• 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: April 26 2009 21:36:20. Today: December 14 2018 02:00:40.

# Week 1, Jan 12-16

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/s2009/
Syllabus S2009 (133.6 K, pdf, 20 Jan 2009)
How to improve written work (25.0 K, pdf, 01 Jan 2009)
Gradesheet S2009 (46.6 K, pdf, 20 Jan 2009)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/firstorderDE/
Method of quadrature (125.8 K, pdf, 26 Aug 2008)
Exercise 1.3-8 template (102.2 K, jpg, 29 Aug 2008)
Partial fraction theory (129.6 K, pdf, 31 Jan 2008)
Picard, Peano, direction fields (247.3 K, pdf, 26 Jul 2009)
Separable DE method, equilibrium solutions (112.0 K, pdf, 20 Jan 2008)

# Week 2, Jan 19-23

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/s2009/lectureslides2250/firstorderDE/
Autonomous DE (61.9 K, pdf, 25 Jan 2008)
Heaviside's method partial fractions (155.7 K, pdf, 31 Jan 2008)
Linear integrating factor method (99.4 K, pdf, 20 Jan 2008)
Earth to the moon (99.7 K, pdf, 27 Jan 2008)
Applications of linear DE (374.2 K, pdf, 28 Jul 2009)
Partial fraction theory (129.6 K, pdf, 31 Jan 2008)
Brink tanks (70.5 K, pdf, 03 Oct 2008)
Home heating (81.5 K, pdf, 03 Oct 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Maple lab 1. Quadratics, plots, derivatives, Jacobian (113.5 K, pdf, 03 Jan 2009)
Maple lab 2. Swamp cooler [option 1] (158.7 K, pdf, 03 Jan 2009)
Maple lab 2. Freezing pipes [option 2] (86.9 K, pdf, 05 Mar 2009)
Using maple at home (3.8 K, txt, 10 Oct 2008)

# Week 3, Jan 26-30

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/s2009/lectureslides2250/firstorderDE/
Earth to the moon (99.7 K, pdf, 27 Jan 2008)
Newton friction models (117.2 K, pdf, 25 Jan 2008)
Numerical methods manuscript (118.3 K, pdf, 29 Sep 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Maple lab 3. Numerical DE (81.8 K, pdf, 03 Jan 2009)
Maple lab 4. Numerical DE (78.5 K, pdf, 03 Jan 2009)
Maple code for maple labs 3 and 4 (5.1 K, txt, 03 Jan 2009)
How to use maple at home (3.8 K, txt, 10 Oct 2008)
Maple lab 3, problem 1 solution (184.6 K, jpg, 08 Feb 2008)
F2008 notes on numerical DE report for Ch2 Ex 10 (34.8 K, pdf, 27 Aug 2008)
F2008 notes on numerical DE report for Ch2 Ex 12 (51.5 K, pdf, 27 Aug 2008)
F2008 notes on numerical DE report for Ch2 Ex 4 (34.4 K, pdf, 27 Aug 2008)
F2008 notes on numerical DE report for Ch2 Ex 6 (47.3 K, pdf, 27 Aug 2008)

# Week 4, Feb 2-6

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/s2009/lectureslides2250/linearalgebra/
Elementary matrix theorems (122.6 K, pdf, 09 Mar 2009)
Beamer slides 3 possibilities with symbol k (89.5 K, pdf, 10 Sep 2008)
Slides 3 possibilities with symbol k (97.9 K, pdf, 10 Sep 2008)
Introduction to linear algebraic equations (163.1 K, pdf, 17 Feb 2008)
Infinitely many solutions case (101.7 K, pdf, 09 Feb 2008)
No solution case (54.1 K, pdf, 07 Feb 2008)
Unique solution case (94.0 K, pdf, 07 Feb 2008)
Linear algebraic equations manuscript (292.7 K, pdf, 08 Mar 2009)
Three possibilities with symbols, rank (108.2 K, pdf, 11 Feb 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Maple lab 5. Linear algebra (94.2 K, pdf, 03 Jan 2009)

