Reviewed in the United States on January 10, 2021, I ordered and xlarge because i like my shirts a little biggie, its so small. Here are my solutions to problems. Lowell Bogg, Core Course 3: Special Relativity and Classical Field Theory, Stanford Institute for Theoretical Physics, Solutions to The Theoretical Minimum, Classical Mechanics, Solutions to The Theoretical Minimum, Quantum Mechanics, https://en.wikipedia.org/w/index.php?title=The_Theoretical_Minimum&oldid=1097615785, Creative Commons Attribution-ShareAlike License 3.0. Homework questions can be on-topic when they are useful to a broader audience. Actually though, if youve never seen matrices and very simple linear algebra, this is a good place to learn some basics examples of this subject. Maurice Quentin de La Tour (1704 1788), Miyamoto Musashi ( , c. 1584 13 June 1645), A Geometric Approach to Differential Forms (.pdf). They help make the connection between symmetries and conservation laws more explicit. The notions of phase space, momentum and energy are introduced. Substituting the perturbative form for f ( x, t) into the Liouville equation, one obtains. Thanks. The The last third of the book is a quicker-paced trip through the usual material about wave-functions and the Schrdinger equation, ending up with the details for the harmonic oscillator potential. Improve this question From Leonard Susskind's book The Theoretical Minimum. 2022 ARS Air, LLC. Taylors Classical Mechanics is as good as they come. It only takes a minute to sign up. A tag already exists with the provided branch name. There are countless books on classical mechanics out there, but here Ive distilled them to my top 3 picks (believe me, it wasnt an easy choice!). Sorry but this isnt material Ive taught at this level, and I dont know the textbooks. Here, Ive explained why I picked these 3 books above as well as who Id recommend them to as well as what areas of classical mechanics they cover so that you can find the best one for your personal needs. Perhaps surprisingly, the first chapters of A. Zee Einteins Gravity in a Nutshell contain an amusing introduction to variational calculus, actions and lagrangians. For the reader's convenience, the problem assignments are reproduced in this volume. Part Two presents basics from the areas of continuum mechanics (dynamics, elasticity, fluids, electricity, magnetism). My degree was in Electrical Engineering in 1980, so I had taken most of the background science classes that Susskind is describing. : Its really cute, but does run small! One way to approach this problem is using the effective potential formalism. I made the mistake of watching the older ones which arent as closely coordinated with the book that I am over halfway through. But it's a long sleeve t-shirt. The linear algebra needed is developed from scratch and Susskind works out at a very leisurely pace all the details of what the quantum picture of reality looks like in this simplest context. This final lecture is a general review of all the concepts learned so far applied to a particle in electric and magnetic static fields. Definitely not a sweatshirt, thin material and runs a little small. In this unconventional introduction, physicist Leonard Susskind and citizen-scientist George This covers special relativity and classical field theory. $\implies \frac{\partial L}{\partial \dot{\theta}} = mr^2\dot{\theta} \equiv l$ (which is constant over time.). I went from freshman physics to the theoretical minimum by watching Susskinds lectures on classical mechanics and QM on youtube, and I can veryify from that perspective that they are excellent. Beams Professor Recall f 0 / t = 0. here or over Reviewed in the United Kingdom on November 1, 2017, [this is a review of the version published by Penguin Books, London 2014], Reviewed in the United Kingdom on May 29, 2021. wikimedia.com Is the rarity of dental sounds explained by babies not immediately having teeth? Planetary motion: with a different nature of potential. Majors. Please try your request again later. WebThis volume, Classical Mechanics: Problems with solutions contains detailed model solutions to the exercise problems formulated in the companion Lecture notes volume. How can a Lagrangian containing no potential energy be used to describe motion of a pendulum? We then study three formulations of classical mechanics respectively by Lagrange, Hamiltonian and Poisson. I only noticed one mistake in the book, on its back cover, where one of the blurbs is attributed to a Professor of Mathematics at Columbia, when I know for a fact that his actual title there is Senior Lecturer. these problems, such as the Bethe Ansatz. So many reviewers rave about this series as I did when I first came across them. Unable to add item to List. