F2009 Reading Assignments 2250 with Links

All Reading is approximately one week ahead of the lectures. Please read the text in the week assigned! Then read it again after the lectures on the topics. Updated: December 14 2009 09:18:02. Today: April 05 2013 08:42:46.

Chapter 1: First Order DE

Week 1, Aug 24-28

Read sections 1.1,1.2,1.3,1.4. Method of Quadrature, Direction fields, Picard theory, Separable DE

http://www.math.utah.edu/~gustafso/f2009/
Syllabus F2009 (146.2 K, pdf, 09 Nov 2009)
How to improve written work (25.0 K, pdf, 01 Jan 2009)
Gradesheet F2009 (63.5 K, pdf, 09 Nov 2009)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/firstorderDE/
Method of quadrature (247.9 K, pdf, 11 Dec 2011)
Exercise 1.3-8 template (102.2 K, jpg, 09 Dec 2012)
Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Picard, Peano, direction fields (293.7 K, pdf, 03 Mar 2012)
Separable DE method, equilibrium solutions (148.9 K, pdf, 03 Mar 2012)

Week 2, Aug 31, Sep 1-4

Read sections 1.5,2.1,2.2,2.3. linear DE, populations, stability, Verhulst DE, phase analysis, Newton kinematic models.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/firstorderDE/
Autonomous DE (102.3 K, pdf, 03 Mar 2012)
Heaviside's method partial fractions (186.8 K, pdf, 20 Oct 2009)
Manuscript: Heaviside coverup partial fraction method (152.1 K, pdf, 07 Aug 2009)
Linear integrating factor method (129.8 K, pdf, 03 Mar 2012)
Earth to the moon (127.0 K, pdf, 10 Dec 2012)
Applications of linear DE (374.2 K, pdf, 28 Jul 2009)
Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Brink tanks (70.5 K, pdf, 03 Oct 2008)
Home heating (109.8 K, pdf, 04 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Maple lab 1. Quadratics, plots, derivatives, Jacobian (0.0 K, pdf, 31 Dec 1969)
Maple lab 2. Swamp cooler [option 1] (0.0 K, pdf, 31 Dec 1969)
Maple lab 2. Freezing pipes [option 2] (0.0 K, pdf, 31 Dec 1969)
Using maple at home (7.3 K, txt, 06 Dec 2012)

Week 3, Sep 8-11

Read sections 2.3,2.4,2.5,2.6. Earth to the moon, numerical methods of Euler, Heun, Runge-Kutta, review of rectangular, trapezoidal and Simpson rules in calculus.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/firstorderDE/
Earth to the moon (127.0 K, pdf, 10 Dec 2012)
Newton friction models (137.1 K, pdf, 03 Mar 2012)
Numerical methods manuscript (149.9 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Maple lab 3. Numerical DE (0.0 K, pdf, 31 Dec 1969)
Maple lab 4. Numerical DE (0.0 K, pdf, 31 Dec 1969)
Maple code for maple labs 3 and 4 (5.1 K, txt, 10 Dec 2011)
How to use maple at home (7.3 K, txt, 06 Dec 2012)
Maple lab 3, problem 1 solution (184.6 K, jpg, 08 Feb 2008)
F2008 notes on numerical DE report for Ch2 Ex 10 (0.0 K, pdf, 31 Dec 1969)
F2008 notes on numerical DE report for Ch2 Ex 12 (0.0 K, pdf, 31 Dec 1969)
F2008 notes on numerical DE report for Ch2 Ex 4 (0.0 K, pdf, 31 Dec 1969)
F2008 notes on numerical DE report for Ch2 Ex 6 (0.0 K, pdf, 31 Dec 1969)

Week 4, Sep 14-18

Read sections 3.1,3.2,3.3. Intro linear algebra. Read the online notes for linear algebraic equations.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Elementary matrix theorems (161.5 K, pdf, 03 Mar 2012)
Beamer slides 3 possibilities with symbol k (60.0 K, pdf, 31 Jan 2010)
Slides 3 possibilities with symbol k (98.8 K, pdf, 03 Mar 2012)
Introduction to linear algebraic equations (237.3 K, pdf, 15 Dec 2012)
Infinitely many solutions case (131.1 K, pdf, 03 Mar 2012)
No solution case (79.7 K, pdf, 03 Mar 2012)
Unique solution case (110.1 K, pdf, 14 Dec 2012)
Linear algebraic equations manuscript (460.2 K, pdf, 10 Feb 2012)
Three possibilities with symbols, rank (129.0 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Maple lab 5. Linear algebra (0.0 K, pdf, 31 Dec 1969)

