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## Notes

- Online Biology Notes – Botany Notes
- Differential Equation – BSc Math Karachi University
- Orthogonal Trajectory – BSc Mathematics Karachi University
- First Year English Notes – Karachi Board
- Pakistan Zindabad – Free Online English Notes Karachi Board
- Count’s Revenge – Free Online English Notes Karachi Board
- Business Finance Notes
- Matric (X) Physics Notes Karachi Board
- Banking and Finance Notes
- Business Management Notes
- Free Online Statistics Notes – (Probability – Vital Statistics – Official Statistics) BSc KU
- Free Online Statisitcs Notes BSc-I

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## Online Biology Notes – Botany Notes

Biology Notes Zoology Botany Online Tutor Saudi Arabia, Online Tuition Saudi Arabia, Biology Notes Zoology Botany: Online biology tutors Saudi Arabia, Kuwait, Qatar, Bahrain, U.A.E., Pakistan.

Al-Saudia Virtual Academy, One of the largest online academy in Saudi Arabia, Kuwait, Qatar, Bahrain, U.A.E., Pakistan provides excellent tutors in Biology, Botany, Zoology, Microbiology, Genetics and other major biological subjects.

**Botany Notes:**

- Study of Microscope
- Structure of Microscope
- Measurement of a Microscopic Object By Micrometry and Calculation
- Study of Bacteria
- Observation of Gram +ve bacteria
- Observation of Gram -ve bacteria
- Investigation of Bacterial Content of Fresh and Stale Milk
- Study of Onion Epidermis Cells
- Study of Nostoc From Fresh Material and Permanent Slide
- Algae : Identification of Different Organisms, volvox, chlorella, euglena, ultothrix and Ulva.
- Chlorella – Euglena
- Ulothrix – Ulva
- Fungi
- Pencillium
- Ustilago Tritici
- Bryophytes: Marchantia – Male Marchantia Plant – Female Marchantia Plant
- Internal Structure of Marchantia Thallus
- Funaria – Funaria Plant with Sporophyte
- Dryopleris (Aspidium)
- Sorus of Adiantum
- Structure of Sorus of Fern
- Gametophyte or Prothallus of Aspedium or Fern
- Gymnosperms – Study of Pinus
- Female Cone (Ovulate Cone) of Pinus
- Physiology – Extraction and Chromatography of Leaf Chloroplast Pigments
- Apparatus for Paper Chromatography
- Determination of Osmosis in Living Plant Cells of Onion Or Rheodiscolour Leaf or Spirogyra
- Deplasmolysis
- Determination of Mean Solute Potential of Cell Sap Using Method of Incepient Plasmolysis
- Concentration of Sucrose solution
- Determination of Mean Solute Potential
- Investigation and Measurements of Factors Affecting Rate of Transpiration
- Investigation of Effect of Different Concentration of Glucose Solution on Opening and Closing of Stomata.
- Investigation of Stomatal Distribution using Epidermal Cells
- Description of Plant Families
- Biological Terms of Plant Families
- Aestivation of Corolla
- Terms Used for Androecium
- Types of Placentation
- Families
- Rosaceae
- Solanaceae (Solanum Nigram)
- Solanaceae ( Petunia Alba)
- Solanaceae (Datura Alba)
- Fabaceae ( Papilionaceae) – Lathyrus odoratus
- Fabaceae ( Papilionaceae) – Clitoria ternatea
- Fabaceae ( Papilionaceae) – Sesbania sesban
- Caesalpiniaceae – Cassia fistula
- 9. Caesalpiniaceae – Caesalpinia pulcherrima
- 10. Mimosaceae – Prosopis juliflora
- 11. Mimosaceae – Acacia arabica
- 12. Mimosaceae – Albizzia lebbek
- 13. Poacea (Graminae) Avena Sativa
**Viva**- Study of bacteria
- Nostoc – Algae
- Fungi
- Bryophytes
- Pteridophytes – Gymnosperms
- Chromatography – Plasmolysis – Deplasmolysis
- Solute Potential
- Transpiration – Opening and Closing Stomata
- Families
- Families – Botanical Terms

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## B.Sc Math Karachi University – Differential Equation

Easy approach to Differential equations – B.Sc Math Karachi University, , Differential Equation Made Easy Series, Notes, Past Papers, Important Question, B.Sc experienced online tutor notes, solutions, and many more.