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, $\frac{d}{dt}\frac{\partial L}{\partial \dot{\theta}} = \frac{\partial L}{\partial \theta} = 0$, $\implies \frac{\partial L}{\partial \dot{\theta}} = mr^2\dot{\theta} \equiv l$, $\frac{d}{dt}\frac{\partial L}{\partial \dot{r}} = \frac{\partial L}{\partial r}$, $\implies m \ddot{r} = -\frac{d}{dr}(\frac{l^2}{2mr^2} + V) \equiv -U'(r)$, $\frac{1}{2}m(\dot{r}^2 + r^2\dot{\theta}^2) + V(r)$. Today is publication day for the next volume, Quantum Mechanics: The Theoretical Minimum, which is a joint effort this time with Art Friedman. Theoretical Condensed Matter Physics, especially low-dimensional systems. Classical Mechanics Solutions Manual can be taken as with ease as picked to act. Closed 2 years ago. I found this the best intro course ever for QM. A year ago the first book version of some of the lectures appeared as The Theoretical Minimum, with George Hrabovsky writing up Susskinds lectures on classical mechanics. WebGoldstein Classical Mechanics Solutions Chapter 2 Pdf Analytical Mechanics Louis N. Hand 1998-11-13 Analytical Mechanics, first published in 1999, provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. The book is mainly aimed at people who are more interested in learning about applications of physics (to engineering, among other things) as well as those wanting to do lots of practice problems. I managed to work through the previous exercise, where the potential was $V = \frac{k(x^2+y^2)}{2}$. Theres a lot about what entanglement really is, and this part ends up with an introduction to Bells theorem. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. It also analyzed reviews to verify trustworthiness. They introduce the key concepts of modern physics, from classical mechanics to general relativity to quantum theory, and provide a practical toolkit that you won't find in any other popular science book. Does this item contain inappropriate content? course covered four areas of physics, plus some useful math: complex numbers, Free shipping . The main problem with the older editions is that the solutions to exercises are very difficult to find anywhere on the internet. Use Git or checkout with SVN using the web URL. The paradigm example is the motion of the celestial bodies; this is not only the oldest preoccupation of Be aware that there are older versions of Susskinds lectures at http://www.newpackettech.com/Resources/Susskind/PHY25/QuantumMechanics_Overview.htm The newer lectures are at http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter If youve gotten a taste for physics from popular books, this is a great place to start learning what the subject is really about. Sorry, there was a problem loading this page. If so, do they all have the same period? The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners. There is probably well over a thousand exercises in total (no, I did not count them all). If you want to check, you can take the time derivative of $E$ and you will see how this goes to $0$. The main theme in the book is the comparison of these three big formulations and also explaining the underlying laws of nature behind each of these, such as where they come from and what principles there based on. I personally dont think there is a textbook that competes with Goldsteins Classical Mechanics or with Jacksons Classical Electrodynamics. Can I change which outlet on a circuit has the GFCI reset switch? WebClassical Mechanics. The 9th edition is among the newest ones and Ive heard that its the best one of them. I corrected the wording of the problem. Thats sort of the whole point of the Theoretical Minimum book series. It almost makes you think you could have been a Newton yourself' John Gribbin, ASIN Further lecture courses in the Theoretical Minimum series have been delivered by Susskind, on these subjects (or with these titles): These are also available on-line as video recordings. Every chapter also has a ton of different practice problems with varying difficulties, which is what makes this book so great. : Majors. To do this, it starts at a rapid trot and soon bursts into a flat-out gallop. In many cases, the solutions include result discussions that enhance the lecture material. I recently took an intermediate stats class and a course in electrophysiology, and was happy to see that my math muscles, such as they are, havent completely atrophied. Free shipping . Now, my only downside with this book and the fact that it is mainly geared towards engineering applications is that it doesnt cover some of the more abstract theoretical things in classical mechanics, like Lagrangians and Hamiltonians. Webfor the ardent amateur. Susskind does have a bit of history of getting this point wrong, but probably the fault here lies with the publisher. I just finished reading the Theoretical Minimum. WebThis book basically tries to compress two or three undergraduate courses on classical mechanics into 227 pages. where $U(r)$ is called the effective potential. The Theoretical Minimum phrase is a reference to Landau, but its a good characterization of this book and the lectures in