The epicenter of the battle around Salaita’s offer withdrawal seems to be located at the question, whether or not political considerations are admissible when appointing a scholar. I checked what Dr. Salaita himself writes about the matter in a 2008 …
About yuliy
september 9
\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}\)
Linear operators; normal forms
Linear operators between different spaces are easy to normalize: the rank is the only invariant; the classification is discrete.
For endomorphisms, the situation is more involved.
Diagonalization corresponds to splitting the …
math 285: the week of september 8
ece515, homework1 (due 9.11).
\(\def\Real{\mathbb{R}}
\def\Comp{\mathbb{C}}
\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}
\)
Consider the space \(V\) of polynomials (with real coefficients) of degree \(\leq 4\). There exists a natural basis in \(V\), comprised of monomials – we will denote this basis as \(\e\)).
 Is
september 5
 Solve separable ODEs:
 \[
\sqrt{y^2+1}=xyy’;
\]  \[
y’=\cos(yx)
\]  \[
y’y=2x3
\]
 \[
 Solve
 \[
(xy)+(x+y)y’=0
\]  \[
2x^3y’=y(2x^2y^2)
\]  \[
xy’y=x\tan{y/x}.
\]
 \[
 Sketch the slope fields and a few trajectories for
 \[
y’=y^2x;
\]  \[
y’=yx^2;
\]  \[
y’=y^2+x^23.
\]
 \[
september 4
\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}\)
Linear operators
Their range=image, nullspace=kernel (both linear subspaces).
Rank=dimension of the image (if finitedimensional).
Important: dimension of the kernel + rank=dimension of the domain…
Example:
\(V=\Fun(S,\Field)\), where, as before \(S=\{0,1,2,3,4,5\}\subset\Comp\). Let \(Z\) is the operator …
math 285: the week of september 1
Review Chapter 1.21.5. Listen to the lectures (four videos altogether).
Additional reading (highly recommended!): chapter 1 of Ordinary differential equations : a practical guide by
Bernd J. Schroers (CUP, 2011).
Homework (due by Monday, 9.8):
 Find general
september 2
\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\)
Fields, vector spaces, subspaces, linear operators, range space, null space
A field \((F,+,·)\) is a set with two commutative associative operations with \(0\) and\(1\), additive and multiplicative inverses and subject to the distributive law.
Examples (Common fields)
…class of 8.29

 express \(\sin(3x)\) in term of \(\sin(x)\).
 express \(\cos(4x)\) in terms of \(\cos(x)\).
 simplify
\[
\sum_{k=20}^{k=20} e^{k\phi}.
\]

solve
 \[
y’=\frac{2t}{1+t^2}, y(0)=0;
\]  \[
y’=\frac{2t}{1t^2}, y(0)=0;
\]  \[
y’=\frac{2t}{1t^2}, y(2)=0.
\]
 \[
 solve
 \[
y’=\frac{2x^24x+3}{x1}, y(0)=2;
\]  \[
y’=\frac{x^24x+3}{x2}, y(0)=2;
\]  \[
 \[
august 28
\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\)
What this course deals with?
Linear control systems. A continuoustime statespace linear system is defined by the following equations:
The signals
\[
x'(t) = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t),
\]
where
\[
x\in \Real^n, …