Tag Archive for: Undergraduate

AVX-512 conclusion

AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion

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1 Comment
In the first part of this article (AVX-512 Assembly Programing - Opmask Registers for Conditional Arithmetic), we looked at how opmask registers can be…
AVX-512 registers

AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic

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2 Comments
This is the second installment in a continuing series of articles on Intel AVX-512 assembly programming. The first installment is An Intro to AVX-512 Assembly…
Simple Harmonic Oscillator Laboratory

An Accurate Simple Harmonic Oscillator Laboratory

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2 Comments
[CONTENT] Learning ObjectivesExecute a specific experimental procedure to test a specific hypothesis. Use the Tracker video analysis software for…
AVX-512 Assembly Programming

An Intro to AVX-512 Assembly Programming

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10 Comments
History In 1998, the Intel Corporation released processors that supported SIMD (single instruction, multiple data) instructions, enabling processors to…
Hooke's Law Experiement

An Example of An Accurate Hooke’s Law Laboratory

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16 Comments
Learning Objectives Gain confidence and experimental care in making accurate measurements. Understand the relationship between force and spring…
Data Structures Programming

Intro to Data Structures for Programming

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11 Comments
Introduction In the first part of this series, I talked about some fundamental notions in the world of algorithms. Beyond the definition of an algorithm,…
Bernoulli's equation

Demystifying the Often Misunderstood Bernoulli’s Equation

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19 Comments
Introduction Bernoulli's equation is one of the most useful equations in the field of fluid mechanics, owing to its simplicity and broad applicability.…
vehicle power

Why Power Determines Vehicle Acceleration Limits

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33 Comments
Introduction One interesting problem when dealing with a vehicle of a certain mass is to determine what is required to get the maximum acceleration while…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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9 Comments
The purpose of this article is not to provide some rigorous statement, neither a rigorous clever proof of the fundamental theorem of calculus. It is rather…
LHC Energies

LHC Relativistic Energies and Time Dilation at 3.5–14 TeV

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Large Hadron Collider and proton energies The Large Hadron Collider has produced collisions at 7 TeV. For collisions at 7 TeV, each proton must be ramped…
Falling in Black Holes

Radial Infall into a Static Mass: Equations & Guide

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From Exploring Black Holes by John Wheeler and Edwin Taylor. The relations below apply to any object falling radially toward a static, spherically symmetric…
stock options math

Intuitive Black‑Scholes Options Pricing Explained Simply

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19 Comments
Introduction Financial options — the right to purchase (call) or sell (put) stock or other assets at a fixed price on a future date — have been around…
unity orbital mechanics

Unity Orbital Mechanics and AR Scaling: Implementation Guide

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2 Comments
In this Insight I describe implementing basic orbital mechanics simulations in the Unity game engine and an approach to scaling the simulation for Augmented…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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16 Comments
Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have the…
walter lewin

Lewin’s Circuit Paradox: Distinguishing E_s and E_m

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65 Comments
Introduction Much has lately been said regarding this paradox that first appeared in one of W. Lewin's MIT lecture series on YouTube (see References [1]).…
information definition

How to Better Define Information in Physics

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11 Comments
Introduction When I ask questions about the conservation of information I frequently get the reply, “It depends on what you mean by information.”  …
algorithms

Intro to Algorithms for Programming

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28 Comments
Many threads here at PF include some questions about how to learn to program. This is asked by Physics students who want to learn programming to help their…
ridler_motion2

Rindler Motion in Special Relativity: Rindler Coordinates

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27 Comments
Our destination In our last article, Hyperbolic Trajectories, we derived some facts about the trajectory of a rocket that is undergoing constant (proper)…
sun_getting_smaller

MESSENGER Detects Sun’s Mass Loss and Solar Expansion

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36 Comments
Paper and context Paper discussion: Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Antonio Genova, Erwan…
ridler_motion

Rindler Motion in Special Relativity: Hyperbolic Trajectories

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5 Comments
Introduction: Why Rindler Motion? When students learn relativity, it's usually taught using inertial (constant velocity) motion. There are lots of reasons…
statmech2

Learn Statistical Mechanics: The Ideal Gas

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11 Comments
Read Part 1: Equilibrium Systems The Ideal Gas: Boltzmann's Approach (The Microcanonical Ensemble) Consider a monatomic gas of ##N## non-interacting…
hilbertspaces

Learn the Basics of Hilbert Spaces and Their Relatives: Definitions

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2 Comments
  Basics Language first: There is no such thing as the Hilbert space.Hilbert spaces can look rather different, and which one is used in…
journeycosmos3