#### Differential Equation:

A differential equation is a mathematical equation that relates an unknown function to its derivatives.

It involves one or more derivatives of an unknown function with respect to one or more independent variables.

In other words, it expresses a relationship between the function and its rates of change.

Differential equations are widely used in many scientific and mathematical disciplines to model various phenomena and describe their behavior.

They play a crucial role in physics, engineering, economics, biology, and other fields where dynamic processes are involved.

Differential equations can be classified into different types based on their order, linearity, and other properties.

The order of a differential equation is determined by the highest order derivative present in the equation.

Linear differential equations are those in which the unknown function and its derivatives appear linearly (i.e., without multiplication or exponentiation) in the equation.

Solving a differential equation involves finding a function that satisfies the equation and any specified initial or boundary conditions.

This can be done analytically, using mathematical techniques, or numerically, using approximation methods on a computer.

Overall, differential equations provide a powerful tool for describing and understanding a wide range of dynamic phenomena in the natural and physical sciences.

#### Different Types of Differential Equation

Differential equations are mathematical equations that involve derivatives and describe the relationships between a function and its derivatives.

There are various types of differential equations, and they can be classified based on their properties and characteristics. Here are some common types of differential equations:

##### 1. Ordinary Differential Equations (ODEs):

These are differential equations that involve only one independent variable. ODEs describe systems where the unknown function depends on a single variable. Examples include:

- First-order ODEs: Equations that involve the first derivative of the unknown function.
- Second-order ODEs: Equations that involve the second derivative of the unknown function.
- Linear ODEs: ODEs where the unknown function and its derivatives appear linearly.
- Nonlinear ODEs: ODEs where the unknown function and its derivatives appear nonlinearly.

##### Example:

Here’s an example of an ordinary differential equation (ODE):

dy/dx = 3 – 2x

In this equation, y is a function of x, and the derivative of y with respect to x is equal to the expression 3 – 2x. This is a first-order ODE because it involves the first derivative of y with respect to x.

Solving this ODE involves finding the function y(x) that satisfies the equation. One way to solve it is by integrating both sides with respect to x:

∫dy = ∫(3 – 2x)dx

Integrating the right-hand side, we get:

y = – + C

Here, C is the constant of integration. This solution represents the family of all possible functions that satisfy the original ODE. By specifying an initial condition or boundary condition, we can determine the particular function within that family.

##### 2. Partial Differential Equations (PDEs):

These are differential equations that involve multiple independent variables. PDEs describe systems where the unknown function depends on several variables. Examples include:

- Elliptic PDEs: Equations that involve second-order derivatives and are associated with steady-state problems.
- Parabolic PDEs: Equations that involve first-order derivatives in time and second-order derivatives in space. They are often used to describe diffusion processes.
- Hyperbolic PDEs: Equations that involve second-order derivatives in both time and space. They are commonly used to model wave phenomena.

##### 3. Linear Differential Equations:

These are differential equations where the unknown function and its derivatives appear linearly. Linear differential equations can often be solved analytically using methods like separation of variables, integrating factors, or Laplace transforms.

##### 4. Nonlinear Differential Equations:

These are differential equations where the unknown function and its derivatives appear nonlinearly. Nonlinear differential equations are generally more challenging to solve analytically, and numerical methods or approximation techniques are often employed to find solutions.

##### 5. Autonomous Differential Equations:

These are differential equations that do not explicitly depend on the independent variable. Autonomous differential equations can often be analyzed using techniques such as phase portraits, stability analysis, and equilibrium solutions.

##### 6. Stochastic Differential Equations:

These are differential equations that involve a random or stochastic component. Stochastic differential equations are used to model systems affected by random noise or uncertainty and are widely employed in fields such as physics, finance, and biology.

