c FW Math 321, 2009/04/20
Elements of Complex Calculus
Basics of Series and Complex Numbers
Algebra of Complex numbers
A complex number z = x + iy is composed of a real part (z) = x and an imaginary part (z) = y, both of which are real numbers, x, y
c F. Walee, Math 321, 2006/02/11
Detailed discussion of charged particle moving in a constant magnetic eld, or in mathematical terms d2 r dv = =bv (1) 2 dt dt where v = v(t) = dr/dt. Physics remark: we have absorbed all the scalar constants like electri
Homework 0- Precollege Geometry Check
What is the sum of the inner angles of a triangle? Prove it.
If A,B,C are 3 distinct points on a circle of center O and the line AC passes through O,
what is the angle ABC? Prove it.
A,B,C are 3 points on a circle of
Cellular Respiration: Food (glucose) is broken down in a series
of steps to form ATP
Ontogeny- developmental history of an organism
Phylogeny- developmental history of a group of organisms
Information is accumulated with time- history of Earth and evolution of life
Transition from single cell to multicellular organisms
1. Suppose Q is an orthogonal matrix with size n n, prove that detQ is either 1 or 1.
2. Suppose A is 3 3 matrix. Aij = 0 if i > j . Show that detA is product of the elements
on the diagonal using both the denition det(A) = ijk Ai1 Aj 2
Part of Hints for Hw 3
Mar. 1. By Lei Li
1. QQT = I , so det(QQT ) = detI = 1 and then detQ detQT = (detQ)2 = 1. detQ = 1 or
Second Part:Vector Calculus
1. s(t) = 0 4z 2 + 81z 4 dz = 0 2z 1 + (81/4)z 2 dz =
and plug back to get the
1. a). Convince yourself that Poisson vector has nothing to do with the motion of the
center of the mass. Its only related to the motion about the center of mass.
b). Consider a ball is rotating about x-axis and its center is xed at the
Part of Hints for to Hw 3
Mar. 1. By Lei Li
1. b). 2 or 2 unit is rad/s
a). cos(/3) = 1/2. cos(/6) = 3/2, 0 Thus e 1 has components [1/2, 3/2, 0]T with
respect to old basis.
b). [ 6/4, 2/4, 2/2]T
c). Use cross product: [ 6/4, 2/4, 2/