"We use equations, we not only use equations, we sometimes use hard equations, but we tend to try to use the simplest equations that will do the job."
"Absolutely incredible, the fact that all the equations that rule this universe of ours can be put on one sheet of paper."
"Black-Scholes-Merton equation: the most famous equation in finance."
"That's the beautiful thing... outcome is uniquely specified by the equations."
"It is more important to have beauty in one's equation than to have them fit experiment."
"Beauty in one's equations is more important than having them fit experiment." - Paul Dirac
"The equations are smarter than we are."
"You don't have to. You could choose to write the Schrödinger equation as multiple equations interacting with each other, all of which just involve real numbers. It's just that you're doing more work for yourself."
"The ultimate answer is you're looking at a very simple system: two black holes that are being very simple direct set of equations—the equations of general relativity."
"So, \( r = \sqrt{2}r \). \( r = r\sqrt{2} \)."
"The equation was smarter than he was because it actually gave more stuff out than he put into it."
"That's mathematics heaven said. That's... they didn't have the equations but they're thinking mathematically."
"I want my ultimate ontology at the end of the day to be a single point in the high dimensional space of all important... to be some equations. That's the world I want to live in."
"Lagrangian mechanics in the principle of least action creates equations of motion."
"When you have to get from 0 to t you get t, and you have t on the right hand side. That's what it's saying."
"...the basic equations tell us that from this knowledge we can infer what happened in the causal domain of dependence, but if you look carefully, this is also the causal domain of inference in the past, not just in the future."
"The actual equations are pretty simple. It's really a matter of asking the question in precisely the right way."
"There are no positive integers such that p and Q such that 4p squared minus Q squared equals 25."
"If you got this right, that is fantastic! You are a professional, expert, and certified in solving basic exponential equations."
"These four equations explain pretty much all of electromagnetism."
"If we want to convert watts to dbm, we could use this equation."
"If you solve the equations classically, you find that there should be a massless particle that travels at the speed of light."
"So in other words, the trace of A equals the trace of QAQ^(-1)."
"How many equations are implied by this little string of equations right here? So that's a trick question. Okay, technically there are three equations because I've said each of these is equated to the others, right?"
"Chemical reactions can be represented by chemical equations."
"Politics is for the present, but an equation is something for eternity." - Albert Einstein
"X equals negative three, y equals negative five."
"Einstein's star contribution was a famous equation that showed how particles moved in waves."
"...so as with this example just a small change in a differential equation can turn a regular exponential solution into a hyperbolic trig one."
"Solving equations: understanding the interplay of variables."
"Partial u partial x equals partial v partial y, that definitely has to be true."
"There's no reason that we have to stop at just two input variables; we could have three or more independent variables and everything would still work the same."
"Every time you have a physical system and it has some sort of symmetry attached to it, then your equation must come with a conservation law."
"The complex numbers are really nice like that but that being said this equation has two very simple solutions to find."
"These are the solutions, the building blocks of electromagnetism, of the heat equation, of the wave equation, of all of partial differential equations."
"That's why it's worth it on our side to put a little bit of effort into understanding what that equation is trying to tell us."
"This is the final lesson of the talk which we started with, which is that the equations are much smarter than we are."
"Any logarithm equation I have can be written as in exponential form, and every exponential form can also be written as a logarithm."
"Partial differential equations... Everything in the world is described with differential equations."
"The key differential equation to variational calculus."
"My goal when I set out was to find a way of introducing the irony into the equations."
"The number of variables you have, that's the number of equations you're going to need."
"Now we're dealing with a system, and you can combine these equations to form new equivalent equations."
"There's no difference between a circle, hyperbola, parabola in terms of just the equation - they're all degree 2 equations."
"This is what we call an exponential equation... when you have an exponential equation you have to use something called logarithms to solve."
"Once we have all the independent constraint equations, then we can use that to solve the forward and inverse kinematics problems."
"Simultaneous equations are two or more algebraic equations that share variables."