#### Questions:

Here are 20 numerical questions on differential equations at the BSc level:

- Solve the differential equation: dy/dx = + 3x – 2.
- Find the particular solution of the differential equation: ( + 1) dy/dx + 2xy = 3x, given that y(0) = 1.
- Solve the differential equation: ( + 1) dy/dx – 2xy = 0.
- Find the solution to the differential equation: dy/dx = 2 + 3 – 6x.
- Solve the differential equation: dy/dx = 2x – 3.
- Find the solution to the initial value problem: dy/dx + y = 2, y(0) = 3.
- Solve the differential equation: (1 + ) dy/dx = 2xy.
- Find the general solution to the differential equation: dy/dx = + 2x.
- Solve the differential equation: dy/dx = y(1 – ).
- Find the particular solution of the differential equation: (2x + 1) dy/dx – y = 3 , given that y(1) = 4.
- Solve the differential equation: dy/dx + 2xy =
- Find the solution to the differential equation: dy/dx = (1 + x) / (1 + y).
- Solve the differential equation: dy/dx = (2x + 1) / (3y – 1).
- Find the particular solution of the differential equation: y’ + y/x = , given that y(1) = 2.
- Solve the differential equation: dy/dx + xy = 2.
- Find the solution to the initial value problem: dy/dx = y + , y(0) = 1.
- Solve the differential equation: dy/dx = ( + 1) / (2y + 3).
- Find the particular solution of the differential equation: ( + 1) dy/dx + 2xy = 3x, given that y(1) = 2.
- Solve the differential equation: dy/dx = – .
- Find the solution to the initial value problem: dy/dx + 2xy = 4, y(0) = 1.

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## Orthogonal Trajectory – B.Sc Mathematics Karachi University

Orthogonal Trajectory – B.Sc Mathematics Karachi University, Definition of orthogonal Trajectory, past papers, free solution, notes, important questions, question from past papers – Complete and comprehensive notes of B.Sc Mathematics, Algebra, Calculus, Differential Equations, Mechanics, Vector etc.

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## First Year English Notes – Karachi Board

1. Counts Revenge

2. Pakistan Zindabad

3. Birkenhead Drill

4. United Nation

5. Science and Scientist

6. Under The Green Wood Tree

7. Character of Happy Life

8. Abu Bin Adhem

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### Pakistan Zindabad – Free Online English Notes Karachi Board

Online Tuition Pakistan, Complete and comprehensive notes of XI English written by experienced english professors, Pakistan Online Tuition, Al-Saudia Virtual Academy, Online Tuition Tutor provider for all subject. Free online English notes XI Karachi Board, Pakistan Zindabad, Character of Quaid-e-Azam, Struggle of Pakistan, Important questions, Reference to context, We have specialized online professors for English, English Language, English literature and Linguistics. Online English Tutor Pakistan, Pakistani English Tutors, Online English Tuition Pakistan.

PAKISTAN ZINDABAD The Arrival: It was the 7th of August 1947. A bright, silver aircraft landed at the airport of Mauripore in Karachi. A huge excited crowd was watching it. Quaid-e-Azam Mohammad Ali Jinnah came out of the plane. The crowd cried out with one voice “Pakistan Zindabad”. Every man ran ahead to welcome him, to get close to him, or at least to see him clearly.

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## Count’s Revenge – Free Online English Notes – Karachi Board

Online Tuition Pakistan, Complete and comprehensive notes of XI English written by experienced English professors, Pakistan Online Tuition, Al-Saudia Virtual Academy, Online Tuition Tutor provider for all subject. Free online englihs notes XI Karachi Board, Counts Revenge, Character sketch of Counts of Monte Cristo (Edmund Dantes), Count of Morcerf (Fernand Mondego), Countess of Morcerf (Mercedes), Albert and other important characters of the drama Count of Monte Cristo, Important questions, Reference to context, We have specialized online professors for English, English Language, English literature and Linguistics. Online English Tutor Pakistan, Pakistani English Tutors, Online English Tuition Pakistan.

One Act Play: A One Act Play: is a short drama depicting a particular incident in the life of a particular character. The incident invariably is significant in revealing of the person’s life in a way that from the part it is easy to understand. The whole, sometimes a plurality of incidents and characters may also occur but even so they are intensely concentrated towards an isolated purpose.

