Differential Definition and 1000 Threads

Hello! I would like to know if anybody here knows if there's any good book on academic-level dfferential geometry(of curves and surfaces preferably) that emphasizes on geometrical intuition(visualization)? For example, it would be great to have a technical textbook that explains the geometrical...

If the slope of the curve (derivative) at a given point is a number .

Homework Statement Find dy of ##~xy^2+x^2y=4## Homework Equations Differential of a product: $$d(uv)=u\cdot dv+v\cdot du$$ The Attempt at a Solution $$2xy~dy+y^2~dx+x^2~dy+2xy~dx=0$$ $$x(2y+x)dy=-(y+2x)dx$$

I've been going through my book learning about differential equations of multiple variables and I have a quick question about differential forms. If you are working a problem and get to the point where you're left with a differential form like ##(y)dx##, does that mean that the change in the...

My book is going through a proof on exact differential forms and the test to see if they're exact, and I'm lost on one part of it. It says: If $$M(x,y)dx + N(x,y)dy = \frac{\partial F}{\partial x}dx + \frac{\partial F}{\partial y}dy$$ then the calculus theorem concerning the equality of...

I wanted to study General Relativity, but when I started with it, I found that I must know tensor analysis and Differential geometry as prequisites, along with multivariable calculus. I already have books on tensors and multivariable calculus, but can anyone recommend me books on differential...

Homework Statement ##\dfrac{dy}{dx} + y = f(x)## ##f(x) = \begin{cases} 2 \qquad x \in [0, 1) \\ 0 \qquad x \ge 1 \end{cases}## ##y(0) = 0## Homework EquationsThe Attempt at a Solution Integrating factor is ##e^x## ##e^x\dfrac{dy}{dx} + e^x y = e^x f(x)## ##\displaystyle ye^x = \int e^x...

Homework Statement Solve the differential equation ##(2x+1)^2y'' + (4x+2)y' - 4y = x^2## Can someone verify whether my solution is correct? Homework EquationsThe Attempt at a Solution We perform the substitution ##t = \ln|2x+1|##. Then, ##e^t = |2x+1|## and ##x = \pm(e^t -1)/2## Without...

So in differential calculus we have the concept of the derivative and I can see why someone would want a derivative (to get rates of change). In integral calculus, there's the idea of a definite integral, which is defined as the area under the curve. Why would Newton or anyone be looking at the...

Homework Statement Homework Equations Circuit Equations. ##U_C=Q^2\2C## ##U_L=Li^2\2## The Attempt at a Solution For (a) I said ##100J## .But I think it might be ##200J## too.Here what I did; ##U_t=Q^2\2C## and I put ##Q=0.1C## and we know ##C##.Here I...

Hi all, I'm wondering if anyone is able to point me in a direction regarding an aspect of stochastic differential equations. I have a situation in which I need to propagate a stochastic DE through time using measurement updates - however, the exact time at which each measurement arrives is...

q''+ 20 q = 100 sin(ωt) I have been asked to find all mathematically possible values of ω for which resonance will occur. From the homogeneous solution, q(t) = Acos(√20 t) +Bsin(√20 t), I can see that resonance occurs when ω=√20. My question is, should I also consider -√20? And if so, what is...

In a text I am reading (that I unfortunately can't find online) it says: "[...] differential forms should be thought of as the basis of the vector space of totally antisymmetric covariant tensors. Changing the usual basis dx^{\mu_1} \otimes ... \otimes dx^{\mu_n} with dx^{\mu_1} \wedge ...

I was trying to picture the third derivative of something Then i came across these ... What does displacement mean? The variable x is often used to represent the horizontal position. The variable y is often used to represent the vertical position Displacement=Delta x=xf-x0xf refers to the...

I have some beginner doubts about Calculus and Differential equations . Is a function always a curve ? Doesn't a function already has a slope ? d/dx of a function gives the gradient of the curve between two points ? The derivative ,d/dx ,The gradient , is the rate of change of a...

Homework Statement "Find the recurrence relation in the power series solution for ##y''-xy'-y=0## centered about ##x_0=1##." Homework Equations ##y=\sum_{n=0}^\infty a_nx^n## Answer as given in book: ##(n+2)a_{n+2}-a_{n+1}-a_n=0## The Attempt at a Solution ##y=\sum_{n=0}^\infty a_n(x-1)^n##...

