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).
r
$ c) Find the directional derivative of F
Phys 208 Theoretical Physics Test 2 (October 29, 2004)
1.(25 pts) Given that
0
e ax sin( kx) dx =
k , a2 + k 2
determine the integral
0
x 2 e ax sin( kx ) dx .
2.(25 pts) In the integral I =
0
0
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 protected] 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
3
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 .
2.(20 pts)
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
3
8i .
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
3
8 .
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