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