Symmetries and Idealizations Homework 1
Due Wednesday 9/26
Problem 1.1 Vectors (quiz) Are the following equalities true or false? Why?1 If your
answer is true, draw a diagram indicating the quantities in the equation.
a)
a b = |a|b| cos
b)
|a b| = |a|b|
Symmetries and Idealizations Homework 2
Due Friday 9/28
Problem 2.1 Simple derivatives (quiz) Evaluate the following derivatives.
a)
d
ax2
dx
b)
d
sin x
dx
c)
d
ln x
dx
d)
dx
e
dx
e)
y
d
x2 + 2
dx
x
Problem 2.2 Polynomials (quiz) Are the following equalit
Symmetries and Idealizations Homework 3
Due Wednesday 10/3
Problem 3.1 Sinusoids (quiz) Are the following equalities true or false? Why?2
a)
tan x =
cos x
sin x
b)
sin(a + b) sin(a) = sin(b)
c)
sin(x + ) = cos(x)
d)
sin2 (x + y ) + cos2 (x + y ) = 1
Probl
Symmetries and Idealizations Homework 4
Due Friday 10/5
Problem 4.1 Approximation (quiz) Use a power series expansion to approximate the
following quantities by hand. Show your work, give a decimal answer, and explicitly state
what your small quantity is.
Symmetries and Idealizations Homework 5
Due Wednesday 10/10
Problem 5.1 Sphere (quiz) Given a sphere with radius R, what do the following quantities represent? Give your answers both in English and via a diagram.
a)
R2
b)
43
R
3
c)
2R
d)
4R2
Problem 5.2 C
Symmetries and Idealizations Homework 6
Due Friday 10/12
Problem 6.1 Product rule (quiz) Evaluate the following derivatives.
a)
d
ax2 sin x
dx
b)
d
cos(ax) sin(kx2 )
dx
c)
d2
cos(kx)
dx2
d)
where i =
d2 ikx
e
dx2
1
Problem 6.2 Exponentials (quiz) Are the