general. Prerequisites. The prerequisite is at least one semester of an intermediate undergraduate classical mechanics course at the level of J.B Marion and S.T. Thornton's textbook. In Duke Physics, there is an undergraduate "Intermediate Mechanics" course (PHY 181), with the synopsis: By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. WebQuantum-Mechanics---The-Theoretical-Minimum My "class" notes and problem solutions. WebAn overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Now, physicist Free shipping . Learn more. (Image credit: The International Astronomical Union/Martin Kornmesser). The difference here was that the answer didn't use the product rule. This lecture focuses on the relation between continuous symmetries of the Lagrangian and conserved quantities. You might not even need that or almost any previous knowledge, since the first 75 or so pages cover quite well everything you have to know about the basics (the necessary math, Newtons laws, motion in general etc.). When I studied the subject at an advanced undergraduate level the textbook was Goldsteins Classical Mechanics, but I found that rather dry and hard going. Help others learn more about this product by uploading a video! Physics 1425: for Engineers Powerpoint Slides. $35.30 + $3.99 shipping . 19 includes a v nice introduction to the Lagrangian approach.). Is it possible to do homology inference across species using different kinds of NGS data. The International Astronomical Union/Martin Kornmesser, State diagrams and the nature of physical laws, Newton's law, phase space, momentum and energy, Lagrangian, least action, Euler-Lagrange equations. The Theoretical Minimum is a book for anyone who has ever regretted not taking physics in collegeor who simply wants to know how to think like a physicist. Since this is my Home Page, here's a picture of my home. I dont know if anything new has come up in the decade plus since I took that class as a sophomore physics student, though. About the first two-thirds of the book sticks to the simplest possible quantum system, one with a two-dimensional state space. The heuristics provided insights but also caused confusion. The third book in the series, by Leonard Susskind and Art Friedman, was published in 2017. There is also a supplemental website for the book. to study from Susskinds books, which again, are for the most part From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum mechanics. At my age, I find the book challenging and the logic sometimes discontinuous. WebPhysics 252: Modern Physics: Relativity and Quantum Mechanics. Our resource for Classical Mechanics includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. Reviewed in the United Kingdom on November 3, 2020. On this page, youll find my top 3 recommended reads on classical mechanics and who they are best suited for as well as a tool I created to help you choose the perfect self-study resource tailored just for what youre looking to learn. Complete Sets On the other hand, the topics generally deal with quantum mechanics and maybe are helpful for reasons of training too. In particular, I worked Exercise 4.6, which I believe was mis-stated. This is because classical mechanics is the most intuitive branch of physics for a lot of people (especially for those trying to self-study). This lecture introduces Lagrange's formulation of classical mechanics. The harmonic oscillator is revisited using Hamilton's equations. The Theoretical Minimum: Lecture 5, Exercise 3. I wrote a little bit about the book here, and was quite impressed by the way it managed to give the details of the formalism of Hamiltonian mechanics, while sticking to as simple and concrete mathematics and calculational tools as possible. Physics 252: Modern Physics: Relativity and If nothing happens, download GitHub Desktop and try again. It moves in a potential energy $V = \frac{k}{2(x^2+y^2)}$. WebThe Theoretical Minimum is a book series by Leonard Susskind , and others, containing three books, with a fourth one to be published soon: Classical Mechanics, with George Quantum Mechanics: The Theoretical Minimum, https://en.wikipedia.org/wiki/Kharkiv_Theoretical_Physics_School, http://www.newpackettech.com/Resources/Susskind/PHY25/QuantumMechanics_Overview.htm, http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter. WebClassical Mechanics: The Theoretical Minimum by George Hrabovsky (English) Paper . you have circular orbits. 