MAT2705 09F [Jantzen] handout log

Occasionally handouts 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. Their quality as prints from .pdf may not be optimal. A red asterisk * will mark the last handout given out in class as the semester progresses.

You are responsible for all asking bob for all paper handouts you missed receiving due to class absences, or you must print these lower quality scans to substitute them. [Fortunately scanning quality is improving!]

course bureaucracy

1. student schedule sheet sections 06 (10:30); 02 (11:30)
2. Course information sheet.

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

• calculus: basic functions [algebra summary]  [print combo] [more rules of algebra NOT! plus checking soln of eqn(s)]
  old version: algebra and basic calculus foundations [separable DE remark will come later]
• characteristic constants for exponential behavior
• on line only: first order linear DE recipe
• 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 logistic deq
  [separable differential equations that don't involve the independent variable explicitly]
• air resistance (another example)

linear algebra

• Why LinAlg with DE?
• reduced row echelon form  matrix reduction algorithm
• solving systems of linear equations (1)
• on line only: chemical reaction problem
• on line only: what does "homogeneous" mean?
• 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]
• solving linear systems revisited (3)
• linear combinations forwards and backwards [maple]
• 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
• exponentially modulated sinusoidal functions and complex exponentials
• linear homogeneous 2nd order DEQ with constant positive coefficients (damped harmonic oscillator)
• 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

• Why LinAlg with DE revisited [linear homogeneous constant coefficient first order systems of DEs]
• 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
• 1st order linear nonhomogeneous DE system [method of undetermined coefficients for systems]
•  reduction of order [optional aside on phase spaces and reduction of order]
• extending eigenvector decoupling
• 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