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.
Last Modified: January 02, 2014, 05:44 MST.    Today: December 16, 2018, 06:49 MST.

Week 1, Jan 6 to 10

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/s2014/2250
Syllabus: 2250 7:30 S2014 (225.7 K, pdf, 30 Mar 2014)
How to improve written work (82.3 K, pdf, 16 Dec 2013)
Homework Book Mark: 2250 7:30 S2014 (76.3 K, pdf, 30 Mar 2014)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/firstorderDE/
Slides: Method of quadrature (237.7 K, pdf, 07 Jan 2014)
Exercise 1.3-8 template (102.2 K, jpg, 09 Dec 2012)
Slides: Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Slides: Picard, Peano, direction fields (293.7 K, pdf, 03 Mar 2012)
Slides: Separable DE method, equilibrium solutions (148.9 K, pdf, 03 Mar 2012)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)

Week 2, Jan 13 to 17

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/s2014/2250/lectureslides2250/firstorderDE/
Slides: Autonomous DE (101.8 K, pdf, 15 Jan 2014)
Slides: Heaviside's method partial fractions (352.3 K, pdf, 07 Jan 2014)
Manuscript: Heaviside coverup partial fraction method (290.2 K, pdf, 07 Jan 2014)
Slides: Linear integrating factor method (129.8 K, pdf, 03 Mar 2012)
Slides: Earth to the moon (127.0 K, pdf, 10 Dec 2012)
Slides: Applications of linear DE (484.2 K, pdf, 16 Jan 2014)
Slides: Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Slides: Brine tanks (95.3 K, pdf, 04 Mar 2012)
Slides: Home heating (99.3 K, pdf, 10 Apr 2014)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Using maple at home (7.3 K, txt, 06 Dec 2012)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)

Week 3, Jan 20 to 24

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/s2014/2250/lectureslides2250/firstorderDE/
Slides: Earth to the moon (127.0 K, pdf, 10 Dec 2012)
Slides: Newton friction models (137.1 K, pdf, 03 Mar 2012)
Slides: Numerical methods (149.7 K, pdf, 27 Jan 2014)
Manuscript: Numerical methods (389.2 K, pdf, 13 Sep 2010)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Maple: code for Chapter 2 (5.1 K, txt, 10 Dec 2011)
Text: How to use maple at home (7.3 K, txt, 06 Dec 2012)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)

Week 4, Jan 27 to 31

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/s2014/2250/lectureslides2250/linearalgebra/
Slides: 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: Three possibilities with symbol k (98.8 K, pdf, 03 Mar 2012)
Slides: Introduction to linear algebraic equations (237.3 K, pdf, 15 Dec 2012)
Slides: Infinitely many solutions case (131.1 K, pdf, 03 Mar 2012)
Slides: No solution case (79.7 K, pdf, 03 Mar 2012)
Slides: Unique solution case (110.1 K, pdf, 14 Dec 2012)
Manuscript: Linear algebraic equations (429.7 K, pdf, 30 Jan 2014)
Slides: Three possibilities with symbols, rank (129.0 K, pdf, 03 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Maple: XC lab 5. Linear algebra (70.4 K, pdf, 14 Dec 2013)

Week 5, Feb 3 to 7

Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (6.6 K, txt, 21 Dec 2012)
Slides: Determinants 2008 (227.1 K, pdf, 03 Mar 2012)
Slides: Digital photos, Maxwell's RGB separations, visualization of matrix add (170.2 K, pdf, 03 Mar 2012)
Slides: Elementary matrix theorems (161.5 K, pdf, 03 Mar 2012)
Slides: Inverse matrix, frame sequence method (97.9 K, pdf, 03 Mar 2012)
Manuscript: Linear algebraic equations (429.7 K, pdf, 30 Jan 2014)
Slides: Matrix operations (156.7 K, pdf, 03 Mar 2012)
Slides: More on digital photos, checkerboard analogy (141.9 K, pdf, 03 Mar 2012)
Slides: Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)