# Week 5, Feb 9-13

Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (4.4 K, txt, 05 Oct 2008)
Determinants 2008 (176.2 K, pdf, 07 Oct 2008)
Digital photos, Maxwell's RGB separations, visualization of matrix add (159.2 K, pdf, 29 Sep 2008)
Elementary matrix theorems (122.6 K, pdf, 09 Mar 2009)
Inverse matrix, frame sequence method (79.3 K, pdf, 20 Feb 2008)
Linear algebraic equations manuscript (292.7 K, pdf, 08 Mar 2009)
Matrix operations (130.8 K, pdf, 29 Sep 2008)
More on digital photos, checkerboard analogy (117.7 K, pdf, 30 Sep 2008)
Rank, nullity and elimination (111.0 K, pdf, 07 Mar 2009)

# Week 6, Feb 16-20

Read sections 4.1,4.2,4.3. Vector space, subspace, independence
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/linearalgebra/
Elementary matrix theorems (122.6 K, pdf, 09 Mar 2009)
Geometry of linear transformations (43.5 K, pdf, 08 Oct 2008)
Linear algebraic equations manuscript (292.7 K, pdf, 08 Mar 2009)
Matrix operations (130.8 K, pdf, 29 Sep 2008)
Rank, nullity and elimination (111.0 K, pdf, 07 Mar 2009)
Vector models, vector spaces (116.9 K, pdf, 17 Feb 2009)
Vector space, subspace, independence (139.3 K, pdf, 29 Sep 2008)

# Week 7, Feb 23-27

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/s2009/lectureslides2250/linearalgebra/
Base atom, atom, basis for linear DE (90.3 K, pdf, 09 Oct 2008)
Elementary matrix theorem (122.6 K, pdf, 09 Mar 2009)
Linear algebraic equations manuscript (292.7 K, pdf, 08 Mar 2009)
Orthogonality (87.0 K, pdf, 07 Oct 2008)
Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Partial fraction theory (129.6 K, pdf, 31 Jan 2008)
The pivot theorem and applications (139.6 K, pdf, 29 Sep 2008)
Rank, nullity and elimination (111.0 K, pdf, 07 Mar 2009)
History of telecom companies (1.1 K, txt, 05 Oct 2008)

# Week 8, Mar 2-6

• http://www.math.utah.edu/~gustafso/s2009/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 (90.3 K, pdf, 09 Oct 2008)
First and second order linear DE (72.1 K, pdf, 28 Oct 2007)
How to solve linear DE or any order (112.2 K, pdf, 11 Mar 2009)
Atoms, Euler's theorem, examples (104.8 K, pdf, 04 Apr 2009)
Picard, linear nth order DE, superposition (130.2 K, pdf, 29 Sep 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
FAQ for maple lab 6, S2009 (1.9 K, txt, 27 Aug 2008)
Maple lab 6. Spring mass systems. (22.2 K, pdf, 03 Jan 2009)

# Week 9, Mar 9-13

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/s2009/lectureslides2250/Laplace/
Laplace theory 2008 (350.5 K, pdf, 06 Mar 2009)
Laplace and Newton calculus. Photos of Newton and Laplace. (153.0 K, pdf, 22 Mar 2009)
Laplace examples (108.9 K, pdf, 22 Mar 2009)
Intro to Laplace theory. Assumes only calculus (117.2 K, pdf, 22 Mar 2009)
Laplace rules (119.9 K, pdf, 22 Mar 2009)
Laplace table proofs (137.9 K, pdf, 22 Mar 2009)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Maple Lab 7. Laplace applications (58.8 K, pdf, 30 Apr 2009)