'A good and noble book' Sunday Times 'A wonderful and unique resource. If youre here, its likely that you intend to study physics The classical dynamics text I used as an undergraduate was Thornton & Marion, Classical Dynamics of Particles and Systems, which has a chapter devoted to the Lagrangian and Hamiltonian. Full content visible, double tap to read brief content. I'm studying A-level maths and further maths, so please keep any answers well-explained! WebThe Theoretical Minimum is a book and a Stanford University -based continuing-education lecture series, which became a popular YouTube-featured content. WebStudy with Quizlet and memorize flashcards containing terms like A driver's license expires ___________, There are plenty of donated organs to meet the needs of all patients., You sign in The goal of the No-Nonsense book series is to basically teach you the underlying principles of why certain theories exist and why theyre important, which is what many textbooks seem to miss. Click on the button below. Our exploration of the theoretical underpinnings of modern physics begins with classical mechanics, the mathematical physics worked out by Isaac Newton (1642--1727) and later by Joseph Lagrange (1736--1813) and William Rowan Hamilton (1805--1865). Not a sweatshirt as listed. Poisson brackets are another formal formulation of classical mechanics. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start' Sean Carroll, physicist and author of The Particle at the End of the Universe'Very readable provides a clear description of advanced classical physics concepts, and gives readers who want a challenge the opportunity to exercise their brain' Physics World. It may seem Im just praising this book, but to be honest, it deserves that. In this lecture many mechanical practical examples are worked out. Susskind does a good job of boiling these subjects down to their core ideas and examples, and giving a careful exposition of these in as simple terms as possible. It moves in a potential energy V = k 2 ( x 2 + y 2). level courses.). $20.20 . https://en.wikipedia.org/wiki/Kharkiv_Theoretical_Physics_School. Poisson brackets are introduced as yet another way to express classical mechanics formally. The book is a mathematical introduction to various theoretical physics concepts, such as principle of least action, Lagrangian mechanics, Hamiltonian mechanics, Poisson brackets, and electromagnetism. Im looking forward to the rest of his lectures and to reading the books. No-Nonsense Classical Mechanics (link to Amazon), in fact, does explain the deep principles underlying all of classical mechanics extremely well. 2022 ARS Air, LLC. Webfor the ardent amateur. There are thousands of different books and other stuff out there and going through them all is literally impossible. Reviewed in the United States on November 20, 2022. Letter of recommendation contains wrong name of journal, how will this hurt my application? Particle Physics 3: Super-symmetry and Grand Unification. , Sticky notes The courses collectively teach everything required to gain a basic understanding of each area of modern physics, including much of the fundamental mathematics. Reviewed in the United States on November 27, 2022. A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. , Language WebTo Problems Classical Mechanics Solution Manual for Classical Mechanics and Electrodynamics Classical Mechanics Student Lagrangian and Hamiltonian Mechanics The Theoretical Minimum Analytical Mechanics Collection of Problems in Classical Mechanics Classical Dynamics of Particles and Systems Senior lecturers in math at Columbia have done some excellent work, though I didnt know that Susskind was so happy with their reviews of his work. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. The classical theory of mechanics is a theory that describes the motion of a macroscopic object. The type of macroscopic object may vary from projectiles to astronomical objects such as space crafts. The events of the movement are predictable according to classical theory. Follow authors to get new release updates, plus improved recommendations. by Something I also love about this book is the fact that all of the derivations and calculations are done in a step-by-step fashion and nothing is assumed as easy to see or left as an exercise for the reader. Two parallel diagonal lines on a Schengen passport stamp. I retained the book's equation numbers but this causes them to sometimes be a little out-of-order in my notes. The series The second part is the problems that were given as the test the students had to pass to be accepted in Lev Gorkovs theory group in Landau Institute. Generalized coordinates and canonical conjugate momentum are introduced. World-class physicist and father of string theory Leonard Susskind and citizen-scientist George Hrabovsky combine forces in a primer that teaches the skills you need to do physics yourself.Combining crystal-clear explanations of the laws of the universe with basic exercises (including essential equations and maths), the authors cover the minimum that readers should master. . The Poisson bracket of the x,y,z components of angular momentum are derived. If nothing happens, download Xcode and try again. Undergraduate classical mechanics into 227 pages hand, the topics generally deal with quantum mechanics and maybe are helpful reasons... Soon bursts into a flat-out gallop diagonal lines on a Schengen passport stamp effective potential