Learn About the FLRW Metric and The Friedmann Equation

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1 Comment
Previous Chapter: A Journey Into the Cosmos – The Friedmann Equation                Chapter 2- FLRW Metric and The Friedmann Equation In…
qm_interpretations

The Fundamental Difference in Interpretations of Quantum Mechanics

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191 Comments
A topic that continually comes up in discussions of quantum mechanics is the existence of many different interpretations. Not only are there different…
statmech1

Learn Statistical Mechanics: Equilibrium Systems

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20 Comments
This is the first of a multi-part series of articles intended to give a concise overview of statistical mechanics and some of its applications. These articles…

Demystifying the Chain Rule in Calculus

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7 Comments
Introduction There are a  number of posts on PF involving a general confusion over the multi-variable chain rule.  The problem is often caused by…
gps1

The Schwarzschild Metric: GPS Satellites

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4 Comments
 A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then…
cosmosintro

Learn About the Friedmann Equation and the Cosmos

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6 Comments
This is an introduction to cosmology for someone who has some knowledge of calculus and basic physics. In this tutorial, we will take a journey into the…
dice

Learn About Intransitive Dice with a Twist

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6 Comments
Intransitive dice are sets of dice that don't follow the usual rules for "is better/larger than". If A<B and B<C, then A<C. If Bob runs faster…
Maxwell equations

What is the Homopolar Generator: An Analytical Example

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8 Comments
Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…
dna_twist

How to Use the Spaghetti-Twist Method to Align DNA

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1 Comment
Twirling DNA Around a Rotating Wire A new paper from a group of Canadian physicists has demonstrated how simply twirling a wire through a solution of…
circuitanalysis

The What and Why of Circuit Analysis Assumptions

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15 Comments
Probably everyone reading this article already has education on elementary circuit analysis (CA) and many of us are much more advanced. Typically, the…
fourierseries2

Learn Further Sums Found Through Fourier Series

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5 Comments
In an earlier insight, I looked at the Fourier series for some simple polynomials and what we could deduce from those series. There is a lot more to be…
Parsevalstheorem

Learn an Integral Result from Parseval’s Theorem

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5 Comments
Introduction: In this Insight article,  Parseval's theorem will be applied to a sinusoidal signal that lasts a finite period of time.  It will be shown…
EdmondHamilton

The Second Satellite: Orbit, Gravity & Tidal Errors

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2 Comments
Introduction This article won't contain much about physics that typical readers of this site don't already know. However, deconstructing improper physics…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

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58 Comments
Introduction Let me start with a counter-question. What is a number? Before you laugh, there is more to this question than one might think. A number can…
dampedforces

Learn Damped Motion in Classical and Quantum Mechanics

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21 Comments
This Insights article is about dissipative forces (friction, air resistance, viscosity...).Damping by friction forces is one of the concepts that is…
SpectralParadox

Exploring the Spectral Paradox in Physics

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16 Comments
In terms of wavelength, peak solar radiation occurs at about 500 nm.  Interestingly, this is well within the range of human vision.  When solar radiation…
undergradresearch

Finding Niches for Publishable Undergraduate Research

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6 Comments
What 'Publishable' Means Undergraduate interest in research is a good thing; it's even better if they aspire to publish their work for review and consideration…
BondiKcalculus

Learn Relativity Using the Bondi K-calculus

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20 Comments
Although Special Relativity was formulated by Einstein (1905), and given a spacetime interpretation by Minkowski (1908) [which helped make special relativity…
lensfocus

Lenses and Pinholes: What Does “In Focus” Mean?

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11 Comments
Introduction In introductory physics, the optics unit often teaches about virtual and real images, focal lengths, indexes of refraction, etc. Some questions…
deriitive5

The Pantheon of Derivatives – Important Theorems (V)

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2 Comments
Implicit Function Theorem [1] Jacobi Matrix (Chain Rule). Let ## (x_0,y_0 ) ## be a point in$$U_1 \times U_2 = \{x \in \mathbb{R}^k\,\vert \,||x-x_0||<…
RelativityVariables

Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity

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8 Comments
Traditional presentations of special relativity place emphasis on "velocity", which of course has an important physical interpretation... carried over…
deriitive

The Pantheon of Derivatives – The Direction (I)

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3 Comments
  Differentiation in a Nutshell I want to gather the various concepts in one place, to reveal the similarities between them, as they are often…
diffractiontheory

The Diffraction Limited Spot Size with Perfect Focusing

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12 Comments
Purpose The purpose of this Insights article is to give the reader a brief introduction to the principles behind diffraction-limited focusing. The reader…
integraltrick

