matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
this file analising the buckling of a simply supported beam in two cases. first case eigen value method for analisig a ideal beam under compressive load and in case two the beam has imperfection .
the imperfection of beam is in the sacles of the mood that the eigen values method gives.
Parallelogram is a quadrilateral with two pairs of parallel sides.
There are 6 properties of parallelogram.
1. A diagonal of a parallelogram divides it into two congruent triangles.
2. Opposites sides of a parallelogram are congruent.
3. Opposite angles of a parallelogram are congruent.
4. Consecutive angles of a parallelogram are supplementary.
5. If one angle in a parallelogram is right, then all angles are right.
6. The diagonals of a parallelogram bisect each other.
this file analising the buckling of a simply supported beam in two cases. first case eigen value method for analisig a ideal beam under compressive load and in case two the beam has imperfection .
the imperfection of beam is in the sacles of the mood that the eigen values method gives.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
Matrix theory" redirects here. For the physics topic, see Matrix string theory.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix.
In mathematics, a matrix (plural matrices) is a rectangular array[1] (see irregular matrix) of numbers, symbols, or expressions, arranged in rows and columns.[2][3] For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns:
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}
Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix). There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field.
Chemistry in our daily life and its importanceAMIR HASSAN
Chemistry in our daily life and its importance
A Short Introduction to Chemistry and its branches.
There are five main branches of Chemistry:
1)Organic Chemistry
2)Inorganic Chemistry
3)Analytical Chemistry
4)Physical Chemistry
5)Biochemistry
Presented By: Amir Hassan Chemistry Department, Government Post Graduate College Mardan KP Pakistan.
Difference Between Environmental Science and Environmental ChemistryAMIR HASSAN
Environmental chemistry is the scientific study of the chemical and biochemical phenomena that occur in natural places.
Environmental science deals with ecosystem maintenance; by using the combined knowledge of the science fields that include the area of physics, geography, astro, biology and chemistry.
Environmental Science & Environmental Chemistry in
Contamination and Pollution
Environmental Science & Environmental Chemistry in
The Atmosphere
Environmental Science & Environmental Chemistry in
The water
Environmental Science & Environmental Chemistry in
The Soil and Rocks
Environmental Science & Environmental Chemistry in
The Trace Toxics
The Haworth Projection or, RepresentationAMIR HASSAN
The Fischer projection does not accurately describe the shape of the cyclic hemiacetal form of D – Glucose (as shown in figure A).
A formulation suggested by the English chemist W.N. Haworth in which ring are written as flat or, planar hexagons is more correct
A simple way of drawing Haworth projection is to omit the ring carbon. Thus α – D – glucose and β – D – glucose may be represented as shown;
Chemistry of Natural Products
Alkaloids
• Introduction; classification; isolation; general methods for structure elucidation; discussion with particular reference to structure and synthesis of ephedrine, nicotine, atropine, quinine, papaverine and morphine.
• Terpenoids
• Introduction; classification; isolation; general methods for structure elucidation; discussion with particular reference to structure and synthesis of citral, α-terpineol, α-pinene, camphor and α-cadinene.
• Steroids
• Introduction; nomenclature and stereochemistry of steroids; structure determination of cholesterol and bile acids; introduction to steroidal hormones with particular reference to adrenal cortical hormones.
Detection Of Free Radical By Different Methods
1. Magnetic Susceptibility Measurement.
2. ESR ( Electron Spin Resonance) Technique.
3. Spin Trapping Technique.
4. NMR (Nuclear magnetic resonance) Spectra by CIDNP effect.
5. X-Ray Technique
Soil,Soil Pollution, Sources of Soil Pollution,
Effects Of Soil Pollution,
Control Of Soil Pollution,
Physically Control of Soil Pollution,
Chemically Control of Soil Pollution,
Thermally Control of Soil Pollution ,
Biologically Control of Soil Pollution
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Neighboring group participation, mechanism, groups, consequencesAMIR HASSAN
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Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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http://sandymillin.wordpress.com/iateflwebinar2024
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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.
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Inverse of a matrix, Transpose Of Matrix, formation of sub-matrices.
1. WrittenBY : AMIR HASSAN OF BS CHEMISTRY DEPARTMENT GPGC MARDAN
INVERSE OF A MATRIX:
Inverse of the matrix is obtained if matrix is non-singular matrix. The inverse of the
matrix is obtained by using three rules:
1) Compute the determinant of the matrix first.
2) Take the adjoint of given matrix.
3) Divide each elements of the given adjoint matrix by the determinant.
The resulting matrix is called inverse of matrix. Denoted by A-1 , B-1, C-1 etc.
DIAGNOLISATION OF A MATRIX:
The process of reducing matrix into a diagonal matrix is called diagnolisation.
Let A be the square matrix of order n.
P is the similarity transformation matrix which reduces A to diagonal matrix D.
Using the following equation.
P-1
AP = D
Let us consider matrix A.
2. WrittenBY : AMIR HASSAN OF BS CHEMISTRY DEPARTMENT GPGC MARDAN
FORMATION OF SUB-MATRICES:Any square matrix can be divided into
sub – matrices as given below.
The given matrix is of order 6. Can be divided into three sub – matrices are as follows:
