Updated: Wednesday March 31: 14:33PM, 2010
Today: Tuesday November 05: 05:15AM, 2024
DE and Linear Algebra Manuscripts S2010
Chapter 1: First Order DE
- Exponential Modeling manuscript
PDF Document (34 pages, 350k)
- Direction fields manuscript
Direction fields (typeset, 11 pages, pdf)
- Computing and Existence manuscript
Picard-Lindelof and Peano Existence theory (9 pages, pdf)
- Separable Equations manuscript
Separable Equations (typeset, 9 pages, PDF)
- 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
- Verhulst Logistic Equation manuscript
Verhulst logistic equation (typeset, 5 pages, pdf)
- Kinetics manuscript
Kinetics, falling bodies, projectiles (typeset, 16 pages, pdf)
- Phase line and bifurcation manuscript
PDF Document (6 pages, 161k)
- Science and Engineering Applications manuscript
Science and Eng Applications, Torricelli law (typeset, 15 pages, pdf)
- Numerical DE manuscript
PDF Document (19 pages, 220k)
- Numerical DE maple coding hints
TEXT Document (1 pages, 2k)
Chapter 3: Linear Algebraic Equations, Matrices, Determinants
- Linear Algebraic Equations manuscript
Linear algebra, no matrices, DRAFT 4Feb2009 (typeset, 45 pages, pdf)
- Vector and matrix manuscript
PDF Document (11 pages, 113k)
- Matrix Equations manuscript
PDF Document (6 pages, 92k)
- Determinants and Cramer's Rule manuscript
PDF Document (11 pages, 140k)
Chapter 4: Vector Space, Subspace, Independence, Basis
- Independence, Rank, Dimension manuscript
PDF Document (17 pages, 180k)
Chapter 5: Second and Higher Order Linear DE
- 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)
- 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)
- 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
- Eigenanalysis manuscript S2010
History, algebraic theory, Cayley-Hamilton, advanced topics.
(pdf)
- Eigenanalysis and Fourier's Method manuscript. Updated S2006.
Eigenanalysis-I manuscript F2007
(19 pages, pdf)
Eigenanalysis-II manuscript F2007
(31 pages, pdf)
- Differential systems examples and theory, manuscript. Updated F2005.
DE systems manuscript F2005 (PDF 66 pages, 909k)
Chapter 7: Systems of Differential Equations and Applications
- under construction 2010
Chapter 8: Matrix Exponential Methods
- under construction 2010
Chapter 9: Nonlinear Dynamical Systems
- under construction 2010
Chapter 10: Laplace Theory, Partial Fractions
- Laplace transform manuscript
PDF Document (34 pages, 300k)
- Heaviside coverup method manuscript
PDF Document (4 pages, 86k)