MAT2705 23S [Jantzen] handout log

Occasionally summary "handouts" (now online only) will attempt clarification of some point to aid in your learning. A log of these will be kept here, with links to .pdf scanned copies of handwritten handouts for your convenience. Not all of these will be mentioned in the homework log.

course bureaucracy

algebra, calculus, special functions, first order deq's, etc

calculus: basic functions [algebra summary] [print combo]
[more rules of algebra NOT!]
initial data: what's the deal?
piecewise first order DE
slope fields exercise
characteristic constants for exponential behavior [explicit plot example]
first order linear DE recipe
how to understand the DE machine (example of switching variables)
antiderivatives as definite integral functions, more explanation of error function
on line only: word problem to math problem (DE) to solution [Maple solution of all such problems]:
bounded population; cooling problem
[hw: deriving a deq from rate information (retirement)]
on line only: mixture problems [solving the mixture DE]
solving the logistic deq
[separable differential equations that don't involve the independent variable explicitly]
air resistance (another example)

linear algebra

Why LinAlg with DE? [only one plot from many here: DEPlot directionfield phaseplot template]
reduced row echelon form matrix reduction algorithm
solving systems of linear equations (1)
chem lin algebra: balancing reactions [maple][extras]
on line only: what does "homogeneous" mean?
matrix multiplication
on line only:determinant and area etc
solving homogeneous linear systems and linear dependence (2)
nonstandard coordinates in R^2; nonstandard coordinates in R^3 [both]
example grid exercise; HW grid exercise
solving linear systems revisited (3)
linear combinations forwards and backwards [maple]
free and leading variables and columns
linear vocabulary [summary]
on-line only: more linear vocabulary
on-line only: the 3d vector space of quadratic expressions in a variable
[maple 3d plot visualizing new basis vectors]

2nd order linear differential equations

DE pictures, the sinusoidal example
visualizing the initial value problem [cute but not necessary]
on line only: power series and differential equations
complex arithmetic and exponentials [maple commands]
sinusoidal functions: amplitude and phase shift [getting the phase shift right]
remember the first day: first day things to remember: checking a DE soln, angles around the circle [.mw]
exponentially modulated sinusoidal functions and complex exponentials
[example,.mw, sinusoidquadrantex.mw, sinusoidquadrantex.pdf, sinusoidaldecay.pdf, sinusoidaldecay.mw]
linear homogeneous 2nd order DEQ with constant positive coefficients (damped harmonic oscillator)
[resonancesidexside.pdf]
damped harmonic oscillator systems in nature
optional: RLC circuits [maple plots]
driven constant coeff linear DEs
damped harmonic oscillator driven by sinusoidal driving function [maple plots] [specific case]
[continued] beating and resonance

systems of linear differential equations

visualizing eigenvectors with a directionfield [again: Why LinAlg with DE?; DEPlot directionfield phaseplot template]
Why LinAlg with DE revisited [linear homogeneous constant coefficient first order systems of DEs]
diagonalization of a matrix by an eigenvector basis
geometry of diagonalization;
1st order linear homogeneous DE systems: 2D case, real eigenvalues
1st order linear homogeneous DE systems: 2D case, complex eigenvalues [Maple phaseplot]
[purely imaginary eigenvalues][phaseplot]
transition from a complex to a real basis of a solution space
eigenvalue decoupling so far
extending eigenvector decoupling [examples handout, Maple]
2nd order linear nonhomogeneous DE system [method of undetermined coefficients for systems]
1st order linear nonhomogeneous DE system [method of undetermined coefficients for systems]
reduction of order [optional aside on phase spaces and reduction of order]
reduction of order: worked example exercise [soln]
3 spring 2 mass example system
two floor earthquake problem [.mw]

Unused Extras:
2 spring 2 mass system with driving function, resonance exploration
[= 2nd order linear nonhomogeneous DE system][spring interpretation]
2 spring 2 mass system with gravity exploration [maple, solution]
1st and (simple) 2nd order linear DE systems compared [with reduction of order]
[3 spring 2 mass system]
3 tank solutions [compartmental analysis: general case description] [maple]
2 spring system (no damping, no driving function) [general case description]
3 spring 2 mass system [general case description]
1st order linear nonhomogeneous DE system

summary pages

ignorable extras

first day things to remember: checking a DE soln, angles around the circle [.mw]