Music: A Mathematical Offering
Department of Mathematics, Meston Building, University
of Aberdeen, Aberdeen AB24 3UE, Scotland, UK
Home page: http:/www.maths.abdn.ac.uk/bensondj/
E-mail address: \/\/b\e/n\s/o\n/d\j/\/ (without the slashes)
The Method Behind The Music
Scales And Key
The Physics of
History of Music
Mathematics & Music (AMath390)
Lecture Notes on
Tuning & Temperament
Dept. of Applied Mathematics, University of Waterloo
A. Morris, 2014
lowest frequency of a note/sound. Generally t
AMath 390 Lecture:
Tuning of Balinese Gamelan Instruments
Prof. Maisie Sum, Department of Music
Conrad Grebel University College, University of Waterloo
1. Two Gamelan Tuning Systems
slendro: 5-tone system
smoother pentatonic subdivision of the oct
Assignment 3 - Paths integrals and gradient fields.
Due Noon January 20, 2017.
Compute the work
1. A force field F~ : R3 R3 is given by F~ (x, y, z) = xi + yj + z k.
moving a particle along the parabola z = 0, y = x2 , from x = 1 to x = 2.
F~ d~s don
Assignment 6 - Surfaces, surface integrals and geodesics.
Due February 10, 2017 (1 pm).
~ v) = (u cos v, u sin v, v), (u, v) [0, 5] [0, 2]. Find its area.
1. Sketch the helicoid S(u,
2. Evaluate the surface integral
f dS where,
(a) f (x, y, z) = xz and
Assignment 2 - Paths and curves.
Due NOON Friday January 13, 2017.
1. Find a path in R2 whose image set is:
(a) The circle with radius 5 and center at (1, 2).
(b) The ellipse which in Cartesian coordinates has the equation,
(c) The branc
Assignment 8 - Vector calculus and continuity equations.
Due March 10, 2017 (1 pm)
1. A force field F~ defined by an inverse square law is given by,
F~ = 3 ,
with ~r = xi + yj + z k and r = |~r|. Show that F~ = 0.
2. Let be a bounded subset of R3 who
Assignment 5 - Circulation, Flux and Divergence theorem.
Due 1 pm February 03, 2017.
1. Compute the area enclosed by the hypocycloid of four cusps
~ : [0, 2] 7 R2 and ~ (t) = (a cos3 t, a sin3 t),
where a > 0 is a constant.
2. Let D be a piecewise C 1 ,
Assignment 11 - Fourier series, Fourier transform and
Not to be handed-in.
1. (a) Knowing that
eu du =
e 2 x cos x dx.
Hint: Use Leibnizs theorem to show that I 0 () = I().
(b) Use 1a to show that,
F e 2 x = 2e
Assignment 4 - Conservative fields and Greens theorem.
Due 1 pm January 27, 2017.
1. A force F~ acts on a particle that is moving in the plane along the semi-circle parameterized by ~ (t) = ( cos t)i+
(sin t)j; t [0, ]. Find the work W = C F~ d~s done b
TA: Thurs 1:00 - 3:00 PM, MC 6496
Zoran: Mon 4 PM - 5 PM, MC 6128
Classification of DEs
1. # of variables
A. One dependent, one independent variables
B. One dependent, two or more independent variables (PARTIAL DE (PDE)
C. TWO OR MORE UNKN
Assgn 5 due on MONDAY 22 feb
Tue feb 28
Mc 4041 4042 4059
Topics for midterm chapters 1-3 inclusive
Assgn 1-5 inclusive
Include exceptional cases
Existence and uniqueness