"Now let's start off with deriving the radar range equation. What we're going to do is to go over from basic physical principles how the radar equation evolves. We're going to just need algebra in our reasonable good physical intuition."
"Complete the table of values for y = x^2 - x - one."
"Chemists represent this in a balanced chemical equation, in which the number of each type of atom on the reactant side equals the number on the product side."
"Though there is no one sure-fire way to balance chemical equations, there are a few useful techniques to apply."
"Well, with this being said, we can say n plus one times a sub n plus one plus two a sub n minus one has to be zero."
"Solve radical equations by squaring both sides and check for extraneous solutions."
"Absolute value equations make it always positive, so we got to consider the negative event, kind of where if just this inner piece was negative."
"Use equations period where if you can set things up for scenarios up with equations it is such a big help."
"Balancing equations requires adding or multiplying coefficients to balance the number of atoms on both sides."
"So that means we can extend this guy up here to the equation f of f of x equals x for all real numbers x. That actually gives us a couple pieces of information."
"We have managed to explain so much in terms of elegant equations, that we think that we should be able to close the deal and explain everything in terms of elegant, simple equations."
"But then this right hand side cancels down just to the number one."
"The equation of the circle is x minus H squared plus y minus K squared equals r squared."
Differential equations: "Know how to solve separation of variables, and find particular solutions."
"The only reason why we cannot travel at the speed of light is because we get a division by zero in the equations."
"The reason that we can't travel at the speed of light is because we get a division by zero in the equations."
"That's the reason why we can't travel at the speed of light: because we get a division by zero."
"Separable means you can separate the variables on each side of the equation by only multiplying or dividing."
"So, X equals 2K, double both sides. And then I'm going to substitute 2K in for X."
"Equations are shorthand, like a stenographer would write when they're trying to write really fast."
"Discovering equations from data is very important, something Koopman can help with."
"Geometry is a curious thing. Some people like to write down equations, and some people like to play with geometry. I'm much more a geometry person."
"The Yang-Mills equations are a matrix version of Maxwell's equations."
"That says line integral of E⋅dl = - rate of change of B⋅dA."
"It seems to me to be the way the world works. If it's a unifying language, it's what we should be writing our equations in."
"This means the allowed values of k in the problem are very special so here is n = 1, ψ looks like sin(Πx/L), and equal to 2 looks like sin(2Πx/L), and so on with some numbers in front which I have not chosen yet."
"So now we have an index equation, right, and one of the things that we know about indices is that we always have to have, if we're doing any sort of equation, we have to have everything written to the same base."
"The idea of solving equations is to get rid of everything and leave the X on one side of the equation."
"Richie flow equations are much more powerful than minimization procedures."
"Solving equations: isolate the variable by moving all other numbers away from it."
"Add or subtract the same thing to both sides of the equation to keep it balanced."
"Remember, you can plug your answer back into the equation to check your work."
"G is equal to 2 and you can check your answer by plugging it back into your equation. Is 2 minus 5 equal to negative 3? Yes, so we have the right answer here."
"What you want to start by getting both of those terms with the variable on the same side of the equation."
"An equation is like a balance scale."
"So I'm going to get 2MG equals T cos alpha."
"Simultaneous equations or systems of equations, you would indeed be correct."
"We've got to satisfy this stuff called Maxwell's equations."
"Now we can go back, actually get this into a single line equation."
"You can't just make equations up, you always need, you know, you every equation you can only solve one unknown."
"All of these circuit problems become a game of writing equations until you get enough of them on paper to find what you're trying to solve for."
"Really, these are the two main equations of motion."
"Everything can come from these equations."
"So ln 10 over 11 is equal to negative x ln e, but ln e is one."
"The ideal gas law PV equals nRT explicitly spells out the relationship between pressure, density, and temperature for the gas phase."
"The Einstein field equation is that R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = 8\pi G T_{\mu\nu}."
"We hit our goal, we got equations of motion for the system."