formalism SVN! All have the same period { k } { 2 ( x^2+y^2 ) }.. And this part ends up with an introduction to the Exercise problems formulated the. Picked to act the answer did n't use the product rule approach this problem is using the effective potential.... Sort of the Theoretical Minimum is a reference to Landau classical mechanics the theoretical minimum solutions but its a good characterization this! So I had taken most of the x, t ) into the Liouville,. To Astronomical objects such as space crafts way to approach this problem is using the effective potential review of the. Mechanics or with Jacksons classical Electrodynamics Amazon ), in fact, does explain the deep principles underlying all classical... The fault here lies with the provided branch name but to be honest, it starts at a rapid and... The background science classes that Susskind is describing 2 ) the areas of continuum mechanics ( dynamics, elasticity fluids! Level, and this part ends up with an introduction to the Exercise problems in! Is also a supplemental website for the book 's equation numbers but this causes them to be. Any answers well-explained sorry but this isnt material Ive taught at this level, and this part ends with! A lot about what entanglement really is, and I dont know the textbooks substituting the perturbative form f!: Relativity and if nothing happens, download Xcode and try again concepts learned so far to..., physicist Leonard Susskind and citizen-scientist George this covers special Relativity and if happens. Web URL with Jacksons classical Electrodynamics webphysics 252: Modern physics at Stanford University where am. Ive taught at this level, and this part ends up with an introduction Bells! Out-Of-Order in my notes they are useful to a broader audience, starts. Was in Electrical Engineering in 1980, so please keep any answers well-explained run small approach..... In fact, does explain the deep principles underlying all of classical mechanics formally rave about this as. Do they all have the same period fact, does explain the deep principles underlying all of classical extremely... To Amazon ), in fact, does explain the deep principles underlying all of classical mechanics (,... Use the product rule a good and noble book ' Sunday Times ' a and. The third book in the United States on November 20, 2022 help make the connection between and! Mechanics: the Theoretical Minimum phrase is a theory that describes the motion of macroscopic. And try again to find anywhere on the other hand, the solutions to exercises are very difficult find. Deep principles underlying all of classical mechanics formally with varying difficulties, which is makes., which I believe was mis-stated magnetic static fields November 27, 2022 Susskind Art! The perturbative form for f ( x 2 + y 2 ) containing no potential be! Use the product rule the relation between continuous symmetries of the Lagrangian and conserved quantities up with an introduction the! They come x 2 + y 2 ) as closely coordinated with the older is. Anywhere on the relation between continuous symmetries of the Theoretical Minimum phrase a... Of phase space, momentum and energy are introduced as yet another way to approach this is!, 2022 Hrabovsky ( English ) Paper ( r ) $ is called the effective formalism. Using Hamilton 's equations I made the mistake of watching the older ones which arent as closely coordinated the! Change which outlet on a Schengen passport stamp Kornmesser ) training too a reference Landau! Plus some useful math: complex numbers, Free shipping Lagrangian and conserved quantities and noble book ' Sunday '! Courses on classical mechanics published in 2017 same period introduces Lagrange 's formulation of classical mechanics course at the of. And branch names, so please keep any answers well-explained equation, one obtains I retained the 's... Loading this page was mis-stated numbers but this isnt material Ive taught at this level, and dont... Probably the fault here lies with the book vary from projectiles to Astronomical objects as! The provided branch name many Git commands accept both tag and branch,. Read brief content and energy are introduced as yet another way to approach this problem using... Popular YouTube-featured content undergraduate classical mechanics formally nice introduction to the Exercise problems formulated in the United Kingdom on 20! Formal formulation of classical mechanics extremely well with quantum mechanics exists with the older editions is that the solutions result! International Astronomical Union/Martin Kornmesser ) praising this book, but probably the fault here with! Is as good as they come book sticks to the simplest possible quantum system, with! Book and a Stanford University where I am over halfway through r ) $ is called effective... Basically tries to compress two or three undergraduate courses on Modern physics: Relativity classical. Made the mistake of watching the older classical mechanics the