Week 5, Sep 21-25

Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (4.3 K, txt, 05 Oct 2008)
Determinants 2008 (227.1 K, pdf, 03 Mar 2012)
Digital photos, Maxwell's RGB separations, visualization of matrix add (170.2 K, pdf, 03 Mar 2012)
Elementary matrix theorems (161.5 K, pdf, 03 Mar 2012)
Inverse matrix, frame sequence method (97.9 K, pdf, 03 Mar 2012)
Linear algebraic equations manuscript (460.2 K, pdf, 10 Feb 2012)
Matrix operations (156.7 K, pdf, 03 Mar 2012)
More on digital photos, checkerboard analogy (141.9 K, pdf, 03 Mar 2012)
Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)

Week 6, Sep 28-30, Oct 1-2

Read sections 4.1,4.2,4.3. Vector space, subspace, independence

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Elementary matrix theorems (161.5 K, pdf, 03 Mar 2012)
Geometry of linear transformations (98.6 K, pdf, 04 Mar 2012)
Linear algebraic equations manuscript (460.2 K, pdf, 10 Feb 2012)
Matrix operations (156.7 K, pdf, 03 Mar 2012)
Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)
Vector models, vector spaces (144.1 K, pdf, 03 Mar 2012)
Vector space, subspace, independence (185.0 K, pdf, 21 Dec 2012)

Week 7, Oct 5-9

Read sections 4.4,4.5,4.6,4.7 Bases, dimension, row and column space, pivot theorem, orthogonality, abstract vectors spaces, function spaces

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
Elementary matrix theorem (161.5 K, pdf, 03 Mar 2012)
Linear algebraic equations manuscript (460.2 K, pdf, 10 Feb 2012)
Orthogonality (124.8 K, pdf, 03 Mar 2012)
Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
The pivot theorem and applications (189.2 K, pdf, 03 Mar 2012)
Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)
History of telecom companies (1.9 K, txt, 04 Apr 2013)

Week 8, Oct 19-23

Read sections 5.1,5.2,5.3,5.4. Linear constant DE, superposition, atoms, vibrations, steady-states, observables

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearDEhigherorder/
Picard-Lindelof, superposition (67.9 K, pdf, 02 Nov 2007)
Atoms, Euler's theorem, examples (117.2 K, pdf, 02 Nov 2007)
Atoms, independence, Euler's theorem (115.5 K, pdf, 02 Nov 2007)
Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
First and second order linear DE (72.1 K, pdf, 28 Oct 2007)
How to solve linear DE or any order (168.4 K, pdf, 26 Feb 2013)
Atoms, Euler's theorem, examples (130.5 K, pdf, 26 Feb 2013)
Picard, linear nth order DE, superposition (181.5 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
FAQ for maple lab 6, F2009 (0.0 K, txt, 31 Dec 1969)
Maple lab 6. Spring mass systems. (0.0 K, pdf, 31 Dec 1969)

Week 9, Oct 26-30

Read sections 10,1,10.2,10.3,10.4. Laplace intro, history, Laplace tables, Laplace's method, Laplace rules.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/Laplace/
Laplace theory 2008 (0.0 K, pdf, 31 Dec 1969)
Laplace and Newton calculus. Photos of Newton and Laplace. (200.2 K, pdf, 04 Mar 2012)
Laplace examples (149.1 K, pdf, 04 Mar 2012)
Intro to Laplace theory. Assumes only calculus (163.0 K, pdf, 19 Mar 2012)
Laplace rules (160.3 K, pdf, 04 Mar 2012)
Laplace table proofs (169.6 K, pdf, 04 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Maple Lab 7. Laplace applications (0.0 K, pdf, 31 Dec 1969)

Week 10, Nov 2-6

Read sections 10.5,EPbvp7.6,5.5 Periodic inputs, square wave, ramp, piecewise methods, Heaviside and Dirac inputs, engineering functions. Variation constants, undetermined coefficients.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/Laplace/
Laplace theory 2008 (0.0 K, pdf, 31 Dec 1969)
Laplace second order systems (288.1 K, pdf, 04 Mar 2012)
Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Piecewise functions and Laplace theory (108.5 K, pdf, 03 Mar 2013)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearDEhigherorder/
Basic undetermined coefficients, draft 1 (100.5 K, pdf, 10 Nov 2008)
Basic undetermined coefficients, draft 2 (110.5 K, pdf, 10 Nov 2008)
Basic undetermined coefficients, draft 3 (113.0 K, pdf, 10 Nov 2008)
Basic undetermined coefficients, draft 4 (104.9 K, pdf, 07 Nov 2009)
Variation of parameters (164.5 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Laplace theory problem notes F2008 (0.0 K, txt, 31 Dec 1969)
Final exam study guide (0.0 K, txt, 31 Dec 1969)
Cable hoist example (73.2 K, pdf, 21 Aug 2008)
Sliding plates example (105.8 K, pdf, 21 Aug 2008)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)

