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Friday, December 23, 2011

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Thursday, November 24, 2011

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Friday, October 21, 2011

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Bevel: INTRODUCTION


Q1. What is Science? How many branches of Science are?
Ans. SCIENCE:
The world Science means to know. In other words, to consider, to observe, to calculate
the result and to done experiment on any substance in the universe is called science.
OR
The observation, identification, description, experiment, investigation and theoretical
explanation of phenomena are called science. In short knowledge gained through
experience is called science.
The following natural phenomena’s give us the knowledge of science.
i. Colour in rainbow
ii. Dropping of an apple from tree
iii. Rusting of an iron
iv. Growing of plants
v. Motion of bodies
vi. Formation of the solar system
BRANCHES OF SCIENCE:
Basically, Science consists of two main branches.
i. Biological Science
ii. Physical Science
Q2. Define Physics. Write down the name of its branches.
Ans. PHYSICS:
The branch of Physical science in which we discuss interaction between
Matter and Energy is call PHYSICS. It is an experimental science, which mostly
depends upon “Experimental observation” as well as quantitative measurement.
BRANCHES OF PHYSICS:
i. MECHANICS:
In this branch, we study about the forces which are acting on matter as well as
the motion & rest of bodies.
ii. ELECTRICITY:
In this branch, we study about the motion & rest of electric charge.
iii. ELECTROMAGNETISM:
We study and observe the laws of electrostatic and magnetism, in
Electromagnetism.
iv. SOLID STATE PHYSICS:
Study about crystalline solid in which atoms are arranged in three dimensions is
called solid State Physics.
v. ATOMIC PHYSICS:
Atomic Physics refers to study about structure, properties and behaviour of
electron.
vi. NUCLEAR PHYSICS:
In this branch we study about structure and properties of Nucleus as well as the
reaction between the Nuclei of atoms.
vii. PLASMA PHYSICS:
The branch, which belongs to highly, ionized atoms. When all electron escape
from an atom then it becomes highly ionized, the mixture of highly ionized
atom and electron is called plasma.
viii. BIO-PHYSICS:
The study of bio-system of its structure according to physics method is known as
Bio-Physics.
ix. ASTRO-PHYSICS:
Study of Astronomical bodies and astronomical system is known as Astro-
Physics.
Q3. Write name of Modern branches of physics.
Ans. The modern branches of Physics are as follows:
i. Electronics
ii. Solid State Physics
iii. Bio-Physics
iv. Geo-Physics
v. Astro Physics
vi. Condense Matter Physics.
Q4. Write a note about the history of Physics?
Ans. HISTORY OF PHYSICS:
The history of Physics is as old as history of man Even the cave man was aware of the
production of fire by rubbing two stone together. The Chinese for the time
manufacture paper. Egyptian used to measure the flood level in the river Nile. The
people of Indus Valley were the pioneers of decimal system. The history of physics
about 5000 yrs old. History of Physics consists on three periods.
1 INITIAL PERIOD:
This period is called Greek Period which remained 9th century, the Greek are
accepted as pioneers in the development of physics as a systematic knowledge.
The names of famous scientists of this period are:
i. Pythagoras
ii. Archimedese
iii. Euclid
iv. Ptolomy
2 GOLDEN PERIOD:
This period from 9th century to 13th century. This period is called Muslim period
in which they rule as a scientist in whole world. Famous scientist’s were:
i. Jaber-Bin Hayyan
ii. Muhammad Bin Moosa Khawarzmi
iii. Al-Razi
iv. Yaqoob Al-Kundi
v. Al-Beruni
vi. Umer Khayyam
vii. Ibn-Al-Haitham
3 MODERN PERIOD:
This period is started from 13th century and still continued. This period was
initiated after the declination of Muslims. The other name of this era is
“European Period”. The famous scientists were:
i. Albert Einstein
ii. Michael Faraday
iii. Graham Bell
iv. Madam Marie Quire
v. Dr. Abdul Salaam
vi. Rutherford vii. Moseley
Q.5 Write a note on the importance of Physics.
Ans. IMPORTANCE OF PHYSICS:
i. Physics is the essential of daily life and technology as: Radio, Radar, artificial
satellite, Hydrostatic power station, Nuclear reactor, Diesel engine, firm reactor
and Computer etc. They belong to daily life as well technology. The electric
power used for domestic purposes is only due to change of magnetic flux.
ii. Laser used for treatment in medical field and Defence.
iii. Electroplating, Astronomy and Defence are working only due to Physics.
iv. Nuclear Physics is used to produce electric power on a large scale.
v. Automobile technology works on the base of thermodynamic Physics.
vi. Radar technology works on the principle of reflection and propagation.
In short, this period is totally at rest without Physics.
Q6. Write the contributions of Ibn-ul-Haitham?
Ans. i. He wrote the book named “Kitab-ul-Manazir”, about the branch of Physics
called Opticalism.
ii. He gave the laws of relfection and refraction.
iii. He explained the luminous, non-luminous transparent and transparent
objectives.
iv. He described the different parts of eye.
v. According to Ibn-ul-Haitham, when light passes through a medium then it
takes minimum time to take its path. This is known as Fermate Principle.
vi. The nature of light is the form of energy according to him.
vii. He explained the refraction of light.
viii. He explained the image formed by concave mirror.
Q7. Write the contribution of Al-Beruni? Or In what way Al-Beruni was a versatile
Scientist.
Ans. i. He was the famous scientist of Golden age.
ii. He was a scholar, astronomer, physician, and mathematician.
iii. He wrote more than one hundred and fifty books on physics Mathematics,
Geography, etc.
iv. His famous book “Kitab-ul-Qanoon-ul-Masoodi” is considered as an
encyclopedia of Astronomy.
v. He discussed the measurement of earth, the shape of the earth, the movement
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planets in his famous book Qanoon Al Masoodi.
vi. He gave the method of determining the longitude and altitude of place.
vii. He also determined the densities of the metals.
In the fight of above contribution, Al-Beruni is called Versatile Scientist.
Q8. What are the contributions of Yaqoob Kundi.
Ans. i. He was a famous Arab philosopher.
ii. He has 244 books at his credit.
iii. He gave the idea about specific gravity and Waves.
iv. He worked in the field of optics and explained the appearance of blue colour in
the sky.
v. He explained the idea that gold cannot be made from other metals.
vi. He also explained music from scientific point of view by expressing the different
notes of music in terms of frequencies.
Q9. Write the part of Muhammad-Bin-Moosa Al-Khurazmi in Science.
Ans. i. He was one of greatest scientists of his time.
ii. He was an important member of the great institution of hearing the Bait-ul-
Hikmat established by the great Abbasied Caliph Mamun-ur-Rasheed.
iii. He was the founder of Algebra.
iv. He wrote first book in the world on subject of Algebra name “Al-jab-al-
Muqabla”.
v. He also gave analytical solutions of linear and quadratic equations.
vi. He introduced the method of counting based on numerals and decimal system
which is used all over the world until now.
vii. He was also involved in the measurement of angles.
viii. He simplified the method of addition, subtraction, multiplications and divisions.
Q10. Write the contribution of Nasi-ud-din Bin Hassan Tusi.
Ans. i. A great mathematician, astronomer, geographer and astrologer of his time.
ii. His chief contribution was his success in persuading Halaku Khan to issue
necessary instructions for the creation of grand observatory and a library.
iii. He prepared very precise and accurate tables about the planetary motion.
Q11. Write the contributon of Abdus-Salaam.
Ans. i. A famous Pakistani scientist passed every examination with flying colours.
ii. He got higher education from UK.
iii. He was awarded Noble prize in Physics for his work on Grand Unification theory
(GUT).
iv. He established International centre for theoretical Physics at Treiste in Italy.
Q12. What branch of Physics do we mean by Electronics?
Ans. Electronics is the branch of Solid State Physics.
Q13. In what areas Laser is used?
Ans. i. It is used in Medicine, like surgery of eye.
ii. It is used in the accurate cutting of metals.
iii. It is used in communication like space communication.
iv. It is used in scientific research.
v. It is used as a detector of certain type of air pollution.


