Two decades of teaching, distilled into one searchable index. Each note shows the derivation, the worked example, and the place where most students get stuck. Read in your browser, print on paper, study at 2 AM. No signup, no ads, no PDFs to download.
100s of notes / 4 subjects / Updated weekly / Free forever
Special relativity changed our understanding of space, time, and energy forever. Einstein’s two postulates lead to mind-bending consequences: time dilation, length contraction, and mass-energy equivalence. This guide covers the mathematical framework of special relativity with clear derivations, thought experiments, and practical applications in modern physics.
Open note →Function notation and rules form the foundation of higher mathematics. Understanding how functions work, including domain, range, composition, and inverse operations, is essential for algebra, calculus, and beyond. This reference page covers function notation conventions, key rules for function operations, graphical interpretation, and worked examples that build solid understanding. Whether you’re studying for exams or reviewing fundamentals, this resource has you covered.
Open note →Proteins are the molecular machines of life, performing virtually every function in living cells. From enzymes and antibodies to structural components and signaling molecules, proteins are extraordinarily diverse. This guide covers protein structure from primary to quaternary levels, amino acid building blocks, protein synthesis, denaturation, and key biological functions.
Open note →
Sets, functions, sequences, identities. The foundations every JEE, IB, and university math student needs in long-term memory.
Trigonometric identities are the backbone of advanced mathematics, appearing in calculus, physics, engineering, and signal processing. This comprehensive reference organizes every essential trig identity with clear explanations and proofs. From Pythagorean and reciprocal identities to double-angle, half-angle, and sum-to-product formulas, everything you need is in one place. Bookmark this page for quick reference during problem-solving and exam preparation.
Whole numbers are the foundation of arithmetic and number theory. Starting from zero and extending infinitely, they form the basis for counting, ordering, and basic mathematical operations. Understanding whole numbers, their properties, and how they relate to integers, natural numbers, and rational numbers builds mathematical fluency. This reference page covers definitions, properties, operations, number line representation, and practice problems.
Supremum and infimum are fundamental concepts in real analysis that extend the ideas of maximum and minimum. The supremum is the least upper bound of a set, while the infimum is the greatest lower bound. These concepts are critical for understanding limits, continuity, and convergence. This reference page covers definitions, properties, theorems, and worked examples for both supremum and infimum in mathematical analysis.
Function notation and rules form the foundation of higher mathematics. Understanding how functions work, including domain, range, composition, and inverse operations, is essential for algebra, calculus, and beyond. This reference page covers function notation conventions, key rules for function operations, graphical interpretation, and worked examples that build solid understanding. Whether you’re studying for exams or reviewing fundamentals, this resource has you covered.
Sets are fundamental mathematical objects that form the basis of modern mathematics. From set notation and types of sets to operations like union, intersection, and complement, understanding set theory is essential for discrete mathematics, probability, and computer science. This reference covers set definitions, notation, operations, Venn diagrams, and key properties.
Mechanics, units, fundamental forces, relativity, particle physics. Notes that show the working, not just the formula.
The International System of Units (SI) is the globally accepted standard for scientific measurement. It defines seven base units: meter, kilogram, second, ampere, kelvin, mole, and candela. This reference covers all SI units, derived units, prefixes, and conversion factors that students need for physics, chemistry, and engineering coursework.
Units and measurements form the foundation of all scientific calculation. From SI units and dimensional analysis to significant figures and unit conversion, mastering these concepts is essential for physics, chemistry, and engineering students. This reference guide covers all standard units, conversion factors, and measurement principles you’ll need throughout your studies.
Physics fundamentals start with understanding forces, motion, and energy. This reference covers the key concepts in classical mechanics, including Newton’s laws, friction, gravity, and work-energy theorems. Designed for students who need a clear, organized review of basic physics principles with formulas, definitions, and examples in one place.
Everything in the universe is governed by four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Understanding these forces is essential for physics students. This guide explains each force, its mediating particle, relative strength, and range, along with the ongoing quest to unify them into a single theoretical framework.
Special relativity changed our understanding of space, time, and energy forever. Einstein’s two postulates lead to mind-bending consequences: time dilation, length contraction, and mass-energy equivalence. This guide covers the mathematical framework of special relativity with clear derivations, thought experiments, and practical applications in modern physics.
Einstein’s field equations are the mathematical heart of general relativity, describing how matter and energy curve spacetime. These ten coupled nonlinear partial differential equations are among the most elegant and complex in all of physics. This reference covers the equations’ formulation, key components like the stress-energy tensor, and their physical significance.
Bosons are the force-carrying particles of the Standard Model. Photons carry electromagnetic force, gluons carry the strong force, W and Z bosons carry the weak force, and the Higgs boson gives particles their mass. This guide covers each boson type, their properties, interactions, and role in fundamental physics, with clear explanations for students studying particle physics.
