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no tidal bulge

Beyond the Tidal Bulge

Overview That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet the tidal bulge is still used to portray why the Moon is receding the Earth. If there is no tidal bulge, some other explanation is in order. That other explanation uses gravitation as…

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Learn Basic Kinematics in Classical Mechanics

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There is an interesting thing in teaching of Classical Mechanics. Several theorems which presented below form a core part of kinematics for all Russian…
groupsandgeometry

Exploring the Relationship Between Group Theory and Geometry

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There is a very deep link between group theory and geometry. Sadly, this link is not emphasized a lot in most courses of group theory, even though it is…
selfstudy

How to Self Study Abstract Algebra

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There are three big parts of mathematics: geometry, analysis, and algebra. In this insight, I will try to give a roadmap towards learning basic abstract…
computers

An Interesting Ramsey Theory Riddle

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Ramsey theory has its origins in a very nice riddle Consider a party of 6 people. Any two of these 6 will either be meeting each other for the first time…

Learn About Spacetime Diagrams of Light Clocks

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We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45 degrees. Many quantitative…
kinematics

Presenting a Rare Kinematic Formula

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Here we present some useful kinematic fact which is uncommon for textbooks in mechanics. Consider a convex rigid body (RB) rolling without slipping…
universestart

Where Did the Big Bang Happen?

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According to standard cosmological models, which are based on general relativity and are found to agree well with observations, time and space did not…
nugatory

Interview with a Physics Mentor: Nugatory

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Give us a little background on yourself? I was born in Washington DC, grew up in Texas, bachelor's in physics from Harvard in 1978 but found a career…

A Black Hole Problem From Greg Egan’s “Incandescence”

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The following problem was inspired by reading Greg Egan's "Incadescence".  Consider a body, orbiting a Schwarzschild black hole and tide locked to it,…
angularvelocity

Elementary Construction of the Angular Velocity

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Physics books seldom contain an accurate definitions of the angular velocity of a rigid body. I believe that the following construction is as simple as…
softwarenotperfect

Why Your Software is Never Perfect

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We occasionally have students ask for help on software, "My software is perfect, but it doesn't work!" Your software is never perfect. My software is never…
selfstudy

5 Problems with Students Self Studying Mathematics

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For several years already I have been trying to help students who have been self-studying math. I did this completely free with no compensation for me.…
irrationalnumbers

Mathematical Irrationality for Dummies

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On one of my restless wanderings around the Internet, I came upon a collection of proofs of the statement that the square root of 2 is an irrational…
Photoacoustic

The Interaction of Sound and Light

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logicp3

Scientific Inference: Balancing Predictive Success with Falsifiability

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seancarroll

Interview with a Physicist: Sean Carroll

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physicsathome

Resources for High School Physics at Home

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A year-long high school Physics course is important preparation for all college majors in science, engineering, and medicine because students in these…
themoon

Moon Quiz: Test Yourself on the Moon

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How to Self Study Intermediate Analysis Math

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MathJax Developer: Peter Krautzberger

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logicp2

Scientific Inference: Do We Really Need Induction?

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linearalgebra_selfstudy

How to Self Study Linear Algebra for Students

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In this insight, I will give a roadmap to learn the basics of linear algebra for students. Aside from calculus, linear algebra is one of the most applicable…
antigravity

Roger Babson’s Anti-Gravity Contest and Modern Physics

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In the early 20th century, an eccentric businessman named Roger Babson declared gravity to be mankind's greatest threat. He devoted part of his fortune…
mathresources

Resources for High School Math at Home

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The popularity of homeschooling and failures of the public schools often present the need for parents to teach or supplement college preparatory math courses…
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Scientific Inference: Logical Induction Ain’t Logical

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Interview with Chemical Physicist: DrClaude

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Interview with a Physics Mentor: PeterDonis

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PeterDonis is a Physics Mentor at Physics Forums Give us a little background on PeterDonisI have been interested in science since childhood.…
mathiq

Am I Cut Out for Mathematics or Sciences?