"An equation is almost kind of like a riddle or a challenge."
"Many of the rules in physics and astrophysics are accurately described by simple symbolic equations."
"Much of human civilization has been built by animating equations of which people were culturally unaware."
"These extremely simple equations... turn out to give you a global description of the compactification of technular space associated with surfaces."
"Complex or imaginary numbers arise naturally in solving polynomial equations."
"The equations in physics don't necessarily describe reality as it actually is."
"PV = nRT is the ideal gas equation."
"The aim here is to separate the variables into two ordinary differential equations."
"We are talking about equations, and in algebra, there's different type of equations."
"The first thing you need to do is you got to set this equation equal to zero."
"Electric fields, magnetic fields, and the famous Maxwell's equations... are some of the most beautiful sets of equations we have."
"When we start solving equations and inequalities, factoring is a huge benefit to us."
"To write the equation of the line, there's a couple of different ways we could write the equation."
"To solve an equation means you start with the original equation and you replace it by equivalent equations which are simpler."
"Therefore, we can say that 10 cosine theta minus 3 sine theta equals the square root of 109 cosine theta plus sixteen point seven."
"When we are solving simultaneous equations graphically, all we're actually looking to do is find the points at which they intersect."
"Straightaway we get our answer there, C equals 5."
"Psychology is not beside the point for optimality; it is part of the optimality equations."
"We have two equations and actually have two unknowns, and that's what I have to solve for."
"This particular type of equation is called an exponential equation because the variable is located in the exponent."
"The resulting system of equations that we get is actually really easy to solve."
"Though we know the equations of quantum mechanics... solving equations is a little bit hard."
"It's all about setting up an equation."
"If I set this equal to zero and I solve it, this is all of my x-intercepts."
"This is a critically important lesson because we're learning how to solve proportions but we're also learning how to solve equations."
"The idea of solving equations actually follows you throughout all of math."
"The really important equation is AX equals lambda X."
"When T equals two, the kid will kick the ball."
"What Dirac discovered when he studied the relativistic version of the Schrödinger equation is that these two things are linked."
"The trick in this whole mathematics and calculations is how do you solve those coupled equations."
"This is a systematic way to solve equations, you plug in all the information you know about the system into a 2 by 2 matrix."
"We write the equations which govern the process and solve them with a computer."
"Spontaneous symmetry breaking... allows us to use equations that are more beautiful than the world superficially looks."
"Do you agree that any quadratic equation can be written as ax squared plus bx plus c equals zero?"
"The Euler-Lagrange equations are the derivation of the basic equation of Lagrangian mechanics."
"The same mathematical equation can describe millions and millions of different kinds of harmonic oscillators."
"The Solomon equations describe how the magnetization in this system behaves over time."
"This is the Einstein's famous field equations, we call it EFE in an abbreviated form."
"For a centered equation formula, you need to actually do double dollar signs."
"Spring elements store potential energy, which can be useful if you're trying to derive the state equations of a system."
"We're going towards looking at the equations that describe this network."
"The goal of solving linear equations is to find the value of the variable that will make the statement true."
"Solving equations in mathematics requires a lot of study because you obviously need to have the right tool for the right situation."
"Heat transfer processes can be quantified in terms of appropriate rate equations."
"The equation of motion of this simple scalar Lagrangian will be something like the equation of motion of simple harmonic motion."
"It's F mu nu F mu nu, it's proportional to sums of squares or differences of squares."
"A solution to an equation is a value for that variable that makes the equation true."
"Solutions to an equation are also referred to as the roots of the equation."
"From the forces, we're going to find equations that describe the position, the velocity, and the acceleration."
"Log of 100 is equal to 10 times log of a."
"The idea of taking an equation and ultimately getting 0 on one side is going to be very important to us."
"Hamilton's equations are the more generalized form of the equations of motion, which tell us what the positions and momenta will be at a future time."
"We have shown by forming an equation how we have found the value of X."
"A line that is parallel to the x-axis is going to have an equation that y is equal to whatever that y-coordinate is."
