DE and Linear Algebra Lecture Slides F2009
Last Modified: January 17, 2010, 14:46 MST. Today: December 26, 2024, 06:33 MST.
Chapter 1: First Order DE
Three Examples. One slide. (11.8 K, pdf, 28 Aug 2006)
Fundamental Theorem of Calculus, Method of quadrature, Decay law derivation, Background formulas. Six slides. (146.9 K, pdf, 25 Jan 2006)
Three Examples, Exercises 1.2-1,2,5,8,10 solved by Tyson Black, Jennifer Lahti, GBG, 11 slides. (292.0 K, pdf, 23 Jul 2009)
Log and exponential Background. Direction fields. Decay law derivation. Problem 1.2-2. Direction field examples. Four slides. (433.9 K, pdf, 21 Aug 2003)
Direction fields. Manuscript, 11 pages. (547.5 K, pdf, 24 Aug 2007)
Picard-Lindelof and Peano Existence theory. Manuscript, 9 pages. (125.9 K, pdf, 18 Jan 2006)
Peano and Picard Theory. Manuscript, 3 pages. (22.5 K, pdf, 17 Jan 2007)
Picard-Lindelof and Peano Existence Example, similar to 1.3-14. One slide. (40.5 K, pdf, 20 Jan 2006)
Exercises 1.4 Page 40, 4 slides. (465.0 K, pdf, 26 Aug 2003)
Separable Equations 2007. Manuscript, 9 pages. (176.0 K, pdf, 27 Aug 2007)
Separable Equations 2008. Slides. (112.0 K, pdf, 20 Jan 2008)
Recipes for linear 1st, 2nd order and 2x2 Systems of DE. Two slides. (57.8 K, pdf, 31 Dec 2003)
Exercises 1.5, 9 slides: 1.5-3,5,11,33. Linear DE method. Brine mixing. (375.0 K, pdf, 29 Jan 2006)
Linear DE part I (Integrating Factor Method). Manuscript, 8 pages. (193.7 K, pdf, 27 Aug 2007)
Linear DE part II (Variation of Parameters, Undetermined Coefficients). Manuscript, 7 pages. (97.1 K, pdf, 22 Jan 2006)
How to do a maple answer check for y'=y+2x. (0.2 K, txt, 27 Jan 2005)
Separable Equations slides, separability test, tests I and II. Manuscript, 6 pages. (38.0 K, pdf, 23 Jan 2007)
Linear first order, integrating factor method, 2 slides. (24.6 K, pdf, 23 Jan 2007)
Chapter 2: First Order Applications, Numerical DE
Verhulst logistic equation. Manuscript, 5 pages. (83.1 K, pdf, 17 Jan 2006)
Autonomous DE slides 2008 (61.9 K, pdf, 25 Jan 2008)
Phase Line and Bifurcation Diagrams. Includes Stability, Funnel, Spout, and bifurcation. Manuscript, 6 pages. (164.6 K, pdf, 20 Jan 2006)
Newton models, projectile slides 2008 (109.3 K, pdf, 29 Aug 2009)
Earth to the moon, Jules Verne slides 2008 (99.7 K, pdf, 27 Jan 2008)
Linear equation applications, brine tanks, home heating. Manuscript, 12 pages. (465.0 K, pdf, 09 Oct 2006)
Kinetics, falling bodies, projectiles. Manuscript, 16 pages. (172.1 K, pdf, 17 Jan 2006)
Science and Eng Applications, Torricelli law. Manuscript, 15 pages. (590.9 K, pdf, 10 Jan 2015)
Exercises ch2, 2.1-6,16,38, 2.2-4,10, 2.3-9,27+Escape velocity, 8 slides. (357.6 K, pdf, 29 Jan 2006)
Numerical Methods ch2, Exercises 2.4-5,2.5-5,2.6-5 plus Rect, Trap, Simp rules, 5 slides. (219.5 K, pdf, 29 Jan 2006)
Problem notes for 2.3-10, 2.3-20, 2.3-22 2.3. (1.8 K, txt, 01 Feb 2007)
ch2 DEplot maple example 1 for exercises 2.2, 2.3. (0.2 K, txt, 04 Feb 2005)
ch2 DEplot maple example 2 for exercises 2.2, 2.3. (0.2 K, txt, 04 Feb 2005)
Slides on Numerical DE 2008 (118.9 K, pdf, 31 Jan 2008)