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We often get threads from new members asking whether they are cut out for mathematics/physics/engineering/whatever. For some reason, they have become discouraged…
personaltheories1

Why Won’t You Look at My New Theory?

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In any forum where science is discussed, there will always be people who have a great new personal theory and can't understand why no one else is interested…
highschoolmath

In High School and Want to Do Advanced Mathematics?

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This insight is written for high school students who don't feel very challenged by their high school courses. Or maybe those high school students who want…
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Learn the Top Misconceptions about Virtual Particles

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This Insight Article is a sequel to the Insight Article ''The Physics of Virtual Particles'', which contains an exposition of definitions that are physically…
acpoweranalysisp3

AC Power Analysis: The 4 Levels of Cyber Resilience

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How Representative is the Night Sky?

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encryption

Is It Possible to Design an Unbreakable Cipher?

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quantumentanglement

How the EPR Paradox Fits Between Entanglement and Nonlocality

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If we violate a Bell inequality, we know we have quantum entanglement, and it used to be thought that these two notions were one and the same.At least,…
acpoweranalysisp2

Intro to AC Power Analysis: Network Analysis

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Newton-Cartan-Theory

The Revival of Newton-Cartan Theory in General Relativity

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virtualparticles

Learn the Physics of Virtual Particles in Quantum Mechanics

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universeexpand

Learn about the Big Bang and the Expansion of the Universe

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Learn the Secrets of Successful Science Projects

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Abstract Over the past few years, the author and his wife have served as teachers, qualified scientists, mentors, and/or parents on dozens of science…
acpoweranalysisp1

Intro to AC Power Analysis: Learn System Basics

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Interview with Mathematical Physicist John Baez Part 2

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Read part 1 of this interview. Tell us about your experience with past projects like "This Week's Finds in Mathematical Physics". I was hired by U.C.…
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Interview with a Mathematical Physicist: John Baez Part 1

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The Monographic Substitution Cipher: From Julius Caesar to the KGB

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Interview with Theoretical Physicist Garrett Lisi

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How to Self Study Geometry for Students

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Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest minds humankind has to offer. It has been described…
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Learn the Basics of Positron Emission Tomography (PET)

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PET Key PointsPaul Dirac first theorized positrons in 1928 and they were observed four years later by Carl Anderson. Positron Emission Tomography…
mathanalysis1

How to Self Study Analysis: Intro to Analysis

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This is a sequel to my posts on self-studying mathematics. I have already given a very detailed road map on how to study high school mathematics and calculus.…
physics_vectors

Frequently Made Errors in Vectors – Elementary Use

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 A vector has magnitude and direction. Pictorially, a vector can be imagined as a location in n-dimensional space relative to some fixed origin. …
berkeman

Interview with an Electrical Engineer: Berkeman

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Can you give us a brief history of berkeman?I grew up in a military family (my dad was an Army colonel), so we moved all over the place when I was…
tcp_ip

How to Manage TCP/IP In Automation or Measurement Networks

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The 1990s saw the widespread adoption of network technology on two fronts: Office automation and factory automation. But while office automation soon standardized…
Ethernettime

Learn Time Synchronization Across Switched Ethernets

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Now and then you come across measurement problems that are tightly associated with the notion of synchronicity, meaning that things need to happen simultaneously.…
qminterpret

Tools to Enrich our Quantum Mechanics Interpretations Discourse

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IntroductionMany times, we encounter ourselves tangled in some Quantum Mechanics (QM) interpretations debates. Unfortunately, the standard…
chemist

Interview with a Chemist: Borek

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Give us a brief history of BorekNote: text below is of a negative pedagogical value, don't read it if you are younger than 20, attending school or…
spacetime6

Struggles with the Continuum – Freeman Dyson and QED

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 Last time I sketched how physicists use quantum electrodynamics, or 'QED', to compute answers to physics problems as power series in the…
lightcone7_3

LightCone 8 Tutorial Part III – How Things are Computed

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In Part I and Part II of this mini-series, we have briefly discussed the basic user interface and the use of charts to depict the LCDM cosmological model.…
universeexpansion

At What Velocity Does the Universe Expand and Can It Be Faster than Light?