# Week 10, Mar 23-27

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/s2009/lectureslides2250/Laplace/
Laplace theory 2008 (350.5 K, pdf, 06 Mar 2009)
Laplace second order systems (249.7 K, pdf, 21 Apr 2009)
Laplace resolvent method (56.4 K, pdf, 21 Apr 2009)
Piecewise functions and Laplace theory (72.4 K, pdf, 22 Mar 2009)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/linearDEhigherorder/
Basic undetermined coefficients, draft 1 (100.5 K, pdf, 09 Nov 2007)
Basic undetermined coefficients, draft 2 (110.5 K, pdf, 10 Sep 2008)
Basic undetermined coefficients, draft 3 (113.0 K, pdf, 09 Nov 2008)
Basic undetermined coefficients, draft 4 (104.9 K, pdf, 11 Mar 2009)
Variation of parameters (113.6 K, pdf, 27 Mar 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Laplace theory problem notes F2008 (8.1 K, txt, 21 Nov 2008)
Final exam study guide (7.3 K, txt, 01 May 2009)
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, Mar 30,31 Apr 1,2,3

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/s2009/lectureslides2250/linearDEhigherorder/
Electrical circuits (94.8 K, pdf, 16 Nov 2008)
Forced damped vibrations (242.6 K, pdf, 29 Sep 2008)
Forced vibrations and resonance (193.0 K, pdf, 29 Sep 2008)
Forced undamped vibrations (183.2 K, pdf, 01 Apr 2008)
Resonance and undetermined coefficients (149.4 K, pdf, 12 Mar 2009)
Unforced vibrations 2008 (628.5 K, pdf, 29 Sep 2008)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/linearalgebra/
Algebraic eigenanalysis (135.4 K, pdf, 29 Sep 2008)
Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
History of telecom companies (1.1 K, txt, 05 Oct 2008)
What's eigenanalysis, draft 1 (152.2 K, pdf, 19 Nov 2007)
What's eigenanalysis, draft 2 (124.0 K, pdf, 14 Nov 2007)
What's eigenanalysis 2008 (129.1 K, pdf, 29 Sep 2008)

# Week 12, Apr 6-10

Read sections 7.1,7.2,7.3,7.4. First order systems, eigenanalysis method, Putzer's algorithm, resolvent method, Cayley-Hamilton method. Second order systems, railway cars, earthquakes, sliding plates, oscillation control of an elevator.
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/systems/
Systems and brine tanks (70.5 K, pdf, 03 Oct 2008)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
Systems and home heating (81.5 K, pdf, 03 Oct 2008)
Systems eigenanalysis, 4 methods (110.2 K, pdf, 11 Apr 2009)
Systems Cayley-Hamilton Method (111.3 K, pdf, 09 Apr 2009)
Second order systems, laplace method (249.7 K, pdf, 21 Apr 2009)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Final exam study guide (7.3 K, txt, 01 May 2009)
Maple Lab 8. Optional. Earthquakes (23.7 K, pdf, 03 Jan 2009)
Maple Lab 9. Optional. Tacoma narrows (22.8 K, pdf, 03 Jan 2009)
Triangular systems of DE (87.4 K, pdf, 08 Apr 2008)
Laplace resolvent method (69.0 K, pdf, 26 Apr 2008)
Cable hoist example (73.2 K, pdf, 21 Aug 2008)
Sliding plates example (105.8 K, pdf, 21 Aug 2008)

# Week 13, Apr 13-17

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/s2009/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/s2009/lectureslides2250/references/
Final exam study guide (7.3 K, txt, 01 May 2009)
Triangular systems of DE (87.4 K, pdf, 08 Apr 2008)
Laplace resolvent method (64.0 K, pdf, 10 Apr 2009)
Systems eigenanalysis, 4 methods (110.2 K, pdf, 11 Apr 2009)

# Week 14, Apr 20-24

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/s2009/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/s2009/lectureslides2250/references/
Final exam study guide (7.3 K, txt, 01 May 2009)

# Week 15, Apr 27-29

Read sections 9.3,9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs.
• http://www.math.utah.edu/~gustafso/s2009/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 (0.0 K, pdf, 31 Dec 1969)
Phase Portraits for Dynamical Systems (201.6 K, pdf, 26 Apr 2009)
Stability for Dynamical Systems (125.8 K, pdf, 26 Apr 2009)
• http://www.math.utah.edu/~gustafso/s2009/lectureslides2250/references/
Final exam study guide (7.3 K, txt, 01 May 2009)

