(a) Show that u(t, x) = e-k2t+ikx is a complex solution to the heat equation u/t =...
Question:
∂u/∂t = ∂2u/∂x2
for any real constant k.
(b) Write down another complex solution by using complex conjugation.
(c) Find two independent real solutions to the heat equation.
(d) Can k be complex? If so, what real solutions are produced?
(e) Which of your solutions decay to zero as t → ∞?
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 57% (7 reviews)
a ut k 2 e k2 ti kx 2 ux 2 b e k2 t i kx c e k2t cos kx e k2t sin kx d Yes Wh...View the full answer
Answered By
Ahan M
I have 3+ Years of experience in teaching different levels of Mathematics and Machine Learning. I have been a Teaching Assistant for various Mathematical Courses such as Algebra, Optimisation and Graph theory, with a great background and knowledge in Trigonometry, Differential Equations, Discrete Mathematics and Numerical Analysis. I also conduct online tutorial sessions for Deep learning with Mathematical insights. Having great exposure to various topics and higher level subjects in Mathematics, I believe I can help and break complex problems faced by students into simple solutions. I also have been part of a few tutoring platforms for nearly 3 years in subjects like Advanced and Other Mathematics. I also conduct seminars for doubt clearing and help needed for students in Sciences as well, in Physics and Chemistry.
0.00
0 Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Find all complex exponential solutions u(t, x) = ewt+kx of the beam equation 2u/t2 = 4u/x4. How many different real solutions can you produce?
-
Write down all solutions to the following boundary value problems. Label your answer as (i) Unique solution, (ii) No solution, (iii) Infinitely many solutions. (a) u" + 2u = 2a, u(0) = 0, u() = 0 (b)...
-
The wave equation c2 (2u/(x2 = (2u/(t2 and the heat equation c (2u/(x2 = (u/(t are two of the most important equations in physics (c is a constant). These are called partial differential equations....
-
Tonight at 7pm a professional basketball game featuring the Golden State Warriors and the Washington Wizards will be played at the Chase Center, an indoor arena in the Mission Bay neighborhood of San...
-
Texaco, Inc., and Shell Oil Co. are competitors in the national and international oil and gasoline markets. They refine crude oil into gasoline and sell it to service station owners and others....
-
The energy dissipated in hysteresis damping per cycle under harmonic excitation can be expressed in the general form where \(\gamma\) is an exponent \((\gamma=2\) was considered in Eq. (2.150)), and...
-
An electric motor of mass \(500 \mathrm{~kg}\) operates on the first floor of a building frame that can be modeled by a steel girder supported by two reinforced concrete columns, as shown in Fig....
-
Target prices, target costs, activity-based costing. Snappy Tiles is a small distributor of marble tiles. Snappy identifies its three major activities and cost pools as ordering, receiving and...
-
What do Headquarters Flood Mitigation Assistance (FMA) and Pre-Disaster Mitigation (PDM) Coordinators need to enter into eGrants to control how long an application for a grant program is available to...
-
Chen plcs income statements for the years ended 31 December 2014 and 2015 and the statements of financial position as at 31 December 2014 and 2015 are as follows: Income statements for the years...
-
(a) Write down the explicit formulas for the harmonic polynomials of degree 4 and check that they are indeed solutions to the Laplace equation. (b) Prove that every homogeneous polynomial solution of...
-
Prove that the real and imaginary parts of a general element of a conjugated vector space, as defined by (7.70), are both real elements.
-
Why could a current asset such as Net Assets of Business Held for Sale distort a firm's liquidity, in terms of working capital or the current ratio?
-
Henrich is a single taxpayer. In 2019, his taxable income is $450,000. What is his income tax and net investment income tax liability in each of the following alternative scenarios? a. All of his...
-
How does a company report its income taxes payable on its financial statements?
-
What is the eco-efficiency ratio formula?
-
What does insufficient funds mean in relation to a transaction on a bank statement?
-
If a product line is making a loss, should it be discontinued. Why or why not?
-
Lake Country Ltd. (LCL) is a Canadian manufacturer of outdoor furniture products. LCL manufactures high-quality, durable, and attractive furniture such as outdoor seating, tables, and accessories....
-
Using Apple, demonstrate how the differentiation strategy can be well implemented.
-
Alter the program MonteCarlo to estimate the area under the graph of y = 1/(x + 1) in the unit square in the same way as in Exercise 4. Calculate the true value of this area and use your simulation...
-
In the preceding exercise, it is natural to ask How do we get the information that the given hand has an ace? Gridgeman considers two different ways that we might get this information. (Again, assume...
-
Using the notation introduced in Example 4.29, let Show that there is exactly one value of x such that if your envelope contains x, then you should switch. if r = 2*. Pa =(4)*. 0, otherwise.
-
9 Question 6 (3 marks) Distance can be measured in kilometres or in miles. The following graph shows the relationship between distance in kilometres and distance in miles. 100 80 (40, 64.4) distance...
-
5.6.4 The pipeline shown in Fig. X5.6.3 supplies water to a hydroelectric power plant, the elevation of which is 650 m below the level of the water at intake to the pipe. If 8 per cent of this total,...
-
The first part of the course we discuss methods of legal dispute settlement (i.e. how the law aims to resolve disputes/ how we use legal processes to settle or end disputes). In W3 and W4 we examine...
Study smarter with the SolutionInn App