Two One Act Play The Count’s Revenge (By J.H. Wash) Introduction: – ‘The Count’s Revenge’ is a fine One-Act play presented as a striking place of melodrama. The author, J.H. Wash, skillfully, adopts an incident from “The Count of Monte Cristo”, a famous novel of the 19th century by the French writer Alexander Dumas.

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## Business Finance Notes

Pakistan Best Online Business Management and Business Finance Tuition, Pakistan Online Tuition Academy, Al-Saudia Virtual Academy is Pakistan First and the Largest Online Tutor Academy. We provide Pakistan expert online tutors for USA, UK and Canada, Saudi Arabia, Kuwait, Qatar, Bahrain, Doha, Dammam, and almost each and every corner of the world. Our expert professor are well experienced, highly educated, dedicated and result oriented with experience of teaching professionally in different high valued colleges, schools and universities. They are well versed with all the curriculum of different countries, specially with the curriculum of different states of America, including Texas, Ohio, Virginia, Alabama, UK, Canada and Australia.

Business refers to all these activities which are concerned with production and distribution of goods and services. It is connected with the creation and supply of utilities in the shape of goods and services for earning profit.

Students can get online statistics help, assignment help, homework help and tutoring classes, just write down to our emial: info@pakistanonlinetuition.com, add our skype id: ascc576, or call +923323343253.

Need for Finance
What is Business Finance Financial Needs of Business Sources of Raising Fixed Capital Factors Influencing Working Capital of Business Types of Business Finance in Pakistan Short Term Finance Medium Term Finance Long Term Finance |
Working Capital
Sources and Uses of Working capital Uses of Working Capital Working Capital Define Accounts Receivable Turnover |

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## Matric (X) Physics Notes Karachi Board

Introduction
Measurement Scalars & Vectors Mechanics Force and Motion Statics Circular Motion & Gravitation Work Power & Enerergy Machines Matter |
Heat
Waves and Sound Propagation and Reflection of Light Reflection of Light and Optical Instruments Nature of Light and Electromagnetics SpectrumElectricity Magnet and Electromagnetism Electronics Nuclear |

Pakistan Best Online Physics Tuition, Pakistan Online Tuition Academy, Al-Saudia Virtual Academy is Pakistan First and the Largest Online Tutor Academy. We provide Pakistan expert online tutors for USA, UK and Canada, Australia, Saudi Arabia, Kuwait, Qatar, Bahrain, Doha, Dammam, and almost each and every corner of the world. Our expert professor are well experienced, highly educated, dedicated and result oriented with experience of teaching professionally in different high valued colleges, schools and universities. They are well versed with all the curriculum of different countries, specially with the curriculum of different states of America, including Texas, Ohio, Virginia, Alabama, UK, Canada and Australia.

Students can get online physics tutor help, assignment help, homework help and tutoring classes, just write down to our email: info@pakistanonlinetuition.com, add our Skype id: ascc576, or call +923323343253.

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## Banking and Finance Notes

Modarba
Purchase of Trade Bills Money and Banking Musharika Financing Musharika Sharing of Profit Markup – Bal-Muajjal Islamic & International Banking Difference between Islamic and International Banking Leasing (Ijrah) RIBA |
Evolution Of Commercial Bank
The Word “Bank” Functions of Banks Kinds of Banks Classification on ownership Cash Reserves Credit Central Bank Functions Of Central Bank Difference B/w Central & Commercial Bank Bill of exchange Negotiable Instrument Promissory Note Crossing of check Difference b/w Promissory Note & Bill Of Exchange |
Letter Of Credit
IDBP-NDFC-BEL-PICIC-NIT-EPF ADBP IMF World Bank Asian Development Bank Islamic Development Bank Factors influencing on Foreign Exchange Types of Advances Five Basic Principles of Lending Types of Deposit Dishonored of Check |

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## Business Management Notes

Pakistan Best Online Tuition, Pakistani Online Business Management Tutor, Business Finance Tutor, ITB Tutor, Scope of Business, Qualities of Businessman, Function of Business, Pakistan best online Business Management tutor and tuition, free online Management notes, online Business management and Business Finance tuition Pakistan.

