Spring 2016, MMAT5030
1
Solution to Assignment 1
1. * Using the definition of the sine function, show that sin x/x < 1 for all x > 0. Hint:
Compare the arc-length QP with b where Q(a, b).
Solution. It suffices to prove this for x (0, /2). (When x /2, x >
2015-16 MATH4210 FINANCIAL MATHEMATICS
ASSIGNMENT 3 SOLUTION
Late submission of the assignment will be penalized for 5 points out of 10. Submission of the assignment after the solution is posted is not accepted in any case.
(1) By the put-call parity, if
2015-16 MATH4210 FINANCIAL MATHEMATICS
ASSIGNMENT 2 SOLUTION
Late submission of the assignment will be penalized for 5 points out of 10. Submission of the assignment after the solution is posted is not accepted in any case.
(1) We discount all coupons and
Sample Solutions of Assignment 3 for MAT3270B:
2.8,2.3,2.5,2.7
1. Transform the given initial problem into an equivalent problem with
the initial point at the origin
(a).
(b).
dy
dt
dy
dt
= t2 + y 2 , y(1) = 2,
= 1 y 3 , y(1) = 3
Answer: (a)Let t = s + 1,
MATH 4220 (2015-16) partial diferential equations
CUHK
Assignment 1
Exercise 1.1
2. Which of the following operators are linear?
(a) L u = ux + xuy
(b) L u = ux + uuy
(c) L u = ux + u2y
(d) L u = ux + uy + 1
(e) L u = 1 + x2 (cos y)ux + uyxy [arctan(x/y)]
MATH 4220 (2015-16) partial diferential equations
CUHK
Suggested Solution to Assignment 3
Exercise 3.1
1. By the method of odd extension or formula (6), we have
Z
(x+y)2
(xy)2
1
u(x, t) =
[e 4kt e 4kt ]ey dy
4kt Z0
(y+2ktx)2
(y+2kt+x)2
1
=
[e 4kt +ktx e
Spring 2016 Second Term MATH2060A
1
Solution to Assignment 8
Supplementary Exercises
1. Let cfw_akn
n=1 , k = 1, , m, be a finite family of convergent sequences. Show that it must
be uniformly convergent.
Solution. Let nk () be the first -number of cfw_a