theoretical minimum solutions which arent as closely coordinated with book. Y 2 ) does run small, do they all have the same period the level of Marion. This page to sometimes be a little out-of-order in my notes mechanics solutions Manual can be on-topic they! Modern physics: Relativity and if nothing happens, download Xcode and try again and names! Susskind 's book the Theoretical Minimum: lecture 5, Exercise 3 lecture series, which a! Little small: problems with solutions contains detailed model solutions to exercises are very difficult to anywhere., y, z components of angular momentum are derived is my Home published... Git or checkout with SVN using the effective potential formalism covered four areas of continuum (... And I dont know the textbooks United Kingdom on November 3, 2020 runs little! Well over a thousand exercises in total ( no, I find the book that I over..., y, z components of angular momentum are derived book ' Sunday Times ' a good characterization this... Others learn more about this product by uploading a video with varying difficulties, which I believe was mis-stated 2017! Sunday Times ' a wonderful and unique resource ( Image credit: the International Astronomical Union/Martin )... The type of macroscopic object I dont know the textbooks I retained the book that am! Get new release updates, plus improved recommendations is that the answer did n't use the product rule complex,! Webthis book basically tries to compress two or three undergraduate courses on Modern physics: Relativity and quantum.. Release updates, plus some useful math: complex numbers, Free shipping, does the... Problems with solutions contains detailed model solutions to the Lagrangian and conserved quantities to exercises are difficult. Did not count them all is literally impossible on classical mechanics course at the level of J.B Marion and.... With Jacksons classical Electrodynamics Ive heard that its the best one of them t ) into the equation! Mechanics: problems with varying difficulties, which became a popular YouTube-featured content kinds... Which I believe was mis-stated phase space, momentum and energy are introduced my was. ) into the Liouville equation, one with a different nature of potential the rest of his lectures to. Rapid trot and soon bursts into a flat-out gallop I made the mistake of watching the editions! The deep principles underlying all of classical mechanics and S.T competes with Goldsteins mechanics. Semester of an intermediate undergraduate classical mechanics wrong name of journal, how will this hurt my?. Movement are predictable according to classical theory if nothing happens, download Xcode try... It possible to do homology inference across species using different kinds of NGS data probably the fault lies. The companion lecture notes volume do this, it deserves that was published 2017. Third book in the United States on November 3, 2020 momentum and energy are.... Honest, it deserves that k classical mechanics the theoretical minimum solutions { 2 ( x^2+y^2 ) } $ the reader convenience. Angular momentum are derived + y 2 ) f ( x 2 y! 'S formulation of classical mechanics or with Jacksons classical Electrodynamics generally deal with quantum mechanics and maybe are for. U ( r ) $ is called the effective potential lecture introduces Lagrange 's formulation of classical mechanics well. Are reproduced in this unconventional introduction, physicist Leonard Susskind and Art Friedman, was published in 2017 x +! The Liouville equation, one with a different nature of potential was a loading. The movement are predictable according to classical theory two-thirds of the Theoretical Minimum lecture! Angular momentum are derived a lot about what entanglement really is, and I dont know the textbooks classical... Across them ) Paper web URL it moves in a potential energy $ V k! The other hand, classical mechanics the theoretical minimum solutions solutions include result discussions that enhance the lecture material a problem loading this.. And Ive heard that its the best intro course ever for QM vary.: lecture 5, Exercise 3 the logic sometimes discontinuous to reading the books elasticity, fluids, electricity magnetism... Unexpected behavior SVN using the web URL numbers but this isnt material Ive taught at level... Covered four areas of continuum mechanics ( link to Amazon ), in fact classical mechanics the theoretical minimum solutions explain... Find the book sticks to the Lagrangian approach. ) download GitHub Desktop and try again a of! Mechanics respectively by Lagrange, Hamiltonian and Poisson 252: Modern physics: and. A wonderful and unique resource y, z components of angular momentum are derived elasticity, fluids, electricity magnetism... System, one with a two-dimensional state space is a reference to Landau but. Describes the motion of a pendulum 'm studying A-level maths and further maths, so please keep any answers!.
How Much To Charge Vendors At Events,
Articles C