Updated: Wednesday March 31: 14:33PM, 2010   Today: Wednesday October 18: 06:50AM, 2017

DE and Linear Algebra Manuscripts S2010

Chapter 1: First Order DE

  1. Exponential Modeling manuscript
    PDF Document (34 pages, 350k)
  2. Direction fields manuscript
    Direction fields (typeset, 11 pages, pdf)
  3. Computing and Existence manuscript
    Picard-Lindelof and Peano Existence theory (9 pages, pdf)
  4. Separable Equations manuscript
    Separable Equations (typeset, 9 pages, PDF)
  5. Linear First Order Differential Equations manuscripts
    Linear DE part I (Integrating Factor Method), (typeset, 8 pages, pdf)
    Linear DE part II (Variation of Parameters, Undetermined Coefficients), (typeset, 7 pages, pdf)

Chapter 2: First Order Applications and Numerical DE

  1. Verhulst Logistic Equation manuscript
    Verhulst logistic equation (typeset, 5 pages, pdf)
  2. Kinetics manuscript
    Kinetics, falling bodies, projectiles (typeset, 16 pages, pdf)
  3. Phase line and bifurcation manuscript
    PDF Document (6 pages, 161k)
  4. Science and Engineering Applications manuscript
    Science and Eng Applications, Torricelli law (typeset, 15 pages, pdf)
  5. Numerical DE manuscript
    PDF Document (19 pages, 220k)
  6. Numerical DE maple coding hints
    TEXT Document (1 pages, 2k)

Chapter 3: Linear Algebraic Equations, Matrices, Determinants

  1. Linear Algebraic Equations manuscript
    Linear algebra, no matrices, DRAFT 4Feb2009 (typeset, 45 pages, pdf)
  2. Vector and matrix manuscript
    PDF Document (11 pages, 113k)
  3. Matrix Equations manuscript
    PDF Document (6 pages, 92k)
  4. Determinants and Cramer's Rule manuscript
    PDF Document (11 pages, 140k)

Chapter 4: Vector Space, Subspace, Independence, Basis

  1. Independence, Rank, Dimension manuscript
    PDF Document (17 pages, 180k)

Chapter 5: Second and Higher Order Linear DE

  1. First and Second order DE manuscripts
    First order constant coefficient recipe + theory + variation of parameters and undetermined coefficients (PDF 11 pages)
    Second order constant coefficient recipe + theory (PDF 7 pages)
    Second order variation of parameters (PDF 7 pages)
    Second order undetermined coefficients (PDF 8 pages)
  2. Higher order equations manuscript
    Document on Higher order linear differential equations. Higher order recipe. Higher order undetermined coefficients. (9 pages pdf)
    History of undetermined coefficients, Kummer's method, Table method (2k text)
  3. Mechanical oscillations and Resonance manuscript
    Document on unforced mechanical oscillations (8 pages pdf)
    Document on forced mechanical oscillations (8 pages pdf)
    Document on resonance (7 pages pdf)

Chapter 6: Eigenanalysis, Diagonalization, Fourier Model

  1. Eigenanalysis manuscript S2010
    History, algebraic theory, Cayley-Hamilton, advanced topics. (pdf)
  2. Eigenanalysis and Fourier's Method manuscript. Updated S2006.
    Eigenanalysis-I manuscript F2007 (19 pages, pdf)
    Eigenanalysis-II manuscript F2007 (31 pages, pdf)
  3. Differential systems examples and theory, manuscript. Updated F2005.
    DE systems manuscript F2005 (PDF 66 pages, 909k)

Chapter 7: Systems of Differential Equations and Applications

  1. under construction 2010

Chapter 8: Matrix Exponential Methods

  1. under construction 2010

Chapter 9: Nonlinear Dynamical Systems

  1. under construction 2010

Chapter 10: Laplace Theory, Partial Fractions

  1. Laplace transform manuscript
    PDF Document (34 pages, 300k)
  2. Heaviside coverup method manuscript
    PDF Document (4 pages, 86k)