![[Main (1).png]] _Built by a physics student at the University of Waterloo, not a company. Made with ❤️_ > [!info] Quick Links > ➤ [[How to Use This Site|How To Learn Off This Site]] - Start here if you're new > ➤ [[Home#Explore Mathematics|Explore Mathematics ]] > ➤ [[Home#Explore Physics|Explore Physics]] > ➤ [[Home#About|About This Site]] > [!tip] Featured Topics > - [[▶ Learn How To Mathematically Prove|📌 Learn How To Prove]] > - Learn how to mathematically prove equations. From using logic to proofing methods. > - [[▶ Learn Physics 1|📌 Learn Classical Physics 1]] > - Learn calculus-based physics 1. From kinematics to rotational motion. > - [[Center of Mass Displacement|Center of Mass Displacement]] > - Vector difference for the displacement of the COM > - [[Indeterminate Forms|Indeterminate Forms]] > - Expressions of limits that can not be evaluated and are not allowed > - [[L'Hôpital's Rule]] > - How to algebraically manipulate and solve indeterminate forms > - [[Proof of Derivative Power Rule]] > - Mathematical proof of the derivative power rule ## About Math & Matter is a growing library of physics and math explanations. Built for students or self-learners who want to see the connections between different concepts. Where each concept is explained in simple language with diagrams, intuition and proofs as support. The goal is to help you _see_ the structure of mechanics and higher math, not just memorize it. **Free Forever.** # Explore Mathematics Build a solid foundation in mathematics through clear, structured notes. From logic and proofs to calculus and linear algebra, each topic is explained step-by-step with examples and diagrams to help you understand the ideas behind the formulas. > [!warning]- Beta Notice > Concepts are complete for **definitions** and **proofs/derivations**, but may lack full examples. Some pages are under active revision, and some sections may be missing topics. > [!info]- Version Beta-1.1.1 ![[Changelog]] ## Linear Algebra 1 Linear algebra 1 lays the groundwork for understanding vector spaces, linear mapping, and matrices. This section acts as a hub for reviewing key topics like subspaces, systems of equations, and the properties of matrices ### Learn - [[Coming Soon...]] - ### Review by Topic - [[▹ Euclidean Vector Spaces]] - Explores vector spaces equipped with a dot product, allowing measurement of angles and lengths - [[▹ Mapping]] - Acts as a central hub for understanding transformations between vector spaces, covering domains, codomains, images, and kernels - [[▹ Properties of Matrices]] - Index of fundamental matrix properties, such as rank, dimensions, and transposing - [[▹ Special Subspaces of a Matrix]] - Organizes the four key subspaces of a matrix — column space, null space, row space, and left null space — and their relationships - [[▹ System of Linear Equations]] - Organizes core concepts related to solving linear systems, including row operations, consistency, and solution sets - [[▹ Vector Spaces Foundations]] - Serves as a base hub for axioms, closure properties, and key theorems that define vector spaces, as well as span, basis, and related topics ## Calculus 1 Calculus 1 builds upon pre-calculus material to better understand limits, derivatives and integration. This section serves as a guide to mastering first principles and applying calculus to real problems. ### Learn - [[▶ Learn How To Mathematically Prove]] - Learn how to mathematically prove equations. From using logic to proofing methods. ### Review by Topic - [[▹ Absolute Values]] - Hub for definitions, properties, and inequalities involving absolute value - [[▹ Counting]] - Hub page listing combinatorics topics such as factorials, permutations, combinations, Pascal’s triangle, and the binomial theorem - [[▹ Derivatives]] - Central index for all derivative content, like rules, proofs, geometric interpretations, and applications - [[▹ Inequalities]] - Describes the squeeze theorem - [[▹ Intermediate Forms]] - Gateway to handling indeterminate forms like $0/0$ and $∞/∞$, featuring L’Hôpital’s rule and limit-based strategies - [[▹ Limits & Continuity]] - Portal to limit concepts and techniques such as epsilon-delta definition, analytical rules, and limit theorems - [[▹ Proofing Methods]] - Guide to proof methods like direct proof, proof by contradiction and proof by contraposition ## Miscellaneous Topics that are not directly related to a course - [[▹ Logic]] - Overview of logical foundations from real numbers, greatest common denominator, and conditional statements - [[▹ Simple Geometry]] - Hub