• 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: September 24 2018 02:03:06.

# 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 (0.0 K, pdf, 31 Dec 1969)
Exercise 1.3-8 template (0.0 K, jpg, 31 Dec 1969)
Partial fraction theory (0.0 K, pdf, 31 Dec 1969)
Picard, Peano, direction fields (0.0 K, pdf, 31 Dec 1969)
Separable DE method, equilibrium solutions (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Heaviside's method partial fractions (0.0 K, pdf, 31 Dec 1969)
Manuscript: Heaviside coverup partial fraction method (0.0 K, pdf, 31 Dec 1969)
Linear integrating factor method (0.0 K, pdf, 31 Dec 1969)
Earth to the moon (0.0 K, pdf, 31 Dec 1969)
Applications of linear DE (0.0 K, pdf, 31 Dec 1969)
Partial fraction theory (0.0 K, pdf, 31 Dec 1969)
Brink tanks (70.5 K, pdf, 03 Oct 2008)
Home heating (0.0 K, pdf, 31 Dec 1969)
• 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 (0.0 K, txt, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Newton friction models (0.0 K, pdf, 31 Dec 1969)
Numerical methods manuscript (0.0 K, pdf, 31 Dec 1969)
• 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 (0.0 K, txt, 31 Dec 1969)
How to use maple at home (0.0 K, txt, 31 Dec 1969)
Maple lab 3, problem 1 solution (0.0 K, jpg, 31 Dec 1969)
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 (0.0 K, pdf, 31 Dec 1969)
Beamer slides 3 possibilities with symbol k (0.0 K, pdf, 31 Dec 1969)
Slides 3 possibilities with symbol k (0.0 K, pdf, 31 Dec 1969)
Introduction to linear algebraic equations (0.0 K, pdf, 31 Dec 1969)
Infinitely many solutions case (0.0 K, pdf, 31 Dec 1969)
No solution case (0.0 K, pdf, 31 Dec 1969)
Unique solution case (0.0 K, pdf, 31 Dec 1969)
Linear algebraic equations manuscript (0.0 K, pdf, 31 Dec 1969)
Three possibilities with symbols, rank (0.0 K, pdf, 31 Dec 1969)
• 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 (0.0 K, pdf, 31 Dec 1969)
Digital photos, Maxwell's RGB separations, visualization of matrix add (0.0 K, pdf, 31 Dec 1969)
Elementary matrix theorems (0.0 K, pdf, 31 Dec 1969)
Inverse matrix, frame sequence method (0.0 K, pdf, 31 Dec 1969)
Linear algebraic equations manuscript (0.0 K, pdf, 31 Dec 1969)
Matrix operations (0.0 K, pdf, 31 Dec 1969)
More on digital photos, checkerboard analogy (0.0 K, pdf, 31 Dec 1969)
Rank, nullity and elimination (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Geometry of linear transformations (0.0 K, pdf, 31 Dec 1969)
Linear algebraic equations manuscript (0.0 K, pdf, 31 Dec 1969)
Matrix operations (0.0 K, pdf, 31 Dec 1969)
Rank, nullity and elimination (0.0 K, pdf, 31 Dec 1969)
Vector models, vector spaces (0.0 K, pdf, 31 Dec 1969)
Vector space, subspace, independence (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Elementary matrix theorem (0.0 K, pdf, 31 Dec 1969)
Linear algebraic equations manuscript (0.0 K, pdf, 31 Dec 1969)
Orthogonality (0.0 K, pdf, 31 Dec 1969)
Lawrence Page's pagerank algorithm (0.0 K, txt, 31 Dec 1969)
Partial fraction theory (0.0 K, pdf, 31 Dec 1969)
The pivot theorem and applications (0.0 K, pdf, 31 Dec 1969)
Rank, nullity and elimination (0.0 K, pdf, 31 Dec 1969)
History of telecom companies (0.0 K, txt, 31 Dec 1969)

