# What is First order: Definition and 585 Discussions

In mathematics and other formal sciences, first-order or first order most often means either:

"linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
"without self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic)In detail, it may refer to:

View More On Wikipedia.org
1. ### I Expansion at first order in QCD counterterm

What is the meaning of the expansion at first order in ##\delta_2## and ##\delta_3## at the second step in the last line? These quantities are not "small" - on the contrary, the entire point is to then take the ##\epsilon \to 0## limit and the counterterms blow up
2. ### Solve the given first order differential equation

My thinking is two-fold, firstly, i noted that we can use separation of variables; i.e ##\dfrac{dy}{y}= \sec^2 x dx## on integrating both sides we have; ##\ln y = \tan x + k## ##y=e^{\tan x+k} ## now i got stuck here as we cannot apply the initial condition ##y(\dfrac {π}{4})=-1##...
3. ### Solving Coupled First Order ODEs: Is There a Closed Form Solution?

Hey all, I am currently struggling decoupling (or just solving) a system of coupled ODEs. The general form I wish to solve is: a'(x)=f(x)a(x)+i*g(x)b(x) b'(x)=i*h(x)a(x)+j(x)a(x) where the ' indicates a derivative with respect to x, i is just the imaginary i, and f(x), g(x), h(x), and j(x) are...
4. ### A First order electroweak correction to the g-2 magnetic moment

We know that we need to go to 5th order in perturbation theory to match 10 decimals of g-2 for electron, theory vs. experiment. But let us not assume QED is pure and independent, but it's a lower energy limit of GSW (not Green-Schwartz-Witten from superstrings) electroweak theory. Has anyone...
5. ### Engineering First order differential equations (movement of a rotary solenoid)

My question i am trying to solve: I have successfully done first order equations before but this one has got me a little stuck. My attempt at the general solution below: $${5} \frac{\text{d}\theta}{\text{d}t}=-6\theta$$ $${5} \frac{\text{d}\theta}{\text{d}t} =\frac{\text{-6}\theta}{5}$$...
6. ### Engineering First order non linear to state space equations

How to represent this system in state space form? where: $$x' = Ax + Bu \text{ and }y = Cx + Du$$ I am trying to create a state space model based on these equations on simulink, need to find A, B, C and D but like I mentioned, i cannot find the solution when the differentials are not of...
7. ### Engineering First Order RL Circuit: Finding a Current I2(0-)

I shorted the inductor and performed mesh analysis. The solutions to the linear system were done using a calculator. The book says that the value for i2(0-) should be 15 mA but I'm getting -2mA. What am I doing wrong? I'm completely confused. Maybe mesh isn't the most efficient way to find I2...
8. ### Comp Sci Mistake while removing implications in first order predicate logic-:

As you can see I am not getting correct result. What have I messed up? I want to learn it. https://slideplayer.com/slide/4942120/ Here is full slide in case anyone wants to refer to it.
9. ### Solve the first order differential equation

From my working...I am getting, ##xy=####\int x^{-1/2}\ dx## ##y##=##\dfrac {2}{x}##+##\dfrac {k}{x}## ##y##=##\dfrac {2}{x}##+##\dfrac {6}{x}## ##y##=##\dfrac {8}{x}## i hope am getting it right...
10. ### A Existence of unique solutions to a first order ODE on this interval

I am trying to find a way to prove that a certain first order ode has a unique solution on the interval (1,infinity). Usually the way to do this is to show that if x' = f(t,x) (derivative with respect to t), then f(t,x) and the partial derivative with respect to f are continuous. However, this...
11. ### Solve this first order differential equation

This is the question; This is the solution; Find my approach here, ##x####\frac {dy}{dx}##=##1-y^2## →##\frac {dx}{x}##=##\frac {dy}{1-y^2}## I let ##u=1-y^2## → ##du=-2ydy##, therefore; ##\int ####\frac {dx}{x}##=##\int ####\frac {du}{-2yu}##, we know that ##y##=##\sqrt {1-u}## ##\int...
12. ### I Usage of First Order Elastic Constants in Soft Body Equations

Hi, I have some soft body equations that require first order elasticity constants. Just trying to figure out the proper indexing. From Finite Elements of Nonlinear Continua by J.T. Oden, the elastic constants I am trying to obtain are the first order, circled below: My particular constitutive...
13. ### MHB First order differential equations

Hi, Is the answer: y(x) _homogenous =v(x) y(x) _private =u(x)v(x) ? Or they refer to something else? I don't know how to approach to it
14. ### Solving a first order differential equation with initial conditions

Hello! Consider this ODE; $$x' = sin(t) (x+2)$$ with initial conditions x(0) = 1; Now I've solved it and according to wolfram alpha it is correct (I got the homogenous and the particular solution) $$x = c * e^{-cos(t)} -2$$ and now I wanted to plug in the initial conditions and this is...
15. ### B First order approx. for a curve

Helping someone with some fictional physics. He's looking for a function that will produce a curve similar to this (poor geometry is my doing, assume smooth curvature): Starts at 0,0. Maximum at n. Reaches zero at infinity. The cusp is not sharp, it's a curve (which, I think suggests at least...
16. ### I How do I solve this first order second degree differential equation?

How to solve this first order second degree differential equation ? ##\left(\frac {dy} {dx}\right)^2 + 2x^3 \frac {dy} {dx} - 4x^2y=0 ## Thanks.

18. ### First order differential equation involving a square root

Summary:: solution of first order derivatives we had in the class a first order derivative equation: ##\frac{dR(t)}{dt}=-\sqrt{\frac{2GM(R)}{R}}## in which R dependent of time. and I don't understand why the solution to this equation is...
19. ### First Order Logic: ∀x,y a(x) ∧ a(y)

An example we were given is as follows: {ua|u∈∑*} (where ∑* is set of all words over ∑) so we have ∀x. last(x) → a(x). I am given {awa|w∈∑*} to do, and I know that I have to express that a is the first letter and last letter in a word. Could I write it as: ∀x,y ( a(x) ∧ a(y) ∧ x<y → ∃z(x<z<y))...
20. ### Solving 1D First Order Equations for 3D Mass Positions and Velocities

Okay so I need to find 12 one dimensional first order equations that describe the position and velocity of both masses in 3 dimensions. The equations for the second body will be easy once I figure out how to do the first body, so I'll ignore that for now. For the first equation, I can rearrange...
21. ### A Non linear diff. eq. first order

I tried to solve for y' the algebric second grade equation but I don't know how to solve the diff. equation either. Any help? Thanks. -- lightarrow

47. ### I Second order ordinary differential equation to a system of first order

I tried to convert the second order ordinary differential equation to a system of first order differential equations and to write it in a matrix form. I took it from the book by LM Hocking on (Optimal control). What did I do wrong in this attachment because mine differs from the book?. I've...
48. ### Convert to a first order ODE

What am I doing wrong here in my attachment?
49. ### First order pertubation of L_y operator

Hi, I am trying to solve an exam question i failed. It's abput pertubation of hydrogen. I am given the following information: The matrix representation of L_y is given by: L_y = \frac{i \hbar}{\sqrt{2}} \left[\begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & -1 & 0 & 1 \\ 0 & 0 & -1...
50. ### Interpreting a statement in first order logic

Homework Statement Rewrite the following statements in symbolic form: a) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a solution. b) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a unique solution. Homework EquationsThe Attempt at a...