Week 6, Feb 10 to 14

Read sections 4.1,4.2,4.3. Vector space, subspace, independence
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearalgebra/
Slides: Elementary matrix theorems (161.5 K, pdf, 03 Mar 2012)
Slides: Geometry of linear transformations (98.6 K, pdf, 04 Mar 2012)
Manuscript: Linear algebraic equations (429.7 K, pdf, 30 Jan 2014)
Slides: Matrix operations (156.7 K, pdf, 03 Mar 2012)
Slides: Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)
Slides: Vector models, vector spaces (144.1 K, pdf, 03 Mar 2012)
Slides: Vector space, subspace, independence (168.4 K, pdf, 17 Feb 2014)

Week 7, Feb 17 to 21

Read sections 4.4,4.7 Bases, dimension, row and column space, pivot theorem, orthogonality, abstract vectors spaces, function spaces Read sections 5.1,5.2. Linear constant DE, superposition, Euler solution atoms
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearalgebra/
Slides: Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
Slides: Elementary matrix theorem (161.5 K, pdf, 03 Mar 2012)
Manuscript: Linear algebraic equations manuscript (429.7 K, pdf, 30 Jan 2014)
Slides: Orthogonality (124.8 K, pdf, 03 Mar 2012)
Text: Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Slides: Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Slides: The pivot theorem and applications (189.2 K, pdf, 03 Mar 2012)
Slides: Rank, nullity and elimination (156.3 K, pdf, 21 Dec 2012)
Text: History of telecom companies (1.9 K, txt, 04 Apr 2013)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearDEhigherorder/
Slides: Picard-Lindelof, superposition (67.9 K, pdf, 02 Nov 2007)
Slides: Atoms, Euler's theorem, examples (117.2 K, pdf, 02 Nov 2007)
Slides: Atoms, independence, Euler's theorem (115.5 K, pdf, 02 Nov 2007)
Slides: Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
Slides: First and second order linear DE (72.1 K, pdf, 28 Oct 2007)
Slides: How to solve linear DE or any order (153.3 K, pdf, 25 Feb 2014)
Slides: Atoms, Euler's theorem, examples (130.5 K, pdf, 26 Feb 2013)
Slides: Picard, linear nth order DE, superposition (181.5 K, pdf, 03 Mar 2012)

Week 8, Feb 24 to 28

• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearDEhigherorder/
Slides: Picard-Lindelof, superposition (67.9 K, pdf, 02 Nov 2007)
Slides: Atoms, Euler's theorem, examples (117.2 K, pdf, 02 Nov 2007)
Slides: Atoms, independence, Euler's theorem (115.5 K, pdf, 02 Nov 2007)
Slides: Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
Slides: First and second order linear DE (72.1 K, pdf, 28 Oct 2007)
Slides: How to solve linear DE or any order (153.3 K, pdf, 25 Feb 2014)
Slides: Atoms, Euler's theorem, examples (130.5 K, pdf, 26 Feb 2013)
Slides: Picard, linear nth order DE, superposition (181.5 K, pdf, 03 Mar 2012)
Slides: Electrical circuits (112.9 K, pdf, 08 Mar 2014)
Slides: Forced damped vibrations (264.0 K, pdf, 08 Mar 2014)
Slides: Forced vibrations and resonance (253.0 K, pdf, 08 Mar 2014)
Slides: Forced undamped vibrations (214.2 K, pdf, 03 Mar 2012)
Slides: Resonance and undetermined coefficients (178.0 K, pdf, 08 Mar 2014)
Slides: Unforced vibrations 2008 (647.6 K, pdf, 28 Feb 2014)
PDF: Beats y=sin(10x)sin(x/2) (68.9 K, pdf, 18 Mar 2013)
PDF: Pure resonance y = x sin(x) (74.7 K, pdf, 18 Mar 2013)
• http://www.math.utah.edu/~gustafso/s2014 /2250/lectureslides2250/linearDEhigherorder/
Slides: Basic undetermined coefficients, draft 1 (100.5 K, pdf, 10 Nov 2008)
Slides: Basic undetermined coefficients, draft 2 (110.5 K, pdf, 10 Nov 2008)
Slides: Basic undetermined coefficients, draft 3 (113.0 K, pdf, 10 Nov 2008)
Slides: Basic undetermined coefficients, draft 4 (104.9 K, pdf, 07 Nov 2009)
Slides: Variation of parameters (164.5 K, pdf, 03 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: FAQ for maple lab 6, S2014 (1.9 K, txt, 23 Nov 2010)
Maple: XC lab 6. Spring mass systems. (52.5 K, pdf, 14 Dec 2013)