Trick to Solving Integrals Involving Tangent and Secant

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6 Comments
This little trick is used for some integration problems involving trigonometric functions is probably well-known, but I only learned it yesterday. So…
linearacceleration

Frames of Reference: Linear Acceleration View

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2 Comments
My previous Insight, Frames of Reference: A Skateboarder's View, explored mechanical energy conservation as seen from an inertial frame moving relative…
cornuspiral

Learn Frenet Equations in 2-D Which Result in the Cornu Spiral

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3 Comments
This Insights article is intended as an introduction to the Frenet-Serret equations by showing an interesting application that results from a case in two-dimensional…
magnet

Permanent Magnets Explained by Magnetic Surface Currents

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38 Comments
Introduction: The purpose of this Insight is to explain permanent magnets in a way that is in agreement with advanced textbooks on the subject, and that…
inferometer

Fabry-Perot and Michelson Interferometry: A Fundamental Approach

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14 Comments
Fabry-Perot Effect: The Fabry-Perot effect is usually treated in most optics textbooks as the interference that results from multiple reflections of the…
FourierSeries

Using the Fourier Series To Find Some Interesting Sums

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4 Comments
Preliminaries If f(x) is periodic with period 2p and f’(x) exists and is finite for -π<x<π, then f can be written as a Fourier series: [itex]f(x)=\sum_{n=-\infty}^{\infty}a_{n}e^{inx}…
quantumapplitudes

Learn About Quantum Amplitudes, Probabilities and EPR

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83 Comments
This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal…
angledimensions

Can Angles be Assigned a Dimension?

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106 Comments
1. Some Background on Dimensional Analysis ... if you are not already familiar with it. 1.1 Dimensions Dimensional Analysis is a way of analyzing…
partial-differentiation

Learn Partial Differentiation Without Tears

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6 Comments
Differentiation is usually taught quite well. Perhaps that's because it is the first introduction to calculus, which is considered a big step in a student's…
frameofreference2

Frames of Reference: A Skateboarder’s View

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22 Comments
My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue…
cubicfunction

Learn How to Solve the Cubic Equation for Dummies

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5 Comments
Everybody learns the "quadratic formula" for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don't really need such a formula,…
rollingmotion

Learn The Basics of Rolling Motion

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50 Comments
Introduction Although rolling wheels are everywhere, when most people are asked "what is the axis of rotation of a wheel that rolls without slipping?",…
ohmslaw

Learn Why Ohm’s Law Is Not a Law

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41 Comments
At first, I wanted this title to say “Ohm’s law is not a Law.”  But someone else used that phrase in a recent PF thread, and a storm of protest…
quantumhard

Why Quantum Mechanics Feels Difficult — Mathematical Bridge

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253 Comments
[CONTENT] QM's formalism Overview of the formalism Strangely enough, quantum mechanics (QM)'s formalism isn't any more difficult than other areas of…
entropy

How to Determine the Change in Entropy

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9 Comments
How do you determine the change in entropy for a closed system that is subjected to an irreversible process?Here are some typical questions we get…
LHC4

LHC Part 4: Searching for New Particles and Decays

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17 Comments
 The LHC experiments are in full swing collecting data this year (more information in the forum), and a while ago the collaboration of the…
acusticbeats

Mathematics of Acoustic Beats: Explanation & Examples

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11 Comments
Introduction Purpose and scope In late high school physics courses and first-year university courses, the phenomenon of acoustical 'beats' (digital audio)…

Learn About Relativity on Rotated Graph Paper

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15 Comments
This Insight is a follow-up to my earlier tutorial Insight (Spacetime Diagrams of Light Clocks). I gave it a different name because I am placing more…
integralmisconceptions

Integration Paradoxes: Indefinite Integrals and Constants

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40 Comments
Introduction Integration is an incredibly useful technique taught in all calculus classes. Nevertheless, there are certain paradoxes involved with integration…
basickinematics

Learn Basic Kinematics in Classical Mechanics

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8 Comments
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

Klein’s Erlangen Program: Groups Define Geometry

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7 Comments
Klein's Erlangen program: groups and geometry There is a very deep link between group theory and geometry. Sadly, this link is not emphasized in most…
selfstudy

Self-Study Roadmap: Abstract Algebra, Groups to Galois

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4 Comments
Overview Roadmap There are three major areas of mathematics: geometry, analysis, and algebra. This insight gives a roadmap for learning basic abstract…
computers

Ramsey Theory: Foundations, Generalizations, Key Results

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

Learn About Spacetime Diagrams of Light Clocks

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

Elementary Construction of the Angular Velocity

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1 Comment
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…
Photoacoustic

Light and Sound Interactions: Photoacoustic & Acousto-Optic

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6 Comments
Introduction I recently wrote a post on my blog about a fairly esoteric idea regarding sound propagating through light. This inspired me to write an…
logicp3

Scientific Inference: Balancing Predictive Success with Falsifiability

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9 Comments
  Bayes' Theorem: Balancing predictive success with falsifiability Despite its murky logical pedigree, confirmation is a key part of learning.…
logicp2

Scientific Inference: Do We Really Need Induction?