Neither of these questions makes sense in the form in which it was posed. To see why, let's start by thinking about how we know the universe is expanding.The…
Mitochondria

When did Mitochondria Evolve?

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Historically, life is categorized into three broad domains: bacteria, archaea, and eukaryota.  Whereas bacteria and archaea are almost all relatively…
zapperz

Interview with a Physicist: ZapperZ

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This is a new Interview category for Insights. While I line up some great new interviews I’ll be migrating some previous mentor interviews.ZapperZ is…
islingmodel

High Temperature and Low Duality for the Ising Model on an Infinite Regular Tree

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Today I felt like sharing a computation that I thought was interesting. I'm sure I'm not the first to explore the Ising-Ising duality in this context,…
secondaryforces

Introduction to the Secondary Forces in Physics

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Many are familiar with the "fundamental forces" of nature: gravity, electromagnetism, and the strong and weak nuclear forces. Three of these tend to bind…
scientistquotes

Which Scientist Said What Quiz

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Interview with a Biophysicist: Andy Resnick

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Let me introduce you to Andy Resnick, a long time Science Advisor at Physics Forums. Tell us a little bit about how you developed an interest…
complexmath

Hear the Case for Learning Complex Math

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Resistance to complex math seems to never die out.  I see it frequently in PF posts.  Often it takes the form of challenges rather than questions. …
spacetime5

Struggles with the Continuum: Quantum Electrodynamics

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  Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics…
complexexponents

Learn Complex and Irrational Exponents for the Layman

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This Insight is part of our "Young Authors" series, where talented young students showcase their knowledge.  This is how both you and I learned…
darkmatter

Learn About Knut Lundmark and the Prehistory of Dark Matter

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Look in your standard cosmology textbook (in my case, the closest one at hand is Barbara Ryden's Introduction to Cosmology) and go to the section that…
docal

Interview with a Physicist: Doc Al

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This is a new Interview category for Insights. While I line up some great new interviews I’ll be migrating some previous mentor interviews.Doc Al is…
computermath

Why Can’t My Computer Do Simple Arithmetic?

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https://www.youtube.com/watch?v=yYSlcBghLZMThe first computer I owned was an Apple IIe computer, with a CPU that ran at slightly over 1 Megahertz…
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Interview with an Engineer: Russ Watters

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This is a new Interview category for Insights. While I line up some great new interviews I'll be migrating some previous mentor interviews.Russ…
lightcone72

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Part I dealt with the basic user interface of LightCone8. This part of the tutorial is about potentially useful cosmological insights to be gained from…
spacetime4

Struggles with the Continuum – Relativity and Quantum

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 In this series, we're looking at mathematical problems that arise in physics due to treating spacetime as a continuum---basically, problems…
quasarredshift

Could Redshifts Be Intrinsic Rather than Cosmological?

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How do we know that the redshifts of galaxies and quasars are cosmological and not "intrinsic?" Evidence for the cosmological interpretation The purpose…
Eigenvectors

What Are Eigenvectors and Eigenvalues in Math?

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Two important concepts in Linear Algebra are eigenvectors and eigenvalues for a linear transformation that is represented by a square matrix. Besides…
lightcone7

LightCone8 Tutorial Part I

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LightCone 8 is a versatile tabulating/charting cosmological calculator, useful for understanding the expansion history of the universe (and even some future…
speedlightframe

Why Is the Speed of Light the Same in All Frames of Reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be…
complexnumbers

Things Which Can Go Wrong with Complex Numbers

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At the first sight, there are many paradoxes in complex number theory. Here are some nice examples of things that don't seem to work:Example A [itex]-1=i^2=\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1[/itex]Example…
theneedforinfinity