Week 9, Mar 3 to 7

Read 5.6. Forced oscillations, beats, resonance, mechanical systems. Read sections 10.1,10.2,10.3. Laplace intro, history, Laplace tables, Laplace's method, Laplace rules.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearDEhigherorder/
Slides: Electrical circuits (112.9 K, pdf, 08 Mar 2014)
Slides: Forced damped vibrations (264.0 K, pdf, 08 Mar 2014)
Slides: Forced vibrations and resonance (253.0 K, pdf, 08 Mar 2014)
Slides: Forced undamped vibrations (214.2 K, pdf, 03 Mar 2012)
Slides: Resonance and undetermined coefficients (178.0 K, pdf, 08 Mar 2014)
Slides: Unforced vibrations 2008 (647.6 K, pdf, 28 Feb 2014)
PDF: Beats y=sin(10x)sin(x/2) (68.9 K, pdf, 18 Mar 2013)
PDF: Pure resonance y = x sin(x) (74.7 K, pdf, 18 Mar 2013)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (500.9 K, pdf, 16 Mar 2014)
Slides: Laplace and Newton calculus. Photos of Newton and Laplace. (200.2 K, pdf, 04 Mar 2012)
Slides: Laplace examples (149.1 K, pdf, 04 Mar 2012)
Slides: Intro to Laplace theory. Assumes only calculus (163.0 K, pdf, 19 Mar 2012)
Slides: Laplace rules (160.3 K, pdf, 04 Mar 2012)
Slides: Laplace table proofs (169.6 K, pdf, 04 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Maple: XC Lab 7. Laplace applications (63.6 K, pdf, 15 Dec 2013)
• Projection: glass-breaking video. Wine glass experiment. Tacoma narrows.
MOVIE: Water glass shattering due to resonant sound waves.(QuickTime MOV) (96.8 K, mov, 21 Mar 2013)
Video: Wine glass experiment (12mb mpg, 2min) (12493.8 K, mpg, 01 Apr 2008)
Video: Tacoma Narrows Bridge Nov 7, 1940 (18mb mpg, 4min) (18185.8 K, mpg, 01 Apr 2008)

Week 10, Mar 10 to 14

This is Spring Break. No classes.

Week 11, Mar 17 to 21

Read sections 10.4,10.5,EPbvp7.6. Periodic inputs, square wave, ramp, piecewise methods, Heaviside and Dirac inputs, engineering functions.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (500.9 K, pdf, 16 Mar 2014)
Slides: Laplace and Newton calculus. Photos of Newton and Laplace. (200.2 K, pdf, 04 Mar 2012)
Slides: Laplace examples (149.1 K, pdf, 04 Mar 2012)
Slides: Intro to Laplace theory. Assumes only calculus (163.0 K, pdf, 19 Mar 2012)
Slides: Laplace rules (160.3 K, pdf, 04 Mar 2012)
Slides: Laplace table proofs (169.6 K, pdf, 04 Mar 2012)
Slides: Laplace second order systems (288.1 K, pdf, 04 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Slides: Piecewise functions and Laplace theory (108.5 K, pdf, 03 Mar 2013)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: Laplace theory problem notes S2014 (17.7 K, txt, 18 Mar 2014)
Text: Final exam study guide (8.0 K, txt, 20 Apr 2014)
Slide: Cable hoist example (73.2 K, pdf, 21 Aug 2008)
Slide: Sliding plates example (105.8 K, pdf, 21 Aug 2008)
Manuscript: Systems of DE examples and theory (730.9 K, pdf, 10 Apr 2014)