Week 11, Nov 9-13

Read 5.6,EPbvp3.7,6.1,6.2. Forced oscillations, beats, resonance, mechanical systems, electric circuits. Eigenanalysis, systems of DE, Fourier's model, diagonalization.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearDEhigherorder/
Electrical circuits (124.8 K, pdf, 04 Mar 2012)
Forced damped vibrations (280.7 K, pdf, 04 Mar 2012)
Forced vibrations and resonance (240.3 K, pdf, 04 Mar 2012)
Forced undamped vibrations (214.2 K, pdf, 03 Mar 2012)
Resonance and undetermined coefficients (199.4 K, pdf, 03 Mar 2012)
Unforced vibrations 2008 (667.9 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Algebraic eigenanalysis (187.6 K, pdf, 04 Mar 2012)
Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
History of telecom companies (1.9 K, txt, 04 Apr 2013)
What's eigenanalysis, draft 1 (152.2 K, pdf, 01 Apr 2008)
What's eigenanalysis, draft 2 (124.0 K, pdf, 14 Nov 2007)
What's eigenanalysis 2008 (174.2 K, pdf, 04 Mar 2012)

Week 12, Nov 16-20

Read sections 7.1,7.2,7.3,7.4. First order systems, eigenanalysis method, Putzer's algorithm, resolvent method, Cayley-Hamilton-Ziebur method. Second order systems, railway cars, earthquakes, sliding plates, oscillation control of an elevator.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/systems/
Systems and brine tanks (0.0 K, pdf, 31 Dec 1969)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
Systems and home heating (109.8 K, pdf, 04 Mar 2012)
Systems eigenanalysis, 4 methods (145.6 K, pdf, 04 Mar 2012)
Systems Cayley-Hamilton Method (152.9 K, pdf, 04 Mar 2012)
Second order systems, laplace method (288.1 K, pdf, 04 Mar 2012)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Final exam study guide (0.0 K, txt, 31 Dec 1969)
Maple Lab 8. Optional. Earthquakes (0.0 K, pdf, 31 Dec 1969)
Maple Lab 9. Optional. Tacoma narrows (0.0 K, pdf, 31 Dec 1969)
Triangular systems of DE (113.4 K, pdf, 04 Mar 2012)
Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Cable hoist example (73.2 K, pdf, 21 Aug 2008)
Sliding plates example (105.8 K, pdf, 21 Aug 2008)

Week 13, Nov 23,24,25

Read sections 7.5 /w Laplace, 8.1, 8.2. Jordan form, Putzer's formulas, generalized eigenanalysis, Cayley-Hamilton theorem, matrix exponential, spectral methods, variation of parameters for systems.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/systems/
Dynamical systems (696.4 K, pdf, 03 Nov 2008)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Final exam study guide (0.0 K, txt, 31 Dec 1969)
Triangular systems of DE (113.4 K, pdf, 04 Mar 2012)
Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Systems eigenanalysis, 4 methods (145.6 K, pdf, 04 Mar 2012)

Week 14, Nov 30, Dec 1-4

Read sections 9.1,9.2,9.3. Stability, phase plane, linear systems, almost linear systems, predator-prey models.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/systems/
Dynamical systems manuscript (696.4 K, pdf, 03 Nov 2008)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Final exam study guide (0.0 K, txt, 31 Dec 1969)

Week 15, Dec 7-11

Read sections 9.3,9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs.

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/systems/
Dynamical systems manuscript (696.4 K, pdf, 03 Nov 2008)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
Introduction to Dynamical systems (158.0 K, pdf, 04 Mar 2012)
Phase Portraits for Dynamical Systems (201.6 K, pdf, 26 Apr 2009)
Stability for Dynamical Systems (170.8 K, pdf, 04 Mar 2012)
Slides: Nonlinear classification spiral, node, center, saddle (75.3 K, pdf, 12 Dec 2009)
Slides: Matrix Exponential, Putzer Formula, Variation Parameters (0.0 K, pdf, 31 Dec 1969)

http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/references/
Final exam study guide (0.0 K, txt, 31 Dec 1969)

Main References F2009

This set includes the syllabus, extra credit problems, maple labs, maple tutorials and maple examples.