Physics/Math Tutorials by Pervez Hoodbhoy

Teach Yourself Probability and Statistics

Languages: Urdu, English

These are self-study lectures on probability theory suitable for college level students studying mathematics, physics, economics, and business.

Module 1.1 (English, Urdu)

  • Random experiments, sample space and events, A quick review of sets, Venn diagrams and consequences, Sample space and events — examples, Axioms of probability, Probability — elementary examples

Module 1.2 (English, Urdu)

  • Factorials and their applications, Pascal’s Triangle, Counting outcomes, Conditional probability, Worked examples of conditional probability, Probability trees, Bayes’ Rule

Module 1.3 (English, Urdu)

  • Random variables, Geometric random variable, Binomial random variable, Expectation (mean) values, Worked examples. Poisson random variable, Call centre problem

Module 1.4 (English, Urdu)

  • Variance and standard variation, E[X] and E[X^2] for binomial distribution, The Chebyshev Rule, Cumulative Distribution Function, Continuous random variables, Connecting discrete to continuous probabilities, Examples of continuous probability distributions

Module 1.5 (English, Urdu)

  • Covariance and Correlation, Some simple properties of covariance, A physical understanding of covariance, Several discrete random variables, Illustrative solved examples

Module 1.6 (English, Urdu)

  • Two continuous random variables, Some basic formulae, Practice with double integrals, Example: trains arriving at a station, Example: aiming darts at a board, Example: Buffon’s needle

Module 1.7 (English, Urdu)

  • A function of generating moments, Example: Binomial Distribution, Example: Poisson Distribution, Example: Exponential Distribution, Introduction to Normal Distribution, Binomial Distribution Normal Distribution (proof), Law of Large Numbers (with proof)

Module 1.8 (English, Urdu)

  • Central Limit Theorem – with potatoes, CLT – why it is astonishing, Generating moments of the normal distribution, Generating moments for n independent variables, Proof of CLT, CLT for i.i.d’s that are uniformly distributed, CLT – three applications

Module 1.9 (English, Urdu)

  • One-dim drunkard’s walk – a first look, Random walk definitions, First return theorem, The eventual return problem, Random walk in two dimensions

Module 1.10 (English, Urdu)

  • States, Transitions, Markov Chains, Three examples of Markovian processes, Markovian basics, Regular (ergodic) Markov Chains, Absorbing Markov Chains

Recommended textbooks and materials:

  1. A Natural Introduction to Probability Theory, Robert Meester, Birkhäuser Verlag (2008).
  2. Introduction to Probability Models, 9th Edition, Elsevier (2009).
  3. Grinstead and Snell’s Introduction to Probability, the CHANCE Project (2006).
  4. Probability Theory and its Applications, William Feller, 3rd edition, John Wiley (1970).

For worked examples, I strongly recommend the books by Hossein Pishro-Nik which you can easily locate with a Google search.

Thermodynamics Made Easy

Languages: Urdu, English

These lectures are suitable for undergraduate level teaching (years 16-20) and provide the conceptual foundations of thermodynamics. Although several examples are worked out here, for a fuller grasp of the subject students should work out at least some problems in the texts recommended below.  

Module 1.1 (English, Urdu)

  • Heat, temperature, zero’th Law of thermodynamics, thermometers, absolute zero, third law of thermodynamics

Module 1.2 (English, Urdu)

  • Conversion of energy from one form to another, units of heat and energy, internal energy (example: ideal gas), thermodynamic variables and equation of state, isolated, closed and open systems, first law of thermodynamics (circa 1840), exact and inexact differentials

Module 1.3 (English, Urdu)

  • Adding heat to a system, various heat capacities of a substance, enthalpy and its uses, moles: a quick reminder from chemistry, measuring heat capacities, heat capacities of a non-ideal gas

Module 1.4 (English, Urdu)

  • Reversible and irreversible processes, isothermal expansion of a gas, adiabatic expansion of a gas, free expansion of a gas, application: speed of sound

Module 1.5 (English, Urdu)

  • Entropy – a qualitative understanding, entropy – formal definition, entropy as a state function, thermodynamic cycles, worked example

Module 2.1 (English, Urdu)

  • Heat engines and efficiency, carnot engine, second law of thermodynamics, equivalence between Clausius and Kelvin statements, the Carnot engine is universal – proof, analyzing the Carnot engine, solved example

Module 2.2 (English, Urdu)

  • Absolute temperature defined, the Clausius inequality – derivation, consequences of the Clausius inequality, why the entropy of the universe has to increase, using entropy as a state variable, solved example I, solved example II

Module 2.3 (English, Urdu)

  • Helmholtz free energy, Gibbs free energy, application to chemical reactions, melting and Gibbs free energy, open systems and Gibbs free energy, chemical potential – physical interpretation, chemical potential for an ideal gas

Module 2.4 (English, Urdu)

  • Examples of phase transitions, melting of ice – worked example, Euler’s theorem and molar quantities, Clausius-Clapeyron equation – derivation, phase diagrams, first and second order phase transitions

Module 2.5 (English, Urdu)

  • Black body basics (Planck, Stefan-Boltzmann, Wien), how hot is that star?, sun as a black body radiator, basics of the photon gas, thermodynamics of the expanding universe

Recommended textbooks and materials:

  1. Feynman Lectures in Physics – chapters 44, 45, 46
  2. Principles of Thermodynamics, Jean-Philippe Ansermet and Sylvain D. Brechet
  3. Essential Classical Thermodynamics, Ulf W. Gedde
  4. Problems and Solutions on Thermodynamics and Statistical Mechanics, World Scientific

Teach Yourself Waves And Oscillations

Language: English

Goal: To enable students to learn this beautiful subject with zero or minimal assistance.

Teach Yourself Quantum Mechanics

Language: Urdu

Goal: To enable students to learn this beautiful subject with zero or minimal assistance.

Teach Yourself Special Relativity

Languages: Urdu, English

Goal: To enable students to learn this beautiful subject with zero or minimal assistance.

Click here to download the contents and instructions for this series of 8 self-learning lectures.

Teach Yourself Calculus

Languages: Urdu, English

Goal: To enable students to learn this beautiful subject with zero or minimal assistance.

Click here to download the contents and instructions for this series of 30 self-learning lectures.

LECTURES

Teach Yourself Physics

Language: Urdu

Click here for accompanying Notes for Video Lectures (1-45) below:

BONUS LECTURES

7 Comments

Israr Karim · April 30, 2022 at 4:51 am

These courses are really helpful. If possible plz make a course on GRE Quantitative reasoning section etc.

Reply

Ani S · May 2, 2022 at 7:25 am

Great learning material! No one should have an excuse that they “missed” the class!

Reply

Muslim Hussain · May 10, 2022 at 5:55 pm

We will follow all lectures Inshallah

Reply

Dania · June 5, 2022 at 10:33 am

A great deal of lectures I found here… keep Up the best work sir 🤗🇵🇰

Reply

Tassawar Iqbal · June 25, 2022 at 3:13 pm

I will follow all lectures Insha Allah

Reply

Zain ul abidin · July 30, 2022 at 6:37 pm

How to get the membership for these tutorials

Reply

Shivam Kumar · May 16, 2023 at 9:26 am

Thank you parvezhoodboy sir I am fan of your way to explain science .I am from India and studying in IIT .The black hole youtube channel Provides Great understanding obout science

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