Week 12, Mar 24 to 28

Read 6.1,6.2,6.3[power method]. Eigenanalysis, Fourier's model, diagonalization. Read 7.1. systems of DE.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/linearalgebra/
Manuscript: Algebraic eigenanalysis (187.6 K, pdf, 04 Mar 2012)
Text: Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Text: History of telecom companies (1.9 K, txt, 04 Apr 2013)
Slides: What's eigenanalysis, draft 1 (152.2 K, pdf, 01 Apr 2008)
Slides: What's eigenanalysis, draft 2 (124.0 K, pdf, 14 Nov 2007)
Slides: What's eigenanalysis 2008 (174.2 K, pdf, 04 Mar 2012)

Week 13, Mar 31 to Apr 4

Read sections 7.2,7.3. First order systems, eigenanalysis method, Putzer's algorithm, resolvent method, Cayley-Hamilton-Ziebur method.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/systems/
Slides: Systems and brine tanks (95.3 K, pdf, 04 Mar 2012)
Manuscript: Systems of DE examples and theory (730.9 K, pdf, 10 Apr 2014)
Slides: Systems and home heating (99.3 K, pdf, 10 Apr 2014)
Slides: Systems eigenanalysis, 4 methods (145.6 K, pdf, 04 Mar 2012)
Slides: Systems Cayley-Hamilton Method (152.9 K, pdf, 04 Mar 2012)
Slides: Second order systems, laplace method (288.1 K, pdf, 04 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: Final exam study guide (8.0 K, txt, 20 Apr 2014)
Maple: XC Lab 8. Optional. Earthquakes (17.6 K, pdf, 15 Dec 2013)
Maple: XC Lab 9. Optional. Tacoma narrows (17.2 K, pdf, 15 Dec 2013)
Slides: Triangular systems of DE (113.4 K, pdf, 04 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Slides: Cable hoist example (73.2 K, pdf, 21 Aug 2008)
Slides: Sliding plates example (105.8 K, pdf, 21 Aug 2008)

Week 14, Apr 7 to 11

Read section 7.4. Second order systems, railway cars, earthquakes, sliding plates, oscillation control of an elevator. Read PDF notes on laplace methods for systems, laplace resolvent method. Read sections 9.1,9.2. Stability, phase plane, linear systems, almost linear systems, predator-prey models.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/systems/
Manuscript: Dynamical systems (696.4 K, pdf, 03 Nov 2008)
Manuscript: Systems of DE examples and theory manuscript (730.9 K, pdf, 10 Apr 2014)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: Final exam study guide (8.0 K, txt, 20 Apr 2014)
Slides: Triangular systems of DE (113.4 K, pdf, 04 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 04 Mar 2012)
Slides: Systems eigenanalysis, 4 methods (145.6 K, pdf, 04 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/systems/
Dynamical systems manuscript (696.4 K, pdf, 03 Nov 2008)
Systems of DE examples and theory manuscript (730.9 K, pdf, 10 Apr 2014)
Slides: Introduction to Dynamical systems (158.0 K, pdf, 04 Mar 2012)
Slides: Phase Portraits for Dynamical Systems (239.3 K, pdf, 04 Mar 2012)
Slides: 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 (130.1 K, pdf, 04 Mar 2012)

Week 15, Apr 14 to 18

Read sections 9.3,9.4. Stability, phase plane, linear systems, almost linear systems, predator-prey models, nonlinear mechanical systems. Pendulum. Soft and hard springs.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/systems/
Dynamical systems manuscript (696.4 K, pdf, 03 Nov 2008)
Systems of DE examples and theory manuscript (730.9 K, pdf, 10 Apr 2014)
Slides: Introduction to Dynamical systems (158.0 K, pdf, 04 Mar 2012)
Slides: Phase Portraits for Dynamical Systems (239.3 K, pdf, 04 Mar 2012)
Slides: 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 (130.1 K, pdf, 04 Mar 2012)