Pakistan Best Online Business Management and Business Finance Tuition, Pakistan Online Tuition Academy, Al-Saudia Virtual Academy is Pakistan First and the Largest Online Tutor Academy. We provide Pakistan expert online tutors for USA, UK and Canada, Saudi Arabia, Kuwait, Qatar, Bahrain, Doha, Dammam, and almost each and every corner of the world. Our expert professor are well experienced, highly educated, dedicated and result oriented with experience of teaching professionally in different high valued colleges, schools and universities. They are well versed with all the curriculums of different countries, specially with the curriculums of different states of America, including Texas, Ohio, Virginia, Alabama, UK, Canada and Australia.

Business refers to all these activities which are concerned with production and distribution of goods and services. It is connected with the creation and supply of utilities in the shape of goods and services for earning profit.

Students can get online statistics help, assignment help, homework help and tutoring classes, just write down to our emial: info@pakistanonlinetuition.com, add our skype id: ascc576, or call +923323343253.

__Business Management Notes__

Scope of Business

Objectives of Business

Functions of Business

Qualities of Businessman

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## Free Online Statistics Notes – B.Sc Part I (Probability – Vital Stats – Official Statistic)

Definition of probability Simple laws of probabiity Combinatorial problems conditional probability
Baye’s theorem with proof and applications Statistical independence (pairwise and mutual) Discrete Random variable Probability mass function Mathematical expectation of random variable and simple functions of random variables Generating functions (Recurring series) Moment Generating functions Cumulants and cumulating generating functions with their properties Discrete probability distributions Binomial, Poisson, Geometric and Hypergeometric distributions – Derivation of mean, variance, moments (ß1) and (ß2) of the above distributions. |
Official Statistics (OS),
Quality of Statistics, generation of OS, pecularities and properties of OS. Limitation of OS. errors in OS, Methods of elimination of errors and mistakes. Sources of OS in Pakistan type of Statistical available Set up of major statistical organization in Pakistan (Federal Bureau of statistics Provincial Bureau of statistics and State Bank of Pakistan) Agriculutural, Population, Banking, Economic and General Statisitcs series National and International Classification |
Source of demoraphic data
Graphical and Numerical studies of Demographic data. Calculation of vital rates and ratios (Mortality and Fertility) Crude and specified rates Rates of Natural increase (simple and geometric) Standarized Death rates T.F.R., G.R.R., N.R.R., Simple Life Table Basic concept of quality control and Internationa quality standards, X and R, and X and s charts |

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## Free Online Statistics Notes – B.Sc Part I

Elementary Statistics
Definition of Statistics Scope & Limitation Statistical Data Nature & Sources of data Collection of Data Quantitative and Qualitative data Classification and Tabulation methods One way and two way classifications Graphs and Diagrams Frequency Distributions Relative & Cummulative frequencies Characteristics of frequency Distributions Measures of Central Tendency Measures of Dispersion Moments Measure of skewness and Kurtosis Sheppard’s correction Charlier’s check |
Interpolation
Interpolation by graph Difference operators and their properties Newton’s forward and backword formulae Newton’s divided difference formula Lagrange’s formula Direct and Inverse Interpolation Central difference formula (Gauss, Stirling, Bessel) Use of Programs and Computers Financial Statistics Progressions Geometric progression simple and compound Interest sinking funds annuities, mortagage terminal values discounting application to depreceiation and investment analysis |
Time Series
Components of Time series Methods of isolation of these components Concept of cycle,trend, seasonal and Random Movements Methods of projection and estimation Uses of Time series data in evaluation of GNP, NNP, Inflation and Deflation. Index Numbers Types of Index numbres Method of construction of simple & weighted Index number, Choics of base year, types of averages to be used. Laspeyer’s, Pasche’s, Fisher and Marshal Edgeworth Index numbres, Consumer price Index (cost of living index), Shifting of Base Tests of Index numbers Uses of Index numbres in daily life and official statistics |