LAB 06: Fourier Transforms III
Notebooks to Download:
doubleexp.nb
1. Open doubleexp.nb. There is not much to do here but make sure you
appreciate the point of the notebook.
2. Use Mathematica to solve the dierential equation that describes the
damped ha
LAB 02: Complex Numbers and Functions
Notebooks to Download:
phasecolor.nb
mapping.nb
1. Eulers relation tells us that ei = cos + i sin . Make a table of ordered
pairs cfw_Re[ei ],Re[ei ] where ranges from 0 to 2 in steps of /2.
Plot this table using Li
LAB 03: Singularties
Notebooks to Download:
viewcomplex.nb
1. Integrate z from 0 to 1 + i. Verify that
2. Generalize the above to show
e2iu = 2
Z
R 1+i
0
zdz = i.
eiu
zdz.
0
That is evaluate the RHS using Mathematica.
3. Using viewcomplex.nb view the exa
LAB 05: Fourier Transforms II
Notebooks to Download:
chirp.nb
1. Find the convolution of a triangle and a square pulse by direct computation of the convolution.
Plot the convolution.
2. Find the cross-correlation of the above triangle and square pulses b
LAB 04: Fourier Transforms I
Notebooks to Download:
showfourier.nb
causal.nb
1. Carefully work through the examples in showfourier.nb. Try to get a
feel fro what is going on. Try to see if you can recognize any patterns
or symmetries, We will have six w
Advanced Mathematics for Theoretical Chemistry
PS07
Problems:
read handout on density operator
4.1, 4.2, 4.6, 4.7, 4.8, 4.10, 4.11, 4.12, 4.14, 4.15, 4.16 from my book
Extra Problems:
4.3, 4.9, 4.13, 4.17, 4.18 from my book
1
Advanced Mathematics for Theoretical Chemistry
PS06
Problems:
1.401.43 from my book
1. Evaluate the Fourier transform of the square pulse
f (t) =
(
1 < t < 1
.
else
1,
0,
2. Explain why Fig. 1b of D.J. Ulness, J.C. Kirkwood and A.C. Albrecht,
Raman scatt
Advanced Mathematics for Theoretical Chemistry
PS01
Problems:
1.1 and 1.2 from my book
9, 15, 16 from chapter 3 of Byron and Fuller p136
11 from chapter 4 of Byron and Fuller p205
Extra Problems:
2, 3, 4, 8, 17, 18 from chapter 3 of Byron and Fuller
Advanced Mathematics for Theoretical Chemistry
PS02
Problems:
1.31.11, 1.14 from my book
1 and 17 from chapter 4 of Byron and Fuller
Extra Problems:
1.12, 1.13, 1.15 from my book
2, 5 from chapter 4 of Byron and Fuller
1
Advanced Mathematics for Theoretical Chemistry
PS03
Problems:
1.161.19 from my book
17a and 17b from chapter 6 of Byron and Fuller p380
The following problems deal with D.J. Ulness, J.C. Kirkwood and A.C.
Albrecht, Raman scattering from a Brownian oscil
Advanced Mathematics for Theoretical Chemistry
PS05
Problems:
1.25, 1.26, 1.27, 1.29, 1.31, 1.32, 1.33, 1.34, 1.36, 1.39 from my book.
1. Evaluate
(a)
Z
(x x0 )e |x| dx
(b)
Z
(x2 x 6)e |x| dx
(c)
Z
(cos x)e |x| dx
2. Take the Fourier transform of the
Advanced Mathematics for Theoretical Chemistry
PS04
Problems:
1.20, 1.22, 1.23 from my book
Read the introduction to D.J. Ulness, J.C. Kirkwood and A.C. Albrecht, Raman scattering from a Brownian oscillator J. Chem. Phys.
109, 4478 (1998).
There is a t