DE and Linear Algebra Manuscripts F2009

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 12Feb2007(typeset, 38 pages, pdf)
   Linear algebra, no matrices, DRAFT 8Feb2008 (typeset, 44 pages, pdf)
   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 and Fourier's Method manuscript. Updated S2006.
   Eigenanalysis-I manuscript F2007 (19 pages, pdf)
   Eigenanalysis-II manuscript F2007 (31 pages, pdf)
2. 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 July 2009

Chapter 8: Matrix Exponential Methods

1. under construction July 2009

Chapter 9: Nonlinear Dynamical Systems

1. under construction July 2009

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)