of simple geometry definitions and proofs # Explore Physics Discover the principles that govern the physical world. Explore mechanics, electricity, magnetism, and more through detailed derivations, intuitive explanations, and visual aids that connect theory to real-world understanding. > [!warning]- Beta Notice > Notes are complete for **definitions** and **proofs/derivations** but may lack full examples. Some pages are under active revision, and some sections may be missing topics. > [!info]- Version Beta-1.1.1 ![[Changelog]] ## Classical Physics 1 Classical Physics 1 is a calculus-based physics section that builds upon previous physics courses, such as pre-physics/high school physics. This section acts as a hub for learning topics such as dynamics, kinematics and rotational motion. ### Learn - [[▶ Learn Physics 1]] - Learn calculus-based physics 1. From kinematics to rotational motion. ### Review by Topic - [[▹ Dynamics]] - Central index for mechanics topics such as motion, forces, Newton’s laws, and related theorems - [[▹ Energy & Work]] - Guide to energy concepts and work topics definitions, work–energy theorem, and power - [[▹ Kinematics]] - Cover the core kinematic quantities such as displacement, distance, velocity, speed, and acceleration - [[▹ Rotational Mechanics]] - (**New!**) Comprehensive index for rotational topics like torque, moment of inertia, angular kinematics, and energy - [[▹ Units & Dimensions]] - Gateway to SI units and dimensional analysis for units like newton, amp, joule, and coulomb ## Classical Physics 2 Classical Physics 2 builds upon Classical Physics 1 to introduce electricity, circuits, magnetism and sound. Using calculus-based derivations. This section acts as guide to learning these concepts. > [!bug]- Sections Being Revisited* > Sections starred with * are being heavily revised in the future. Sections starred mean they are hard to understand or are lacking explanations. > You can still use the note, but it may be hard to understand or have grammar mistakes. ### Learn - [[Coming Soon...]] - ### Review by Topic - [[▹ Circuits]] - Hub for circuit theory covering components, laws (KCL/KVL), and analysis techniques - [[▹ Electricity]] - A portal to electrostatics surrounding topics like charge, electric fields, potential, and related concepts - [[▹ Magnetism| ▹ Magnetism*]] - Overview of magnetic fields and interactions, including forces on moving charges - [[▹ Sound & Waves|▹ Sound & Waves*]] - Collection of wave phenomena - [[▹ Units & Dimensions]] - Gateway to SI units and dimensional analysis for units like newton, amp, joule, and coulomb --- <!-- Light Mode Newsletter Embed --> <div class="mm-form-light"> <iframe src="https://updates.cyberleadhub.com/widget/form/Y0kpQVpjJQuxEfX59m17" id="inline-Y0kpQVpjJQuxEfX59m17" title="Join Math & Matter Newsletter (Light)" data-height="900" scrolling="no" allowtransparency="true" loading="lazy" style="width:100%;height:350px;border:none;border-radius:10px;background:transparent;overflow:hidden" ></iframe> </div> <!-- Dark Mode Newsletter Embed --> <div class="mm-form-dark"> <iframe src="https://updates.cyberleadhub.com/widget/form/lbeDLm24VjuaFxhjccA1" id="inline-lbeDLm24VjuaFxhjccA1" title="Join Math & Matter Newsletter (Dark)" data-height="900" scrolling="no" allowtransparency="true" loading="lazy" style="width:100%;height:350px;border:none;border-radius:10px;background:transparent;overflow:hidden" ></iframe> </div> <script src="https://updates.cyberleadhub.com/js/form_embed.js"></script> --- # Site Information Core information of this site - [[Changelog]] - Highlights of changes to the website - [[How to Use This Site]] - A 3-minute read of the features of this website - [[License]] - Licensed under CC BY-NC-SA 4.0 - [[Purpose & About|Purpose & About Me]] - About the creator of the page & purpose - [[References]] - Key reference for videos used in understanding materials or notes taken from sites - [[Contributing]] - Help expand Math&Matter concepts - [[Support]] - Page for submitting errors & supporting future development - [[Privacy Policy]] - A notice of privacy statements and policies - [GitHub](https://github.com/rajeevphysics/Obsidian-MathMatter) - Github repository (Incomplete as of yet) <div class="mm-mobile-banner"> <input type="checkbox" id="mm-mobile-dismiss" /> <label class="mm-mobile-card" for="mm-mobile-dismiss"> <span class="mm-mobile-text"> <strong>Best on a larger screen.</strong> Mobile works, but hover previews and graph view are not available. 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