# Week 8, Oct 19-23

• http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearDEhigherorder/
Picard-Lindelof, superposition (0.0 K, pdf, 31 Dec 1969)
Atoms, Euler's theorem, examples (0.0 K, pdf, 31 Dec 1969)
Atoms, independence, Euler's theorem (0.0 K, pdf, 31 Dec 1969)
Base atom, atom, basis for linear DE (0.0 K, pdf, 31 Dec 1969)
First and second order linear DE (0.0 K, pdf, 31 Dec 1969)
How to solve linear DE or any order (0.0 K, pdf, 31 Dec 1969)
Atoms, Euler's theorem, examples (0.0 K, pdf, 31 Dec 1969)
Picard, linear nth order DE, superposition (0.0 K, pdf, 31 Dec 1969)
• 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. (0.0 K, pdf, 31 Dec 1969)
Laplace examples (0.0 K, pdf, 31 Dec 1969)
Intro to Laplace theory. Assumes only calculus (0.0 K, pdf, 31 Dec 1969)
Laplace rules (0.0 K, pdf, 31 Dec 1969)
Laplace table proofs (0.0 K, pdf, 31 Dec 1969)
• 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 (0.0 K, pdf, 31 Dec 1969)
Laplace resolvent method (0.0 K, pdf, 31 Dec 1969)
Piecewise functions and Laplace theory (0.0 K, pdf, 31 Dec 1969)
• http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearDEhigherorder/
Basic undetermined coefficients, draft 1 (0.0 K, pdf, 31 Dec 1969)
Basic undetermined coefficients, draft 2 (0.0 K, pdf, 31 Dec 1969)
Basic undetermined coefficients, draft 3 (0.0 K, pdf, 31 Dec 1969)
Basic undetermined coefficients, draft 4 (0.0 K, pdf, 31 Dec 1969)
Variation of parameters (0.0 K, pdf, 31 Dec 1969)
• 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 (0.0 K, pdf, 31 Dec 1969)
Sliding plates example (0.0 K, pdf, 31 Dec 1969)
Systems of DE examples and theory manuscript (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Forced damped vibrations (0.0 K, pdf, 31 Dec 1969)
Forced vibrations and resonance (0.0 K, pdf, 31 Dec 1969)
Forced undamped vibrations (0.0 K, pdf, 31 Dec 1969)
Resonance and undetermined coefficients (0.0 K, pdf, 31 Dec 1969)
Unforced vibrations 2008 (0.0 K, pdf, 31 Dec 1969)
• http://www.math.utah.edu/~gustafso/f2009/lectureslides2250/linearalgebra/
Algebraic eigenanalysis (0.0 K, pdf, 31 Dec 1969)
Lawrence Page's pagerank algorithm (0.0 K, txt, 31 Dec 1969)
History of telecom companies (0.0 K, txt, 31 Dec 1969)
What's eigenanalysis, draft 1 (0.0 K, pdf, 31 Dec 1969)
What's eigenanalysis, draft 2 (124.0 K, pdf, 14 Nov 2007)
What's eigenanalysis 2008 (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Systems and home heating (0.0 K, pdf, 31 Dec 1969)
Systems eigenanalysis, 4 methods (0.0 K, pdf, 31 Dec 1969)
Systems Cayley-Hamilton Method (0.0 K, pdf, 31 Dec 1969)
Second order systems, laplace method (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)
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 (0.0 K, pdf, 31 Dec 1969)
Laplace resolvent method (0.0 K, pdf, 31 Dec 1969)
Cable hoist example (0.0 K, pdf, 31 Dec 1969)
Sliding plates example (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Systems of DE examples and theory manuscript (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)
Triangular systems of DE (0.0 K, pdf, 31 Dec 1969)
Laplace resolvent method (0.0 K, pdf, 31 Dec 1969)
Systems eigenanalysis, 4 methods (0.0 K, pdf, 31 Dec 1969)

# 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 (0.0 K, pdf, 31 Dec 1969)
Systems of DE examples and theory manuscript (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)