Homework Statement Solve for y: ##\frac {dy}{dx} = \frac {1+y^6}{xy^5}## , where y(1) = 1. Answer ## y = \sqrt[6] {2x-1}## Homework EquationsThe Attempt at a Solution ##\frac {dy}{dx} = \frac {1+y^6}{xy^5}## ##\frac{dy (y^5)}{1+y^6} = dx \frac {1}{x}## u= 1+y6 ##\frac {du}{y^5}=dx## ##\int...

I'm not sure about the physical behavior of a RLC circuit and I have to give a presentation that involves one. So I've decided to plot the current. I found a book that gives a differential equation to describe the circuit. ##L\frac{d^2i}{dt^2} + R\frac{di}{dt} + \frac{1}{C}i = \frac{dv}{dt}##...

Homework Statement A submarine engine provides maximum constant force ##F## to propel it through the water. Assume that the magnitude of the resistive drag force of the water experienced by the submarine is ##kv##, where ##k## is the drag coefficient and ##v## is the instantaneous speed of...

Homework Statement A simple pendulum is formed by a light string of length ##l## and with a small bob ##B## of mass ##m## at one end. The strings hang from a fixed point at another end. The string makes an angle ##\theta## with the vertical at time ##t##. Write down an equation of motion of...

Hi was reading about differential forms, when I tried to solve the example given in this pdf https://www.rose-hulman.edu/~bryan/lottamath/difform.pdf. According to it, the answer is that on the image above. But when I tried to solve this same example by following the expression for ##w## given...

Homework Statement Solve ## \frac{d^2y}{dt^2} + \omega^2y = 2te^{-t}## and find the amplitude of the resulting oscillation when ##t \rightarrow \infty ## given ##y=dy/dt=0## at ##t=0##. Homework EquationsThe Attempt at a Solution I have found the homogenious solution to be: ##y_h = A\cos\omega...

Homework Statement It is the driven series RLC circuit. It is given in the following images. It is from the section 12.3 in this note. Homework Equations The differential equation, as given by 12.3.3, is ##L \frac{d^2 Q}{d t^2} + R \frac{d Q}{d t} + \frac{Q}{C} = V_0 \sin{(\omega t)}##...

Homework Statement http://imgur.com/a/k7fwG Find the vector magnetic potential at point P1. Homework Equations Vector magnetic potential given by: $$ d \bar{A} = \frac{\mu I d\bar{l'}}{4 \pi | \bar{r} - \bar{r'} | } $$ The Attempt at a Solution I split up the problem in 3 parts, first...

I have a question that I believe requires knowledge on the graduate level, but I can't necessarily express it in terms more complicated than plain English. If this is not so, moderator, please adjust to your taste, and thank you! If it helps to know this, I'm an audio/video systems designer and...

Dear all, I have a question concerning chaos. As you may well know, the logistic mapping $$x_{n+1} = rx_n (1-x_n) $$ exhibits chaos, depending on the value of r. This logistic mapping is a reparametrized version of the difference equation $$x_{n+1} = x_n + k x_n (1 - \frac{x_n}{M}) $$...

Homework Statement I really cannot seem to be able to follow the logic of how you would use the product rule when using 4 vector differential operator. ∂μ is the differential operator, Aμ is a scalar field and φ and φ* is it's complex conjugate scalar field. I have the answer, I'd just really...

Homework Statement Hy guys I am have a problem with the last part of this question. part d), ii) I get the general formal which I have displayed below, but what I done understand is if I take the limits as show in ii) I get ##0=\ \infty## which obviously I am doing something wrong. Have I...

1. find the differential coefficient of root 2 sin x + 4x power5 -3/x power 4 2. if y=(3x square +1)(x square + 2x) find dy/dx.

Can i have help with this linear differential equation ? First, i divided by (1-x^2) to be like dy/dx + p(x)y= q(x). But i could not obtain Q(x). Any help will be welcomed.

Homework Statement Find the general solution of y^{(5)}-y(1)=x The Attempt at a Solution I found the complementary function by substitution of the solution form y=e^{kx} giving k=0,1,-1,i,-i, so y_{cf}=a_0+a_1e^x+a_2e^{-x}+a_3e^{ix}+a_4e^{-ix} Now for the particular integral, the general...

Hi everyone. In reading some popular textbooks I noticed that in (maybe) most of GR and SR we don't encounter situations where we can use wedge-product and differential forms. However, these things are presented to us in most of the textbooks. But... if most of the books present them, it means...

is the fancy term I've been using to describe how I mine various network and system log data for interesting events that I want to be aware of. Since I never pursued a college degree or studied big data analytics, I'm hoping somone can help me identify a more appropriate term to use besides the...

