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    Simple Integral

    Homework Statement Hello. I have a simple integral here that has been stumping me for the last 30 minutes. It appears that my basic integration skills have gotten very rusty. Homework Equations \int{x^3}\sqrt{1+x^2}dx The Attempt at a Solution I am pretty sure a simple...
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    Finding position and velocity from Force (analytic mechanics)

    Homework Statement A body of mass "m" is repelled from the origin by a force F(x). The body is at rest at x_0, a distance from the origin, at t=0. Find v(x) and x(t). Homework Equations F(x)=\frac{k}{x^3} \ddot{x}=\frac{d\dot{x}}{dt}=\frac{dx}{dt}\frac{d\dot{x}}{dx}=v\frac{dv}{dx}...
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    How fast is the distance changing? (FODE, I think)

    Homework Statement 2 cars start from the same point. Car A travels a constant 50 mph due west. Car B travels a constant 27 mph due south. After 3 hours, how fast is the distance changing between them? Homework Equations The Attempt at a Solution I saw this problem online...
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    Fit P(w) to determine Q,w, and R (Series RLC AC circuit)

    Homework Statement Fit P(w) to determine Q, and w_0, and R. You should put in Vrms as a known constant. Homework Equations P(\omega)={\frac{V_{rms}^{2}}{R(1+Q^2(\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega})^2)} Q=\frac{\omega_0}{\Delta\omega} R=R_load+r The Attempt at a...
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    Laplace Eq with Dirichlet boundary conditions in 2D (solution check)

    Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...
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    How to check Fourier series solution (complex)

    Homework Statement Find the complex Fourier series for: f(t)=t(1-t), 0<t<1 Homework Equations f(t)=\sum_{n=-\infty}^{\infty}c_n{e^{i\omega_n{t}}} c_n=\frac{1}{\tau}\int_{t_0}^{t_0+\tau}e^{-i\omega_n{t}}f(t)dt \omega_n=2\pi{n}\quad\tau=1 The Attempt at a Solution I solved...
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    Writing a polynomial in terms of other polynomials (Hermite, Legendre, Laguerre)

    Homework Statement The first 3 parts of this 4 part problem were to derive the first 5 Hermite polynomials (thanks vela), The first 5 Legendre polynomials, and the first 5 Laguerre polynomials. Here is the last part: Write the polynomial 2x^4-x^3+3x^2+5x+2 in terms of each of the sets of...
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    Indefinite integral (Hermite polynomials)

    Homework Statement I need to evaluate the following integral: \int_{-\infty}^{\infty}x^mx^ne^{-x^2}dx I need the result to construct the first 5 Hermite polynomials. Homework Equations The Attempt at a Solution First I tried arbitrary values for "m" and "n". I was not able to...
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    Fourier series proof

    Homework Statement Suppose, in turn, that the periodic function is symmetric or antisymmetric about the point x=a. Show that the Fourier series contains, respectively, only cos(k_{n}(x-a)) (including the a_0) or sin(k_{n}(x-a)) terms. Homework Equations The Fourier expansion for the...
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    Orthogonality integral help

    Homework Statement If there exists no function, f(x), except zero, with the property that \int_{a}^{b}{\phi_{n}(x)}f(x)w(x)dx=0 for all \phi_{n}, then the set {\phi_{n}(x)} is said to be complete. Write a similar statement expressing the completeness of a set of basis vectors in...
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    Differential Equation (Homogeneous / scale-invariant

    Homework Statement Test the following equation to show that they are scale invariant. Find their general solutions (It is not necessary to do the anti-derivative.) (x+y^2)dy+ydx=0 I believe what my tutorial wants me to do is to check for homogeneity. I'm not sure though. This is not a...
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    Derivative notation

    Homework Statement Is it correct to say that if "y" is a function of x, then y'=\frac{dy}{dx} ??
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    Finding the angle without a calculator (CA)

    Homework Statement In my math class, we are not permitted to use a calculator. I am currently reviewing for a test and came across a small problem. Perform the following operation using the Euler (polar) form for the complex numbers involved. (1-3i)/i Homework Equations The...
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    Mental math question

    Homework Statement I am currently taking a mathematical methods in physics course. We were given a prerequisite inventory on the first day of class. There are 4 problems that we are assumed to be able to do in our head to 4 or 5 digit accuracy. I am not sure of how to compute these...
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    Linearly independent vectors

