. 1.1](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)