Date: 20 Oct 2014 08:50:51 -0400
Date: Mon, 20 Oct 2014 08:50:51 -0400
Subject: Partial list of topics for Exam-C, Wednesday, 22Oct2014
To: (DiffyQ, both classes)
Dear DiffyQ Enthusiasts
Here is a partial list of topics for Exam-C, Wednesday,
22Oct2014. The exam is cumulative, with older material as
well as newer material.
==================
Previous material:
==================
SoV, FOLDE, Exact DEs and "exactifying factor", CCLDE,
CCLDE with polynomial or exponential target; Undetermined
coeffs. IVP with any of these.
Discriminant of a quadratic polynomial.
Arithmetic of complex numbers, complex-conjugation, Re(), Im().
Formal defn of complex exp(), cos(), sin() and evaluation thereof.
Identities between exp(), cos(), sin().
Rewriting a linear-combination of complex-exponentials as a
linear-combination of cosines and sines.
Falling things, drag.
Compartmental analysis, cascading tanks, saline water example.
================
Newish material:
================
Substitutions, section 2.6: Homogeneous-fnc target.
Fnc-of-linear-combination target. Bernoulli eqn.
Writing a sum of cosines/sines with same-freq as a single cosine/sine.
Formal statement of the Fund. Thm of Algebra.
Multiplying & adding matrices. Determinant of 2x2 matrix.
Formal defn. of what a /linear map/ is, between vector spaces.
Formal defn. of a set of vectors being linearly-independent.
Theorems that imply a list of /functions/ is
linearly-independent or linearly-dependent.
Formal statement of Cramer's theorem [Cramer's Rule].
Formal stmt. of our Wronskian Linearly-Independence Thm.
Computation of the Wronskian-matrix of a list of fncs.
VoP [Variation of Parameters]. VoP with variable-coeff-fncs.
Equidimensional DEs.
Roo algorithm [Reduction of order].
RLC circuits. Harmonic DEs, i.e, Mass-spring.
================
Material is from our text, my posted notes, and class lectures.
Text material includes sections
1,1,1.2
2.1-2.6
3.1,3.2,3.4,3.5
4.1-4.7
Cheers, -PJLFK