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Partial Differential Equations
1) Solve xut + uux = 0 with u(x,0) = x. (Hint: Change variables x→x2)
2) Solve ut + uux = 0 with the initial condition u(x,0)=1 for x≤0, 1-x for 0≤x≤1, and 0 for x≥1. Solve it for all t≥0, allowing for a shock wave. Find exactly where the shock is and show that it satisfies the entropy condition. Sketch the characteristics.
3) Show that the mass, momentum, and energy are constants of motion (invariants) for the KdV equation by direct differentiation with respect to time.
Find the probability that B beats A, that is, that the number that appears on die B is greater than the number on die A.
A particle is projected vertically upward with an initial velocity of 48 ft/sec and moves according to the law of motion s= 48t - 16t^2
Write a system of equations and use a matrix equation to find the total number of acres of each type of flower.
Let G be a group. x and y are elements of G. Prove that: The inverse of xy is y^-1x^-1. The identity element, e, is unique
We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II:
A high school graduating class has 487 students. there are 171 more girls than boys.. How many boys are in the class?
The bank will close your account when the amount becomes less than 1500 AED. Write a program that accepts the amount you want to save in the bank and prints for you the depreciation (decrease) in your savings every year because of only the bank ch..
Given one period of a function expand it in a sine-cosine Fourier Series and in a complex exponential Fourier Series. Do not use even or odd function shortcuts.
A student walks and jogs to college each day. She averages 5 km/h walking and 9 km/h jogging. The distance from home to college is 8 km and she makes the trip in 1 hour. How far does the student jog?
350 million test are expected to be sold this year. this represents 114% increase from last year. how many test were sold last year?
Your textbook outlines a specific 4-step strategy that is used to solve general algebraic equations.
two investments were made totaling #15000. for a certain year these investments yielded $1326 in simple intrest. part of the $8800 was invented at 14 and part at 16% find the amount invested at each rate.
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