Why the Need of Infinity in Physics

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It is beyond doubt that the notion of infinity lies somewhere near the core of all mathematics, probably in a finite vicinity of zero. But where does it…
complexscience

Thoughts on the Complexity of Modern Science

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Science today is incredibly complex. Anyone who ever did scientific research knows that, but many in the general public seem to be completely unaware of…
MillenniumPrize

Intro to the Millennium Prize Problems

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IntroductionIn this Insight, I will go over the background information for the Millennium Prize problems and briefly describe three of them. A future…
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Exploration into the Physics of Rainbows

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https://www.youtube.com/watch?v=JYr0LNWwhAs For several years, I have been contemplating this beautiful picture by photographer Brian McPhee.  I have…
micro2

Learn Axioms for the Natural Numbers

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** Bloch Chapter 1.2The Peano system in Bloch has a special element ##1\in \mathbb{N}##. The intuitive idea here is that ##\mathbb{N} = \{1,2,3,...\}##.…
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Introduction to Partial Fractions Decomposition

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Partial fractions decomposition is an algebraic technique that can be used to decompose (break down) a product of rational expressions into a sum…
micro3

An Intro on Real Numbers and Real Analysis

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It is important to realize that in standard mathematics, we attempt to characterize everything in terms of sets. This means that notions such as natural…
earthgravity

Learn All About Earth’s Gravity

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Earth's gravitational field at the surface is approximately 9.8 Newtons/kilogram or 9.8 meters/second/second. But how does that change due to its shape,…
earlyuniverse

Was the Early Universe in a Disordered State?

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blackholeexists

Do Black Holes Really Exist?

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Introduction The purpose of this article is to discuss the title question from several different viewpoints, to show that it isn't as simple as it looks.…
greenhouse

Frequently Made Errors in Climate Science – The Greenhouse Effect

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1.What is meant by "The Greenhouse Effect"? Many gases, such as H2O, CO2, CH4, are transparent to visible light but absorb and emit parts of the infrared…
speedoflight1

Learn About the Speed of Light and Galilean Relativity

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Speed of Light Key PointsEarly experiments attempted to measure the speed of light, including Galileo's lantern experiment, Ole Rømer's eclipse…
icequiz

Ice Quiz: All About Ice Trivia

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Winter is coming. First day of Winter is December 22nd. Time to learn a bit about a substance that the northern regions will encounter. Don't forget to…
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What Causes Cancer: Bad Luck or Bad Lifestyles?

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What causes cancer? For the most part, cancer is a disease that arises from mutations in the body that accumulate over time.  These mutations knock out…
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Understanding Buoyancy: The Limits of Archimedes

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It’s a principle as old as science itself, and remarkably, remains essentially unchanged in the light of revolution after revolution in our understanding…
observableuniverse

Radius of the Observable Universe in Light-years Is Greater than Its Age

The radius of the observable universe is about 46 billion light-years, which is considerably greater than its age of about 14 billion years. The radius…
heat

How to Build a Definition for Heat

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One of the most frustrating misconceptions in Thermodynamics centers on the actual definition of heat. Many science/engineering students often refer to…
ODE2

How to Solve Nonhomogeneous Linear ODEs using Annihilators

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My previous Insights article, Solving Homogeneous Linear ODEs using Annihilators, discussed several examples of homogeneous differential equations, equations…
steadystate

What Is the Steady-state Model and Why It’s No Longer Viable

Introduction to the Steady State Model Back in 2011, I wrote a FAQ entry for Physics Forums on the steady state model and why it is no longer viable.…
ODE1

Solving Homogeneous Linear ODEs using Annihilators

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In this Insights article we'll look at a limited class of ordinary differential equations -- homogeneous linear ODES with constant coefficients. Although…
physicsturnedmath

Trials and Tribulations of a Physicist who Became a Math Geek

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How did I go from the brink of changing my major from physics to ceramics (no more math) to the Math faculty of the Air Force Academy? How did I go from…