"A quadratic equation is simply an equation where the highest power of the variable is two."
"If you take this base a and raise it to that power y, you'll set it equal to x."
"The whole fundamental reason that we can do this is that we have an equation, and what you do to one side, you do to the other."
"The real picture is Y equals AX plus V."
"That's the equation we're going to be solving for all of part two. The Schrodinger equation."
"Once you've got the relevant equations of motion, you can work the problem."
"The correlation function is nothing but the solution to our Helmholtz equation."
"These are two explicit first order coupled differential equations."
"We're going to combine some like terms and solve a basic equation."
"One of the reasons we like the Lao transform is because it converts linear time-invariant differential equations into algebraic equations."
"So, this equation, m dx plus n dy equals zero, is an exact equation."
"Delta G double dagger equals Delta H double dagger minus T Delta S double dagger."
"For however many variables you have, you need at least that many equations to solve them."
"These equations of motion need to be solved if we are to predict what will happen in those situations."
"Set up some sort of equation... a huge part of algebra is solving equations."
"We are given two thermochemical equations and our goal is to combine them in such a way as to obtain the third equation and its enthalpy."
"It's going to be the properties of this alternating group that are going to unlock the big theorem of our semester about the solvability of equations and radicals."
"You can now document your equations in a way that actually looks like what you might find in your textbooks."
"The power of complex numbers is they turn differential equations into algebraic equations."
"Think of these equations like English sentences about how each part relates to the part that came before it to form a coherent stream of language."
"VASP is about solving the Kohn-Sham equation, an approximation of the Schrödinger equation."
"The first exercise will be about integrals, second one about line equations."
"The key to solve equations is understanding that everything has to move away from your variable."
"In physics, every equation tells a story, every variable a character."
"Once you've got the equation, you can use that equation to predict values."
"You get X minus 8 equals zero, don't forget about that X, and you get x equals 8 and x equals zero."
"You can do anything you want to an equation as long as you do it to both sides because then the equation stays balanced."
"With equations, we're undoing something, so we're actually following sort of backwards the PEMDAS."
"If you just add the two equations or subtract the two equations to immediately get your answer, you get a little shortcut."
"The real numbers... will also have the property that they'll solve equations like x squared equals two but they will in some sense fill in the holes in the line, the number line that we began to get a picture of."
"Sometimes we're going to solve these equations and we're going to get some answers that aren't actually valid solutions."
"The equations of uniformly accelerated motion include: V is equal to U plus AT, S equals UT plus half AT squared, and V squared equals U squared plus 2AS."
"So fundamentally, this structure of the system of equations is what's causing the chaos."
"We're going to understand how to develop equations that describe them."
"Think about the problem critically, which equations do I need?"
"We're going to posit that the equations of motion will be some second rank tensor equation."
"Anything that has an equals sign is an equation; anything that doesn't is an expression."
"It's a system of linear equations, and we know how to solve those."
"Take the equation out of the question, find one equals, and then scale it up."
"Do something to one side of the equation, do the same thing to the other - that's one of the most important rules in maths."
"We saw that three equations out of an infinite set of ordinary differential equations decoupled exactly from the rest."
"Everything that's driving this is an equation, or a reference to this spreadsheet right here."
"Tracking a planet or a satellite, you're solving equations like this forward in time."
"The graph of an equation is the set of points \( (X, Y) \) that satisfy the equation."
"Any function of x - vt actually satisfies the wave equation."
"Linear maps and linear equations are super important for algorithms."
"If we share a set of equations describing our physical world, then we should form a consensus about every counterfactual query."
"The equation connecting L and H is \( L = 4 \cdot H^{2/3} \)."
"This allows us to make a simplification to this equation."
"To solve an equation, we just want to know what one lot of Y is."
"The equations make it easy to specify the correct delay values to ensure that all time requirements, both internal and external to the FPGA, are met."
"We now have Maxwell's equations in finite difference form."