Homework Statement determine by inspection at least two solutions of the given first-order IVP dy/dx = 3y2/3 y(0)=0 2. Equations: integral xa dx= xa+1/(a+1)+constant The Attempt at a Solution change its form to 1/y2/3 dy/dx =3 integrate both sides with respect to x then it will be 1/y2/3 dy =...

Hello, I'm trying to get some feedback on my circuit design (picture below). I am attempting to use a differential op amp to impedance match a 100 ohm transmission line. The transmission line is CAT6A twisted pair. I'm using CAT6A as a feed through into a vacuum chamber. The design is to...

Homework Statement Hi guys, I am having a problem, knowing where to start with this question. Before I spend trying derive the partial derivative chain rule from first principles I would just like to know if this is what this questions is asking. If it is not asking that, how do I go about...

Homework Statement We assume from ODE theory that given a smooth A: I → gl(n;R) there exists a unique smooth solution F : I → gl(n;R), defined on the same interval I on which A is defined, of the initial value problem F' = FA and F(t0) = F0 ∈ gl(n;R) given.(i) Show that two solutions Fi : I →...

Homework Statement The Frenet frame of a curve in R 3 . For a regular plane curve (and more generally for a regular curve on a 2-dimensional surface - e.g. the 2-sphere above) we could construct a unique adapted frame F. This is not the case for curves in higher dimensional spaces. Besides the...

Homework Statement Let γ : I → R3 be an arclength parametrized curve whose image lies in the 2-sphere S2 , i.e. ||γ(t)||2 = 1 for all t ∈ I. Consider the “moving basis” {T, γ × T, γ} where T = γ'. (i) Writing the moving basis as a 3 × 3 matrix F := (T, γ × T, γ) (where we think of T and etc...

Homework Statement Find the values of a and b that make f a differentiable function. Note: F(x) is a piecewise function f(x): Ax^2 - Bx, X ≤ 1 Alnx + B, X > 1 Homework EquationsThe Attempt at a Solution Made the two equations equal each other. Ax^2 - Bx = Alnx + B Inserting x=1 gives, A - B =...

Homework Statement Please bear with the length of this post, I'm taking it one step at a time starting with i) Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices. (i) If F : I → gl(n, R) satisfies the matrix ODE F'...

Homework Statement Consider the illustration of 3 springs: In A, we hang a very light spring and pan from a hinge. The pan and spring are so light, we can neglect any stretching of the original length ##l_{0}##. In B we add a weight ##mg## which force is balanced by ##kl## (Hooke's Law; the...

<Moved from a technical forum, therefore no template.> How is it coming (-1)^n(p+n-1)!/(p-1)! please help...!

Homework Statement (a) Light waves satisfy the wave equation ##u_{tt}-c^2u_{xx}## where ##c## is the speed of light. Consider change of coordinates $$x'=x-Vt$$ $$t'=t$$ where V is a constant. Use the chain rule to show that ##u_x=u_{x'}## and ##u_{tt}=-Vu_{x'}+u_{t'}## Find ##u_{xx},u_{tt},##...

Homework Statement [/B] Calculate the work done by a force, against an electric field, to bring a charged particle (2 coulomb) from the point (2,0,0) to (0,0,0). Also calculate the work from (0,0,0) to (0,2,0). Finally calculate the work done going directly from (2,0,0) to (0,2,0) and...

Hi, the problem is parametric families: To find Differential equation of all the conics in the plane with the origin in the center But when you speak of center at the origin being the equation of the conics: Ax ^ 2 + Bxy + cy ^ 2 + Dx + ey + F, is it correct to take the origin by making x and...

22. According to Lambert's law of absorption, the percentage of incident light absorbed by a thin layer of translucent material is proportional to the thickness of the layer. If sunlight falling vertically on ocean water is reduced to one-half its initial intensity at a depth of 10 feet, at...

In general I'm wondering if \lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right] holds true for all f(x,y). Thanks.

Hi, I have an equation that takes the form: ax''-by' + c = 0 where x'' is second order with respect to time and y' is first order with respect to time. Would this be classed as a partial differential equation? Thanks very much for your help :)

Homework Statement Find the solution of the differential equation by using appropriate method: t^{2}y^{\prime} + 2ty - y^{3} = 0 Homework Equations I'm thinking substitution method of a Bernoulli equation: v = y^{1-n} The Attempt at a Solution [/B] t^{2}y^{\prime} + 2ty - y^{3} = 0...