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14 Comments
  Part 2. "We don't need no stinkin' induction" -- Sir Karl Popper The traditional scientific method supposedly employs induction both in the…
linearalgebra_selfstudy

Linear Algebra Roadmap: Prereqs, Books & Topics Guide

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11 Comments
Overview This article gives a roadmap for students to learn the basics of linear algebra. Aside from calculus, linear algebra is one of the most applicable…
logic1

Hume and the Problem of Induction in Science Explained

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39 Comments
Click for Full SeriesPart 1: Logical induction ain’t logical Part 2: We don’t need no stinkin’ induction Part 3: Balancing Predictive Success…
encryption

Is It Possible to Design an Unbreakable Cipher?

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10 Comments
Is it possible to design an unbreakable cipher? Do methods of encryption exist that guarantee privacy from even the most capable and highly-resourced…
acpoweranalysisp2

Intro to AC Power Analysis: Network Analysis

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26 Comments
 Let me use the terms “power grid” and “network” interchangeably. What is the Power Grid Required to Do?Deliver energy to customers,…
universeexpand

Big Bang Models: Expansion, Dark Energy, Inflation

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29 Comments
Big Bang and expansion (no inflation, no dark energy) Empty-universe solution (FLRW) Einstein's General Relativity allows a solution (the FLRW metric)…
acpoweranalysisp1

Intro to AC Power Analysis: Learn System Basics

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13 Comments
 Instantaneous PowerThe formula for power is: ##P=V\cdot I## , power= voltage*current.   We call that, instantaneous power.   Even…
geometry1

Pure Geometry Study Guide: Books & Roadmap for Students

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3 Comments
Introduction to Pure Geometry Why study pure geometry? Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest…
mathanalysis1

Self-Study Analysis Roadmap: From Proofs to Manifolds

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26 Comments
Introduction 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…
physics_vectors

Frequently Made Errors in Vectors – Elementary Use

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

TCP/IP Protocols for Plug-and-Play Industrial Automation

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10 Comments
Background: Ethernet vs Fieldbus in the 1990s The 1990s saw the widespread adoption of network technology on two fronts: Office automation and factory…
Ethernettime

Network Time Synchronization Guide: NTP vs IEEE 1588

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18 Comments
Overview of Synchronization Needs Now and then you come across measurement problems that are tightly associated with the notion of synchronicity, meaning…
lightcone7_3

LightCone 8 Tutorial Part III – How Things are Computed

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1 Comment
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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7 Comments
Eukaryote evolution and cellular complexity Historically, life is categorized into three broad domains: bacteria, archaea, and eukaryota.  Whereas bacteria…
secondaryforces

Introduction to the Secondary Forces in Physics

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

Hear the Case for Learning Complex Math

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15 Comments
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. …
computermath

Why Can’t My Computer Do Simple Arithmetic?

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46 Comments
The first computer I owned was an Apple IIe computer, with a CPU that ran at slightly over 1 Megahertz (MHz), and with 64 Kilobytes (KB) of RAM, together…
lightcone72

LightCone8 Tutorial Part II – Charts

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3 Comments
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…
quasarredshift

Evidence that Galaxy and Quasar Redshifts Are 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 Historical…
Eigenvectors

What Are Eigenvectors and Eigenvalues in Math?

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37 Comments
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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2 Comments
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?

Why ask "why" about physical laws? The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you…
complexnumbers

Things Which Can Go Wrong with Complex Numbers

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3 Comments
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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31 Comments
Infinity in Mathematics and Physics It is beyond doubt that the notion of infinity lies somewhere near the core of all mathematics, probably in a finite…
MillenniumPrize

Millennium Problems: Poincaré, P vs NP, Riemann

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13 Comments
IntroductionWhat this Insight Covers In this Insight, I will go over the background information for the Millennium Prize problems and briefly describe…
micro2

Peano Axioms: Construction of Natural Numbers and Properties

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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,...\}##.…