# Main References S2009

This set includes the syllabus, extra credit problems, maple labs, maple tutorials and maple examples.
• http://www.math.utah.edu/~gustafso/s2009/
Syllabus (133.6 K, pdf, 20 Jan 2009)
How to improve your written work (25.0 K, pdf, 01 Jan 2009)
Grade sheet for record keeping (46.6 K, pdf, 20 Jan 2009)
Extra credit ch1 (34.0 K, pdf, 01 Jan 2009)
Extra credit ch2 (31.3 K, pdf, 01 Jan 2009)
Extra credit ch3 (69.5 K, pdf, 01 Jan 2009)
Extra credit ch4 (49.0 K, pdf, 01 Jan 2009)
Extra credit ch5 (68.3 K, pdf, 01 Jan 2009)
Extra credit ch6 (28.4 K, pdf, 01 Jan 2009)
Extra credit ch7 (41.5 K, pdf, 01 Jan 2009)
Extra credit ch8 (45.0 K, pdf, 01 Jan 2009)
Extra credit ch9 (40.8 K, pdf, 01 Jan 2009)
Extra credit ch10 (37.8 K, pdf, 01 Jan 2009)
Midterm 1 solution key (395.7 K, pdf, 02 Mar 2009)
Final exam study guide (7.3 K, txt, 01 May 2009)
Maple lab 6 FAQ (1.9 K, txt, 27 Aug 2008)
Maple lab 1 (113.7 K, pdf, 04 Feb 2009)
Maple lab 1 code (0.8 K, txt, 03 Jan 2009)
Maple lab 2 Swamp cooler (134.2 K, pdf, 05 Mar 2009)
Maple lab 2 Swamp cooler code (1.3 K, txt, 05 Mar 2009)
Maple lab 2a Freezing pipes (86.9 K, pdf, 05 Mar 2009)
Maple lab 2a Freezing pipes code (1.2 K, txt, 03 Jan 2009)
Maple lab 3 code snips (6.6 K, mws, 03 Jan 2009)
Maple lab 3 Numerical DE (81.8 K, pdf, 03 Jan 2009)
Maple lab 3 Numerical DE code (5.2 K, txt, 03 Jan 2009)
Maple lab 4 code snips (4.3 K, mws, 03 Jan 2009)
Maple lab 4 Numerical DE (78.5 K, pdf, 03 Jan 2009)
Maple lab 4 text (3.2 K, txt, 03 Jan 2009)
Maple lab 5 maple work sheet (10.8 K, mws, 03 Jan 2009)
Maple lab 5 Linear algebra (94.2 K, pdf, 03 Jan 2009)
Maple lab 5 Linear algebra text (2.1 K, txt, 03 Jan 2009)
Maple lab 6 Spring mass system worksheet (10.3 K, mws, 03 Jan 2009)
Maple lab 6 Spring mass system (22.2 K, pdf, 03 Jan 2009)
Maple lab 6 Spring mass system text (5.0 K, txt, 03 Jan 2009)
Maple lab 7 worksheet (13.4 K, mws, 30 Apr 2009)
Maple lab 7 Laplace applications (58.8 K, pdf, 30 Apr 2009)
Maple lab 7 Laplace applications text (2.5 K, txt, 03 Jan 2009)
Maple lab 8 earthquakes worksheet (16.3 K, mws, 03 Jan 2009)
Maple lab 8 earthquakes (23.7 K, pdf, 03 Jan 2009)
Maple lab 8 earthquajes text (7.0 K, txt, 03 Jan 2009)
Maple lab 9 Tacoma narrows worksheet (14.0 K, mws, 03 Jan 2009)
Maple lab 9 Tacoma narrows (22.8 K, pdf, 03 Jan 2009)
Maple lab 9 Tacoma narrows text (6.5 K, txt, 03 Jan 2009)
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)