Phys 208 Theoretical Physics Test 3 - Dec. 3, 2004 1.(25 pts) Given F ( x , y , z ) = xy + sin( z ) . a) Find F at (1, 2, /2). b) Find a unit vector in the direction of most rapid increase of F at (1, 2, /2). c) Find the directional derivative of F at (1,
Phys 208 Theoretical Physics Test 3 - Nov. 19, 2001 1.(25 pts) Given F ( x , y , z ) = xy + yz + z sin x . a) Find F at (0, 1, 2). b) Find a unit vector in the direction of most rapid increase of F at (0, 1, 2).
$ c) Find the directional derivative of F
Phys 208 Theoretical Physics Test 2 (October 29, 2004)
1.(25 pts) Given that
e ax sin( kx) dx =
k , a2 + k 2
determine the integral
x 2 e ax sin( kx ) dx .
2.(25 pts) In the integral I =
x2 + y2 2 xy dxdy make the change of variables 2 2 2e 1+ (
Phys 208 Theoretical Physics Test 2 (October 22, 2001) 1.(25 pts) a) Suppose you want to transform from Cartesian (x, y) to Polar coordinates (r, ). Determine the Jacobian for the area; namely J so that dxdy = J drd . b) Express the following integral in
Phys 208 Theoretical Physics Test 1 ( Sept. 29, 2004) 1. (20 pts) Find the interval of convergence for the following power series; be sure to investigate the endpoints of the interval.
( 1) n x 2 n ( 2n) 3 2 n =1
2. (20 pts)
Recall the binomial series is
Phys 208 Theoretical Physics Test 1 ( Sept. 24, 2001) a) Expand the function ln( 1 + x ) in a Maclaurin series. b) Determine the interval of convergence. 2. (20 pts) a) Given that
1. (20 pts)
1 = 1 x + x2 x3 + L , 1+ x
find the Maclaurin series for the fu
Phys 208 Test 3 April 9, 2007 dt (a + t 2 ) = a , determine the integral Hint: differentiate a few times with respect to a and then set a = 4. 1.(20 pts) Given the integral
dt . (4 + t 2 )3
1 x ( x + y) y 2. (20 pts) In the integral I = e x + y dy dx ,
Phys 208 Theoretical Physics Test 2 (March 2, 2007) 1. (20 pts) An AC voltage source has a voltage amplitude of 20 volts. It is connected to a resistor of 2 ohms and an inductor and capacitor as shown. The frequency of the voltage source is such that L =
Phys 208 Theoretical Physics Test 1 (Feb. 2, 2007)
1.(15 pts) Find the interval of convergence for the following power series. Be sure to check the endpoints of the interval.
(1) n ( x + 1) n n n =1
2. (20 pts) Recall the binomial series is defined as p p
PHYSICS 208 - THEORETICAL PHYSICS SP10 Instructor: Jerry Peacher 109 Physics Phone: 341- 4704 e-mail: email@example.com Generally available at other times by appointment.
Office Hours: MTWTh 3:00 - 4:00 p.m.
Text: MATHEMATICAL METHODS IN THE PHYSICAL SCIENC
Phys 208 Theoretical Physics Final exam May 10, 2007 8i .
1.(15 pts) a) Find and plot the roots of
b) Evaluate ( i)i in Cartesian form, i.e., x + iy form. c) Determine the points in the (x, y) plane that satisfy the equation | z 2 + 3i |= 4 .
Phys 208 Theoretical Physics Final Dec. 14, 2004
1. (17 pts) Consider an AC circuit which has a resistor and inductor in series which is in parallel with a capacitor. The voltage source has an amplitude of 160 volts and operates at a radial frequency such
Phys 208 Theoretical Physics Final Exam Dec. 19, 2003 1. (17 pts) a) Find and plot the roots of
b) Evaluate ( i ) i in Cartesian form, i.e., x + iy form. c) Determine the points in the (x, y) plane satisfying the equation | z 1 + i| = 2 .
2. (17 p
Phys 208 Theoretical Physics Final Exam Dec. 10, 2001 1. (25 pts) a) Find and plot the roots of b) Evaluate sin( + i ln 2 ) . 2 2. (25 pts) a) Evaluate the derivative
d 100 2 x . (x e ) dx100 n! n ax b) Show that x e dx = n + 1 . 0 a
Z r / 2 a0 Ze
To show that
z r p z r i i
See Chapter II page 11:
z r cos sin
1 r r 2 sin i
u1 u2 u3 u1 r u2 r u3 r r
u 1 g 11 u 1 r u 2 g 22 u 2 r 2 g 22 r u 3 g 33 u 3 r 2 sin 2 g 33 r sin z r r cos sin i i r r r sin 1 0 r 2 sin r 0 r r r r sin 1 0 i r2 r 0 r 1
Problem Set 8 Fall 2010 Solutiuon to Problem 3.
a) Show that a solution to 2 Fr EFr 2m
is given by Fr where 2mE/ 2 1/2 .
al, mj arY ,m ,
Solution: First we note that the differential equation can be written: 2 E F r 0 2m 2 2 F r 0 1 d r 2 d L L 2
The Dirac Delta Function, (x-xo)
Dirac Delta Function In one dimension, (x-xo) is defined to be such that: ma to b f(x) (x-xo)dx /
+ *0 if xo is not in [a,b]. *f(xo) if xo = a or b; *f(xo) if xo (a,b). .
Properties of (x-xo): (you should know those
Math 402 Final Exam
Name_ This exam will not be returned. However, you may examine your graded solutions.
1. _( 75 points) 2. _( 20 points) 3. _( 10 points) 4. _( 20 points) 5. _( 25 points)
g11=1, g22=r, g33=rsin (spherical coord.) dxi= A j dqj
Math 402 Exam I 2005
g11=1, g22 = r, g33 = rsin2 d x i=
1. _(40 points) 2. _(30 points) 3. _(30 points)
AT i j
-1 j = i
BT m n = A-1 m n
x = rsincos = cos y = rsinsin = sin m = Bn z = rcos = z
dxi = R (,)ij d x
Chapter IV: Vector Analysis
In this chapter we shall be working primarily in the Cartesian system. Unless stated otherwise assume the system is Cartesian and any transformation, A, to another system is a rotation.
Chapter III: Tensors
This will be a brief summary of what we have already covered (as it applies to tensors), plus a little about tensors in general.
Definition: a tensor is an array of covariant and contravariant components, T kRmnp ( functions of
Chapter II: General Coordinate Transformations
Before beginning this chapter, please note the Cartesian coordinate system belowand the definitions of the angles and in the spherical coordinate system. In the spherical coordinate system, (r,) we shall us
MATHEMATICAL PHYSICS: SEMESTER I
University of Missouri-Rolla
Barbara Hale University of Missouri-Rolla
CHAPTER I - VECTOR SPACES Page I-n Vector spaces, S, over field, F field, space definitions examples of vector spaces symbols defined 2. Normed vector
MATHEMATICAL PHYSICS I: MATH 402
Dr. Barbara Hale firstname.lastname@example.org 205 Physics Hours: Tuesday, Thursday P.M.
None is required. If you wish to buy a book to brush up on your background, "Mathematical Methods for Physicists", 5th Edi
Math 402 Set VI
1. Convert [L(x,y,z) - (x,y,z) = 0 ] to a "covariant" form which transforms like a tensor under a generalized coordinate transformation, dxi= Aijdqj. is a scalar ( a numerical constant and independent of the coordinate system). What is the