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...
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}...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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)...
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=...
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=...
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...
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 =...
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...
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...
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...
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...
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...