# 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 (0.0 K, pdf, 31 Dec 1969)
Systems of DE examples and theory manuscript (0.0 K, pdf, 31 Dec 1969)
Introduction to Dynamical systems (0.0 K, pdf, 31 Dec 1969)
Phase Portraits for Dynamical Systems (201.6 K, pdf, 26 Apr 2009)
Stability for Dynamical Systems (0.0 K, pdf, 31 Dec 1969)
Slides: Nonlinear classification spiral, node, center, saddle (0.0 K, pdf, 31 Dec 1969)
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.
• http://www.math.utah.edu/~gustafso/f2009/
Syllabus (146.2 K, pdf, 09 Nov 2009)
How to improve your written work (25.0 K, pdf, 01 Jan 2009)
Grade sheet for record keeping (63.5 K, pdf, 09 Nov 2009)
Extra credit ch1 (53.3 K, pdf, 19 Jul 2009)
Extra credit ch2 (48.2 K, pdf, 19 Jul 2009)
Extra credit ch3 (101.3 K, pdf, 19 Jul 2009)
Extra credit ch4 (67.4 K, pdf, 19 Jul 2009)
Extra credit ch5 (95.8 K, pdf, 19 Jul 2009)
Extra credit ch6 (44.2 K, pdf, 19 Jul 2009)
Extra credit ch7 (62.4 K, pdf, 19 Jul 2009)
Extra credit ch8 (71.4 K, pdf, 19 Jul 2009)
Extra credit ch9 (60.7 K, pdf, 19 Jul 2009)
Extra credit ch10 (57.9 K, pdf, 19 Jul 2009)
Final exam study guide (7.6 K, txt, 12 Dec 2009)
Maple lab 6 FAQ (1.9 K, txt, 19 Jul 2009)
Maple lab 1 (111.9 K, pdf, 19 Jul 2009)
Maple lab 1 code (0.8 K, txt, 02 Jan 2009)
Maple lab 2 Swamp cooler (158.5 K, pdf, 09 Oct 2009)
Maple lab 2 Swamp cooler code (1.3 K, txt, 09 Oct 2009)
Maple lab 2a Freezing pipes (112.3 K, pdf, 19 Jul 2009)
Maple lab 2a Freezing pipes code (1.2 K, txt, 19 Jul 2009)
Maple lab 3 code snips (6.6 K, mws, 25 May 2007)
Maple lab 3 Numerical DE (81.9 K, pdf, 19 Jul 2009)
Maple lab 3 Numerical DE code (5.0 K, txt, 24 May 2007)
Maple lab 4 code snips (4.3 K, mws, 24 May 2007)
Maple lab 4 Numerical DE (78.2 K, pdf, 19 Jul 2009)
Maple lab 4 text (3.1 K, txt, 24 May 2007)
Maple lab 5 maple work sheet (10.8 K, mws, 25 Oct 2008)
Maple lab 5 Linear algebra (94.3 K, pdf, 19 Jul 2009)
Maple lab 5 Linear algebra text (2.1 K, txt, 03 Jan 2009)
Maple lab 6 Spring mass system worksheet (18.1 K, mws, 19 Jul 2009)
Maple lab 6 Spring mass system (22.1 K, pdf, 19 Jul 2009)
Maple lab 6 Spring mass system text (4.9 K, txt, 03 Jan 2009)
Maple lab 7 worksheet (11.0 K, mws, 19 Jul 2009)
Maple lab 7 Laplace applications (84.3 K, pdf, 19 Jul 2009)
Maple lab 7 Laplace applications text (2.5 K, txt, 03 Jan 2009)
Maple lab 8 earthquakes worksheet (16.3 K, mws, 27 Aug 2008)
Maple lab 8 earthquakes (23.7 K, pdf, 19 Jul 2009)
Maple lab 8 earthquakes text (6.8 K, txt, 27 Aug 2008)
Maple lab 9 Tacoma narrows worksheet (19.6 K, mws, 19 Jul 2009)
Maple lab 9 Tacoma narrows (22.8 K, pdf, 19 Jul 2009)
Maple lab 9 Tacoma narrows text (6.3 K, txt, 27 Aug 2008)
Numerical DE hints (5.1 K, txt, 03 Jan 2009)
Numerical DE manuscript (203.0 K, pdf, 04 Sep 2004)
Sample maple numerical DE snips (2.1 K, mws, 21 Feb 2006)
Sample problem numerical DE (1.9 K, mws, 21 Feb 2006)
How to use maple 12 (2.0 K, txt, 30 Nov 2008)
How to use maple at home (3.8 K, txt, 10 Oct 2008)
Angie Gardiner's maple intro (138.8 K, mws, 19 Jan 2009)
Sita Gakkhar's maple lab 2 example worksheet (178.4 K, mw, 02 Mar 2009)
Sita Gakkhar's maple lab 2 example (136.7 K, pdf, 02 Mar 2009)
Special problems for ch1 (47.0 K, pdf, 31 Jan 2009)