2250 lecture slides Fall 2006

DE and Linear Algebra Lecture Slides Fall 2006

1. Week 1 slides
   Three Examples, Fundamental Theorem of Calculus, Method of quadrature, Decay law derivation, Background formulae (6 pages, pdf)
   Three Examples (pdf)
   Three Examples, solved 1.2-1,2,5,8,10 by Tyson Black, Jennifer Lahti, GBG (11 pages, pdf)
   Recipes for 1st, 2nd order and 2x2 Systems of DE PDF Document (2 pages, 50kb)
   Log+exponential Background+Direction fields PDF Document (4 pages, 450k). Decay law derivation. Problem 1.2-2. Direction field examples.
   For more on direction fields, print Direction fields document (typeset, 11 pages, pdf)
2. Week 2 slides
   Picard-Lindelof and Peano Existence theory (typeset, 9 pages, pdf)
   Peano and Picard Theory (3 pages, pdf)
   Picard-Lindelof and Peano Existence Example, similar to 1.3-14 (1 page, pdf)
   1.4 Page 40 Exercise slides (4 pages, 500k)
   Separable Equations (typeset, 9 pages, PDF)
   Linear DE method, Section 1.5 slides: 1.5-3,5,11,33+Brine mixing (9 pages, pdf)
   Linear DE part I (Integrating Factor Method), (typeset, 8 pages, pdf)
   Linear DE part II (Variation of Parameters, Undetermined Coefficients), (typeset, 7 pages, pdf)
   How to do a maple answer check for y'=y+2x (TEXT 1k)
3. Week 3 slides
   Verhulst logistic equation (typeset, 5 pages, pdf)
   Linear equation applications, brine tanks, home heating (typeset, 12 pages, pdf)
   Kinetics, falling bodies, projectiles (typeset, 16 pages, pdf)
   Science and Eng Applications, Torricelli law (typeset, 15 pages, pdf)
   Phase Line and Bifurcation Diagrams (includes "Stability, Funnel, Spout, and bifurcation") (typeset, 6 pages, 161k pdf)
   ch2 sections 1,2,3 Slides: 2.1-6,16,38, 2.2-4,10, 2.3-9,27+Escape velocity (8 pages, pdf)
   ch2 Numerical Methods Slides, Exercises 2.4-5,2.5-5,2.6-5 plus Rect, Trap, Simp rules (5 pages, pdf)
   ch2 DEplot maple example 1 for exercises 2.2, 2.3 (1 page, 1k)
   ch2 DEplot maple example 2 for exercises 2.2, 2.3 (1 page, 1k)
4. Week 4 slides
   Slides on Rect,Trap,Simp,Euler,Heun,RK4
   Report details on 2.4,2.5,2.6 prob 6
   Report details on 2.4,2.5,2.6 prob 12
   Numerical Solution of First Order DE (typeset, 19 pages, 220k pdf)
   Sample symbolic solution report for 2.4-3 (pdf 1 page, 120k)
   Sample Report for 2.4-3 (pdf 3 pages, 350k. Page 1 is symbolic sol.)
   Numerical DE coding hints, TEXT Document (1 pages, 2k)
   Sample maple code for Euler, Heun, RK4 (maple worksheet)
   Sample maple code for exact/error reporting (maple worksheet)
5. Weeks 5,6 slides
   Linear equations, reduced echelon, three rules (typeset, 7 pages, pdf)
   Three rules, frame sequence, maple syntax (typeset, 7 pages, pdf, 12 Oct 2006)
   Elementary matrices, vector spaces, slides (8 pages, pdf, 12 Oct 2006)
   Snapshot sequence and general solution, 3x3 system (1 page, pdf, 28-Sep-2006)
   Linear algebra, no matrices, (typeset, 21 pages, pdf)
   vectors and matrices (typeset, 14 pages)
   Matrix equations (typeset, 12 pages)
   Ch3 Page 149+ slides, Exercises 3.1 to 3.6 (6 pages, 890k pdf)
6. Week 7 slides
   Determinants and Cramer's Rule (typeset, 11 pages, 140k pdf)
   Vector space, Independence, Basis, Dimension, Rank (typeset, 17 pages, 180k pdf)
   Lecture slides on Vector space, Independence, Basis, Dimension, Rank (typeset, 4 pages, pdf)
   Lecture slides on Vector spaces, Independence tests. Corrected 20oct06. (typeset, 4 pages, pdf)
   Ch4 Page 237+ slides, Exercises 4.1 to 4.4, some 4.9 (4 pages, 480k pdf)
7. Weeks 8,9 slides
   Basic Reference: First order constant coefficient recipe, structure of solutions, superposition(slides, 3 pages pdf)
   Atoms and constant-coefficient DE (slides, 5 pages pdf)
   Basic Reference: First order constant coefficient recipe + theory + variation of parameters and undetermined coefficients (typeset, 11 pages pdf)
   Ch5. Constant coefficient recipe (typeset, 2 pages, pdf)
   Second order constant coefficient recipe + theory (typeset, 7 pages pdf)
   Second order variation of parameters (typeset, 7 pages pdf)
   Second order undetermined coefficients (typeset, 8 pages pdf)
   Higher order linear differential equations. Higher order recipe. Higher order undetermined coefficients. (typeset, 9 pages pdf)
   History of undetermined coefficients, Kummer's method, Table method (2k text)
   Ch5. Slides for exercises 5.1 to 5.6 (16 pages, 1.9mb pdf)
   Ignore the 5.5 examples which refer to Kummer's method or Cauchy's kernel. When edited out this message will vanish.
8. Weeks 9,10 slides
   Ch5 undetermined coeff illustration (3 pages, pdf)
   Ch5 undetermined coeff example PDF Document (3 pages, 0,5mb)
   This is a basic undetermined coffficient example. The textbook references are to an older edition.
   Problem notes 5.4: 34 (1 page, text)
   Problem notes 5.5: 48, 52, 60 (1 page, text)
   Undetermined coeff, Fixup rules I,II,II (slides, 4 pages pdf)
   Atoms, constant-coefficient DE, examples (slides, 8 pages pdf)
   Unforced mechanical oscillations (typeset, 8 pages pdf)
   Forced mechanical oscillations (typeset, 8 pages pdf)
   Resonance (typeset, 7 pages pdf)
   Undetermined coefficient example, Phase-amplitude conversion, Damping, Resonance, Cafe door, Pet door (12 slides, pdf)
9. Week 11 slides
   Fourier's Model slides (5 pages, pdf)
   Ch6 Eigenanalysis slides, 6.1 and 6.2 (6 pages, 1.3mb pdf)
   Eigenanalysis-I manuscript F2006 (typeset 17 pages, 145k pdf)
10. Week 12 slides
    Slides, solving triangular and non-triangular systems (4 pages, pdf)
    Ch7 Systems of DE slides 7.1,7.2,7.3 (4 pages, 0.8mb pdf)
    Recipes for 1st, 2nd order and 2x2 Systems of DE PDF Document (2 pages, 50kb)
    DE systems manuscript F2005 (typeset 66 pages, 909k pdf)
11. Week 13 slides
    Ch10 Laplace slides, 10.1 to 10.4 (9 pages, 1.95mb pdf)
    Laplace theory manuscript (typeset, 34 pages, 300k pdf)
    Heaviside's method (typeset, 4 pages, 86k pdf)