    Homework Statement Suppose that A, B, and C are not linearly independent. Then show how the \alpha_{i} can be computed, up to a common factor, from the scalar products of these vectors with each other. Hint: Suppose that there are non-zero values of the \alpha_{i}'s that satisfy...
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    Conceptual circuit question

    Hi. I'm not sure if this is the right place to pose this question as it is not homework question. I'm studying RC circuits in second semester physics and I have a question about the electrons traveling through a circuit. Is it true that electrons won't travel down a branch of a circuit in...
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    Series vs. parallel capacitors

    Homework Statement I have some results of my lab here and I just want to check to make sure they make sense. The lab write-up refers to this part of the experiment as "capacitors in parallel" but I think they are actually in series (either that or we connected them incorrectly). Here is...
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    Row boat FODE

    Homework Statement The following problem involve the setting up and solving of a first-order differential equation for a physical situation. Once, derived the equation itself is not difficult to solve. A boater rows across a straight river of constant width "w", always heading (i.e., pointing...
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    Good math methods in physics book?

    Hello. I am looking for a good math methods in physics book. I am currently taking Mathematical methods in physics at my university. The tutorial we use isn't very helpful. Does anyone have any suggestions?
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    Separable FODE

    Homework Statement The following is an explanation from my tutorial. I do not understand it. {\frac{d}{dx}(y_1{{y_2}'}-y_2{{y_1}'})+P(x)(y_1{{y_2}'}-y_2{{y_1}'})=0 Overlooking for the moment that P(x) may be undefined at certain values of x(so-called-singular points of the equation), we...
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    Easy Peasy CA problem

    Homework Statement I have a very simple complex arithmetic question. How do I express the quantity cos(1+i) in Cartesian (a+ib) and Euler(re^i*theta) Is this the right track?: cos(1+i)={e^{i(1+i)}\over2}+{e^{-i(1+i)}\over2} I know that: cos(1+i)=cos(1)cos(i)-sin(1)sin(i)...
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    Seemingly difficult complex arithmetic problem

    Homework Statement Transmission of a quantum mechanical wave past a one-dimensional square well results in the following expressions relating initial to final wave amplitudes: A= (cos(2ka)-{i\epsilon\over2}sin(2ka))e^{2ia\lambda}F+{i\eta\over2}sin(2ka)G B=...
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    LaTeX Help using latex

    Hello. I have a very large, very complex equation to post here at the forums. I just finished writing it in Latex but I am having problems posting it. In the past I have always used the short cut keys, but this time a wrote out the whole thing. Here is one part in Latex: A=...
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    Complex arithmetic/Geo Series proof

    Homework Statement Applications from multiple-slit diffraction involve sums like the following. Prove that: \sum^{N-1}_{n=0} cos (nx) = \frac{sin(N(x/2))}{sin(x/2)} * cos((N-1)x/2) Homework Equations According to my instructions, this should involve only algebraic manipulations...
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    Speed of a Rocket far from Earth

    Homework Statement A rocket is launched straight up from the earth's surface at a speed of 1.60×10^4 m/s. What is its speed when it is very far away from the earth? Homework Equations F= (GMm)/r^2 G= 6.67 X 10^-11 M= 5.98 X 10^24 Potential Energy = (Gm1m2)/r Kinetic Energy =...
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    Triple integral to find volume of ice cream cone

    Homework Statement Use a triple integral in rectangular coordinates to find the volume of the ice cream cone defined as follows The region R in the xy-plane is the circle of radius 1 with center at the origin. The sides of the cone are defined by the function z= \sqrt{x^2+y&2} The top of...
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    Is this problem missing info?

    Homework Statement A sailboat is heading due east at 8 mph. The wind appears to blow from the south west (toward the north east – that is 45 degrees north of east) as observed from the sailboat. What is the speed and direction of the wind as observed from the ground? Homework Equations...
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    Rain drops relative velocity

    Homework Statement While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38 degrees with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these...
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    Sliding down a hill with friction

    Homework Statement Johnny jumps off a swing, lands sitting down on a grassy 20 degree slope, and slides 3.5m down the slope before stopping. The coefficient of kinetic friction between grass and the seat of Johnny's pants is 0.5 Homework Equations F=ma Frictional force = \muN...
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    Conceptual Friction problem

    Homework Statement There is a box drawn on a horizontal surace. A force is being applied at an unkown angle in the positive x direction to the box. The angle is greater than 0 and less than 90. I'm assuming a standard coordinate system. "In the diagram above the box is stationary as the...
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