Slides on Rect,Trap,Simp,Euler,Heun,RK4. Numerical DE, ch 2. (37.8 K, pdf, 19 Sep 2006)
Report details on 2.4,2.5,2.6 prob 6 (48.3 K, pdf, 30 Dec 2006)
Report details on 2.4,2.5,2.6 prob 12. (50.4 K, pdf, 30 Dec 2006)
Numerical Solution of First Order D. Manuscript, 19 pages. (203.0 K, pdf, 04 Sep 2004)
Sample symbolic solution report for 2.4-3. One slide. (22.6 K, pdf, 19 Sep 2006)
Sample Report for 2.4-3, 3 slides. Slide 1 is symbolic sol. (342.9 K, pdf, 06 Feb 2005)
Numerical DE coding hints. Numerical DE, ch2. (5.1 K, txt, 30 Dec 2006)
Sample maple code for Euler, Heun, RK4. Numerical DE, ch2. (1.9 K, mws, 21 Feb 2006)
Sample maple code for exact/error reporting. Numerical DE, ch2. (2.1 K, mws, 21 Feb 2006)
Maple L3 snips worksheet. Numerical DE. ch2. (6.2 K, mws, 26 Feb 2007)
Maple L4 snips worksheet. Numerical DE, ch2. (4.3 K, mws, 29 Dec 2006)
Chapter 3: Linear Algebraic Equations, Matrices, Determinants
Linear equations, reduced echelon, three rules. All slides. (45.8 K, pdf, 22 Sep 2006)
Three rules, frame sequence, maple syntax. All slides. (35.8 K, pdf, 25 Jan 2007)
Elementary matrices, vector spaces. All slides. (35.8 K, pdf, 18 Feb 2007)
Snapshot sequence and general solution, 3x3 system. All slides. (90.0 K, pdf, 28 Sep 2006)
Linear algebraic equations, no matrices, DRAFT manuscript F2007 (295.4 K, pdf, 26 Sep 2007)
Linear algebraic equations, manuscript, no matrices (579.4 K, pdf, 22 Aug 2007)
Linear algebraic equations, no matrices, DRAFT manuscript S2007 (266.0 K, pdf, 18 Feb 2007)
The three possibilities with symbol k, slides S2007. (23.6 K, pdf, 14 Feb 2007)
The three possibilities with symbol k, Beamer slides F2007. (89.5 K, pdf, 05 Oct 2007)
Vectors and Matrices. Manuscript. (189.7 K, pdf, 27 Feb 2007)
Matrix equations. Manuscript. (116.3 K, pdf, 27 Feb 2007)
Exercises Page 149, ch3, 3.1 to 3.6, 6 slides (869.6 K, pdf, 25 Sep 2003)
Linear equation, frame sequences, general solution slides F2007 (222.4 K, pdf, 25 Oct 2007)
The three possibilities with symbol k F2007. (97.9 K, pdf, 25 Oct 2007)
Elementary matrix slides F2007 (121.6 K, pdf, 25 Oct 2007)
Vector space, subspace, independence slides F2007 (137.6 K, pdf, 26 Oct 2007)
Undetermined coefficients, cafe door, pet door, phase-amplitude, resonance slides F2007 (193.6 K, pdf, 29 Oct 2007)
Pivot theorem, column space, row space, equivalence of bases slides F2007 (149.1 K, pdf, 26 Oct 2007)
Determinants and Cramer's Rule. Manuscript. (185.8 K, pdf, 28 Feb 2008)
Chapter 4: Vector Space, Subspace, Independence, Basis
Vector space, Independence, Basis, Dimension, Rank. Manuscript. (206.4 K, pdf, 27 Feb 2007)
Pivot, Basis, Dimension, Rank, Pivot Method, Row and Column spaces, Equivalence of bases. All slides. (44.9 K, pdf, 10 Mar 2007)
Vector spaces, Independence tests. All slides. (40.0 K, pdf, 24 Oct 2006)
Exercises Page 237, ch4, 4.1 to 4.4, some 4.9, all slides (463.2 K, pdf, 25 Sep 2003)
Chapter 5: Second and Higher Order Linear DE and Applications
