Determine the leading order term the asymptotic expansion, Mathematics

Submit your working in (neat) handwritten form (do not type up your solutions). For the plots that you generate in Maple or Matlab, you can print them out and attach them at the end or cut them out and stick them in. Either way, make sure they are labelled properly.

It is OK to discuss these questions with other students, but the written version of this Problem Solving

Task must be your own. It is not OK to copy another student's work.

1. Use the method of Stationary Phase to determine the leading order term in the asymptotic expansion as k → ∞ for the integral

2365_sin theta.png

2. Consider the integral

503_cos theta.png

where

g(x) = x + 2 cos(x/2).

(a) Use Maple or Matlab is similar to plot cos[k(g(x))] over the domain [0, 2p] for each of

k = 2, 10 and 50.

(b) Find the point in [0, 2p] at which g0(x) = 0, and write out g(x) as a Taylor expansion about this point, including the first two non-zero terms (show all working, calculating derivatives by hand).

(c) Call the two-term Taylor expansion h(x), and plot h(x) over the domain [0, 2p] for each of k = 2, 10 and 50.

(d) Use the method of Stationary Phase to determine the leading order term in the asymptotic expansion of J(k) as k →∞.

Posted Date: 4/2/2013 6:28:26 AM | Location : United States







Related Discussions:- Determine the leading order term the asymptotic expansion, Assignment Help, Ask Question on Determine the leading order term the asymptotic expansion, Get Answer, Expert's Help, Determine the leading order term the asymptotic expansion Discussions

Write discussion on Determine the leading order term the asymptotic expansion
Your posts are moderated
Related Questions
Interpretations of the Derivative : Before moving on to the section where we study how to calculate derivatives by ignoring the limits we were evaluating in the earlier secti

i am a student of class 10 and need help for making my project on shares and dividend

i have trouble going through problem in this lesson. Markdown and Markups are theh ones im stuck in

Example    Write down the equation of a circle  alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i

Following is some more common functions that are "nice enough". Polynomials are nice enough for all x's. If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provid

Joey participated within a dance-a-thon. His team begin dancing at on Friday 10 A.M. and stopped at 6 P.M. on Saturday. How many hours did Joey's team dance? From 10 A.M. Frida

why is multiplying inportent in our lifes

) Show that the following argument is valid: (~p ? q) => r s ? ~q ~t p => t (~p ? r) => ~s ------------------------ ? ~q 2) Show that the following argum

fixed cost of $1400 ,printing cost of .40 cents -each item to sell for $1.05. what is linear cost function, linear revenue function and number of items to be sold to make a profit

Example of division of fractions: Example: (4/5)/(2/9) = Solution: Step 1:             Invert the divisor fraction (2/9) to (9/2). Step 2:             Multip