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Tuesday, October 18, 2011

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The Course of Calculus:

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Bounds, Limits and continuity, properties of continuous functions, Derivatives, Leibniz's Theorem, Rolles Theorem Lagrange's Mean Value Theorem, Cauchy's Mean Value Theorem, Generalized Mean value theorem, indeterminate forms, Taylor's and Maclaurin's series.

2. Intergral Calculus:
Antiderivatives Techniques of Intergration, Riemann Integral, Properties of definite Integrals, Mean value theorem, Reduction formulae Improper Integrals, Beta and Gamma Integrals.

3. Fourier Series:
Periodic function, periodic extensions, even and odd functions, Fourier coefficients. Expansion of functions in Fourier series. Functions with arbitrary periods. Fourier sine and cosine series.

4. Differential Equations: I. Differential equations, formation and solutions, equations of first order, Initial and boundary value problems. Various methods for solving first order differential equations. Orthogonal trajectories. Non-linear first order differential equations, Envelopes and singular solutions.

5. Differential Equations: II. Higher order differential equations with constant coefficients, Superposition of solution. Cauchy-Euler's equations System of two first order linear homogenous equations. Non-Linear equation discussed with the help of population growth.

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We cover the following Algebra Bsc syllabus during classes:

Number System: Real and complex number system, Demoivres theorem with
applications, exponential, trigonometric, hyperbolic, logarithmic,
inverse hyperbolic and inverse circular functions.

Infinite Series: Sequences, limits and bounds of sequences, infinite series,
comparison test, limit comparison test, integral; ratio and root tests.
Alternating series,absolute and conditional convergence.

Set Theory: Binary relation, functions and their graphs, composition of functions.

Group Theory: Groups and their properties, subgroups, order of groups, cyclic
groups, cosets, lagrage's theorem, permutation groups.
Rings, fields, vector spaces, subspaces, linear combinations and spanning set,
linear dependence and basis, dimension, linear transformations.

Matrices: Elementary row operations, echelon and reduced echelon forms,
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Partitioning of a matrix.

Determinants: Axiomatic definitions of a determinant, determinant as sum of
products of elements, adjoint and inverse of matrix.

System of Linear Equations: Gauss elimination and Gauss Jordan methods,
Cramer's Rule, consistent and inconsistent systems.

Equations: Solution of cubic and biquadratic equations, Numerical solution of
equations, Newton-Raphson, Regular Falsi and bisection methods.

Probability: Axioms of probability, conditional probability, Discrete and
continuous random variables, probability distributions, Binomial, Poisson's
and normal distributions.