Week 16, Apr 21,22,23

In-class comprehensive final exam review.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: Final exam study guide (8.0 K, txt, 20 Apr 2014)

Week 17, Apr 28, 29, 30

Final exam week. Extra credit due dates on Monday 28 April and Wednesday 30 April. Final exam at 7:30am in JTB 140 on Tuesday 29 April 2014.
• http://www.math.utah.edu/~gustafso/s2014/2250/lectureslides2250/references/
Text: Final exam study guide (8.0 K, txt, 20 Apr 2014)

Main References S2014

This set includes the syllabus, extra credit problems, maple labs, maple tutorials and maple examples.
• http://www.math.utah.edu/~gustafso/s2014/2250/
PDF: Syllabus for 3350-1 S2014 (225.7 K, pdf, 30 Mar 2014)
PDF: How to improve your written work (82.3 K, pdf, 16 Dec 2013)
PDF: Book mark with exercise list (76.3 K, pdf, 30 Mar 2014)
Extra credit ch1 (36.5 K, pdf, 14 Dec 2013)
Extra credit ch2 (38.0 K, pdf, 14 Dec 2013)
Extra credit ch3 (66.7 K, pdf, 14 Dec 2013)
Extra credit ch4 (45.4 K, pdf, 14 Dec 2013)
Extra credit ch5 (65.8 K, pdf, 14 Dec 2013)
Extra credit ch6 (27.5 K, pdf, 14 Dec 2013)
Extra credit ch7 (41.0 K, pdf, 14 Dec 2013)
Extra credit ch8 (44.9 K, pdf, 14 Dec 2013)
Extra credit ch9 (42.0 K, pdf, 14 Dec 2013)
Extra credit ch10 (39.6 K, pdf, 14 Dec 2013)
Extra credit ch10X (38.6 K, pdf, 14 Dec 2013)
Final exam study guide (8.0 K, txt, 20 Apr 2014)
Numerical DE hints (5.1 K, txt, 10 Dec 2011)
Numerical DE manuscript (203.0 K, pdf, 04 Sep 2004)
Sample maple numerical DE snips (2.1 K, mws, 21 Aug 2010)
Sample problem numerical DE (1.9 K, mws, 21 Aug 2010)
Maple: XC lab 5 Linear algebra (70.4 K, pdf, 14 Dec 2013)
Maple: XC lab 5 Linear algebra text (2.6 K, txt, 15 Dec 2013)
Maple: XC lab 6 Spring mass system (52.5 K, pdf, 14 Dec 2013)
Maple: XC lab 6 Spring mass system text (0.8 K, txt, 15 Dec 2013)
Maple: XC lab 7 Laplace applications (63.6 K, pdf, 15 Dec 2013)
Maple: XC lab 7 Laplace applications text (3.1 K, txt, 15 Dec 2013)
Maple: XC lab 8 Extra Credit earthquakes (17.6 K, pdf, 15 Dec 2013)
Maple: XC lab 8 earthquakes text (5.6 K, txt, 15 Dec 2013)
Maple: XC lab 9 Extra Credit: Tacoma narrows (17.2 K, pdf, 15 Dec 2013)
Maple: XC lab 9 Tacoma narrows text (6.0 K, txt, 15 Dec 2013)
Maple: XC lab 9 Tacoma narrows worksheet (15.4 K, mws, 15 Dec 2013)
Maple: XC lab 10 Brine Tanks. Glucose-Insulin. (291.9 K, pdf, 15 Dec 2013)
Maple: XC lab 10 Brine Tanks and Glucose-Insulin text. (0.8 K, txt, 15 Dec 2013)
How to use maple 17 (3.2 K, txt, 09 Dec 2013)
How to use maple at home (7.3 K, txt, 06 Dec 2012)
Angie Gardiner's maple intro (138.8 K, mws, 19 Jan 2009)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)