The Standard Model of particle physics is the most successful scientific theory ever tested. It describes 17 fundamental particles and three of the four fundamental forces. This guide covers quarks, leptons, bosons, the Higgs mechanism, and the mathematical framework that holds it all together. Essential reading for physics students wanting to understand the building blocks of matter.
Acids, bonds, supramolecular chemistry. Concept-first notes for CBSE, NEET, and undergraduate organic and inorganic.
Muriatic acid, also known as hydrochloric acid, is one of the most commonly used industrial and household acids. From pool maintenance and masonry cleaning to metal processing, understanding its properties, handling procedures, and safety precautions is essential. This reference covers muriatic acid’s chemistry, common uses, safety guidelines, and storage requirements.
Inclusion compounds are fascinating chemical structures where one molecule (the host) traps another molecule (the guest) inside a cage or channel. I explain the types, formation mechanisms, and real-world applications of these compounds, from drug delivery systems to industrial separations. No covalent bonds involved. Just geometry doing the work.
Foundation for NEET, CBSE class 11/12, and pre-med biochem.
Enzymes are biological catalysts that speed up chemical reactions in living organisms without being consumed in the process. They’re essential for digestion, metabolism, DNA replication, and virtually every biological process. This guide covers enzyme structure, classification, kinetics, inhibition, and regulation, providing a clear reference for biology and biochemistry students.
Nucleic acids, specifically DNA and RNA, carry the genetic information that defines every living organism. Understanding their structure, function, and replication is fundamental to molecular biology. This guide covers nucleic acid structure, base pairing, DNA replication, RNA types, gene expression, and the central dogma of molecular biology for science students.
Lipids are the diverse group of biomolecules that include fats, oils, waxes, steroids, and phospholipids. They serve critical roles in energy storage, cell membrane structure, insulation, and hormone production. This reference covers lipid classification, structure, properties, and biological functions, providing a comprehensive overview for biology and chemistry students.
Proteins are the molecular machines of life, performing virtually every function in living cells. From enzymes and antibodies to structural components and signaling molecules, proteins are extraordinarily diverse. This guide covers protein structure from primary to quaternary levels, amino acid building blocks, protein synthesis, denaturation, and key biological functions.
Carbohydrates are the body’s primary energy source and one of the four major biomolecules. From simple sugars like glucose and fructose to complex polysaccharides like starch and cellulose, carbohydrates serve diverse biological functions. This reference covers carbohydrate structure, classification, metabolism, and their essential role in living organisms.
Two decades of educating IIT-JEE math, NDA prep, and more. Every note is what I wish someone had handed me at exam time.
Read any free study note unlimited times without an account or email gate. The page loads in under a second on a 3G connection.
Whenever CBSE, JEE, or NEET update their syllabus, the affected notes get a refresh within the week. Updated dates show under each note.
This index updates automatically. Whenever a new free study note goes live, it appears here within minutes — no manual page edit needed.
Yes. Every note on this page is free to read, free to download, free to print. No signup, no email gate, no paywall. The site is funded by my consulting work and a few honest affiliate links elsewhere — none of that touches what you read here.
The notes work for school boards (CBSE, ICSE, IB), engineering entrance (JEE Main, JEE Advanced, BITSAT), medical (NEET), civil services prelims (IAS, UPSC general science), and most undergraduate or postgraduate university courses in math, physics, chemistry, and biology. They’re built around the underlying concepts, so the same note works across exam boards.
By subject — mathematics, physics, chemistry, and biology — then by topic within each subject. Each topic has its own page with a focused explainer, worked examples, and where useful a problem set with step-by-step solutions. The full index lower on this page lists everything currently published.
I add 1–2 new notes per week, mostly in response to what students ask me on email or in comments. Existing notes get refreshed whenever a syllabus update lands or a reader spots an error. The most recently updated dates show under each note.
Most notes are designed to print cleanly straight from the browser — the print stylesheet strips the menu, ads, and sidebar so you get just the content on plain paper. A formal PDF version of the highest-traffic notes is on my list; subscribe to the Friday Drop newsletter for the release announcement.
Because that’s the cluster I taught for years — IIT-JEE math, NDA prep, B.Ed pedagogy. The connections between sets and functions in math, units and measurements in physics, and reaction stoichiometry in chemistry are the hard part for most students. Keeping all four subjects in one place makes those connections explicit.
Three things. First, every note is written by one person — me — so the voice and depth are consistent. Second, the focus is on the why before the how: derivations and intuition before plug-and-chug formulas. Third, no ads or signup walls between you and the content.
Email gaurav@gauravtiwari.org with the exact topic, the exam or course you’re prepping for, and one question you wish a good note would answer. If it would help more than one student, I usually publish a draft within a week and reply with the link.
One Friday email a week. Subject-tagged so you can filter to just math, just physics, etc. No spam, easy unsubscribe.
Email me the topic and the exam you are preparing for. If it would help more than one student, I will publish the note within the week and reply with the link.
Request a study note →