2250 lecture slides Spring 2007

DE and Linear Algebra Lecture Slides S2007

1. Week 1 slides
   Three Examples (pdf)
   Three Examples, Fundamental Theorem of Calculus, Method of quadrature, Decay law derivation, Background formulae (6 pages, 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)
   Separable Equations slides, separability test, tests I and II (6 pages, pdf)
   Linear first order slides, integrating factor method (2 pages, pdf)
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)
   Problem notes for 2.3-10, 2.3-20, 2.3-22 2.3 (1 page, 1k)
   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)
   Maple L3 snips worksheet Spring 2007 (.mws)
   Maple L4 snips worksheet Spring 2007 (.mws)
5. Weeks 5,6 slides
   Linear equations, reduced echelon, three rules ( 46K pdf)
   Three rules, frame sequence, maple syntax ( 36K pdf)
   Elementary matrices, vector spaces, slides ( 36K pdf)
   Snapshot sequence and general solution, 3x3 system ( 90K pdf)
   Linear algebraic equations, no matrices (579K pdf)
   Linear algebraic equations, no matrices, DRAFT 27Feb2007 (266K pdf)
   Slides on three possibilities with symbol k, 14Feb2007 ( 24K pdf)
   vectors and matrices (190K pdf)
   Matrix equations (116K pdf)
   Ch3 Page 149+ slides, Exercises 3.1 to 3.6 (6 pages) (870K pdf)
6. Week 7 slides
   Determinants and Cramer's Rule (186K pdf)
   Vector space, Independence, Basis, Dimension, Rank (206K pdf)
   Lecture slides on Vector space, Independence, Basis, Dimension, Rank ( 45K pdf)
   Lecture slides on Vector spaces, Independence tests. Corrected 20oct06. Ver: 27Feb2007 ( 40K pdf)
   Ch4 Page 237+ slides, Exercises 4.1 to 4.4, some 4.9 (463K 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)
   How to solve linear nth order constant coefficient linear homogeneous DE by constructing an atom list from the characteristic equation. (slides, 2 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 ( 36K pdf)
   Ch6 Eigenanalysis slides, 6.1 and 6.2 (6 pages, 1.3M pdf)
   Eigenanalysis-I manuscript S2007 (19 pages, 203K pdf)
   Eigenanalysis-II manuscript S2007 (31 pages, 268K 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 solved problems (4 pages, 0.8mb pdf)
    Recipes for 1st, 2nd order and 2x2 Systems of DE PDF Document (2 pages, 50kb)
    DE systems manuscript S2007 (typeset 69 pages, 970k 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)