Basic Reference: First order constant coefficient recipe, structure of solutions, superposition, 3 slides (25.7 K, pdf, 24 Oct 2006)
Atoms and constant-coefficient DE, 5 slides (32.2 K, pdf, 27 Oct 2006)
How to solve linear nth order constant coefficient linear homogeneous DE by constructing an atom list from the characteristic equation, 2 slides (28.8 K, pdf, 21 Mar 2007)
Basic Reference: First order constant coefficient recipe + theory + variation of parameters and undetermined coefficients, manuscript, 11 pages. (134.5 K, pdf, 29 Mar 2005)
Constant coefficient recipe, ch5, manuscript, 2 pages. (57.8 K, pdf, 31 Dec 2003)
Second order constant coefficient recipe + theory, manuscript, 7 pages. (100.2 K, pdf, 29 Mar 2005)
Second order variation of parameters, manuscript, 7 pages. (83.0 K, pdf, 06 Apr 2005)
Second order undetermined coefficients manuscript, 8 pages. (94.0 K, pdf, 06 Apr 2005)
Higher order linear differential equations. Higher order recipe. Higher order undetermined coefficients. Manuscript, 9 pages. (107.8 K, pdf, 02 Nov 2005)
History of undetermined coefficients, Kummer's method, Table method (6.8 K, txt, 08 Nov 2004)
Ch5 exercises 5.1 to 5.6, 16 slides (1924.1 K, pdf, 23 Oct 2003)
Ignore the 5.5 examples which refer to Kummer's method or Cauchy's kernel. When edited out this message will vanish.
Undetermined coeff illustration, ch5.5, 3 slides (30.4 K, pdf, 07 Nov 2006)
Undetermined coefficient example, ch5.5, 3 slides (564.0 K, pdf, 29 Oct 2003)
This is a basic undetermined coffficient example. The textbook references are to an older edition.
Problem notes 5.4: 34.> (0.3 K, txt, 20 Jan 2006)
Problem notes 5.5: 48, 52, 60. (1.2 K, txt, 20 Jan 2006)
Undetermined coefficients, Fixup rules I,II,II, 4 slides (29.8 K, pdf, 06 Nov 2006)
Atoms, constant-coefficient DE, examples, 8 slides (37.0 K, pdf, 06 Nov 2006)
Unforced mechanical oscillations manuscript, 8 pages. (583.1 K, pdf, 02 Nov 2005)
Forced mechanical oscillations manuscript, 8 pages. (299.3 K, pdf, 02 Nov 2005)
Resonance manuscript, 7 pages. (104.6 K, pdf, 02 Nov 2005)
Undetermined coefficient example, Phase-amplitude conversion, Damping, Resonance, Cafe door, Pet door, 12 slides (74.5 K, pdf, 08 Nov 2006)
Chapter 6: Eigenanalysis, Diagonalization, Fourier Model
Fourier's Model slides (36.4 K, pdf, 17 Nov 2006)
Eigenanalysis, ch6, 6.1,6.2, 6 slides (1323.4 K, pdf, 06 Nov 2003)
Eigenanalysis-I manuscript, 19 pages. (202.6 K, pdf, 11 Apr 2009)
Eigenanalysis-II manuscript, 31 pages. (268.0 K, pdf, 06 May 2007)
Chapter 7: Systems of DE and Applications
Solving triangular and non-triangular systems, 4 slides (83.4 K, pdf, 07 Apr 2008)
Systems of DE Ch7, 7.1,7.2,7.3 solved problems, 4 slides (864.8 K, pdf, 13 Nov 2003)
Recipes for 1st, 2nd order and 2x2 Systems of DE (57.8 K, pdf, 31 Dec 2003)
DE systems manuscript, 69 pages. (900.2 K, pdf, 11 Apr 2007)
Chapter 10: Laplace Theory
Ch10 Laplace slides, 10.1 to 10.4, 9 pages. (1968.3 K, pdf, 13 Nov 2003)
Laplace theory manuscript, 34 pages. (289.8 K, pdf, 21 Nov 2003)
Heaviside's method manuscript, 4 pages. (84.4 K, pdf, 24 Mar 2004)