Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 3
Due Monday, October 21, 2013
1. This exercise shows that pointwise convergence of a sequence of functions on a nite
and closed interval [a, b] does not in
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 2
Due Monday, October 14, 2013
1. Let z be a complex number. Investigate the convergence of innite product
1
k=1
z2
k2
.
2. The quantum states for a simple
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 9
(This assignment will not be collected and graded.)
1. Denote by C ([1, 1]) the set of all real, continuous functions on [1, 1]. Dene (x) =
1 if 1 x < 0 a
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 1
Due Monday, October 7, 2013
1. Let ak and bk be complex numbers (k = 0, 1, . . . , q ). Let An = n=0 ak if n 1 and
k
A1 = 0. Let 0 p q. Prove the followin
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 5
Due Monday, November 4, 2013
1. Let and u be an eigenvalue and a corresponding eigenvector of a square matrix A.
Show that 7 and u are an eigenvalue and a
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 6
Due Friday, November 15, 2013
1. Find conditions on real numbers a, b, and c such that the matrix A =
ab
is symbc
metric positive denite.
2. Let A = [aij
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 4
Due Monday, October 28, 2013
1. Compute the determinant
2
1
(a) det
1
1
of each of the following matrices:
1 a a2
111
1 b b 2
2 1 1
;
(b) det
1 c c 2
1
Mathematical Methods in Physical Sciences and Engineering
MATH 210a

Winter 2014
Math 210A: Mathematical Methods in Physical Sciences and Engineering
Fall 2013
Homework Assignment 7
Due Friday, November 22, 2013
1. Let x and y be two vectors in Rn . Show that x y is orthogonal to x + y if and only
if x = y .
2. Let U and V be two n n