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: March 02, 2013, 09:50 MST.    Today: September 24, 2018, 11:18 MDT.

#### Week 1, Jan 7 to 11

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/s2013/2250
Syllabus: 2250 7:30 S2013 (155.7 K, pdf, 04 Mar 2013)
How to improve written work (82.8 K, pdf, 03 Dec 2012)
Gradesheet: 2250 7:30 S2013 (57.3 K, pdf, 04 Mar 2013)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/firstorderDE/
Slides: Method of quadrature (247.9 K, pdf, 11 Dec 2011)
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 14 to 18

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/s2013/2250/lectureslides2250/firstorderDE/
Slides: Autonomous DE (102.3 K, pdf, 03 Mar 2012)
Slides: 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)
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 (374.2 K, pdf, 28 Jul 2009)
Slides: Partial fraction theory (160.7 K, pdf, 03 Mar 2012)
Slides: Brine tanks (95.3 K, pdf, 04 Mar 2012)
Slides: Home heating (109.8 K, pdf, 04 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Maple: lab 1. Quadratics, plots, derivatives, Jacobian (215.4 K, pdf, 04 Dec 2012)
Maple: lab 2. Swamp cooler [option 1] (240.5 K, pdf, 04 Dec 2012)
Maple: lab 2. Freezing pipes [option 2] (198.3 K, pdf, 04 Dec 2012)
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 21 to 25

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/s2013/2250/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 (149.9 K, pdf, 03 Mar 2012)
Manuscript: Numerical methods (389.2 K, pdf, 13 Sep 2010)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Maple: lab 3. Numerical DE (152.4 K, pdf, 04 Dec 2012)
Maple: lab 4. Numerical DE (138.2 K, pdf, 04 Dec 2012)
Maple: code for maple labs 3 and 4 (5.1 K, txt, 10 Dec 2011)
Text: How to use maple at home (7.3 K, txt, 06 Dec 2012)
Special problems for Maple lab 3 and 4, statements (109.6 K, pdf, 04 Dec 2012)
Special problems for Maple lab 3 and 4, problem 1 solution (184.6 K, jpg, 08 Feb 2008)
Notes on numerical DE report for Ch2 Ex 10 (98.3 K, pdf, 04 Dec 2012)
Notes on numerical DE report for Ch2 Ex 12 (108.7 K, pdf, 04 Dec 2012)
Notes on numerical DE report for Ch2 Ex 4 (98.2 K, pdf, 04 Dec 2012)
Notes on numerical DE report for Ch2 Ex 6 (126.1 K, pdf, 04 Dec 2012)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)

#### Week 4, Jan 28 to Feb 1

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/s2013/2250/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 (460.2 K, pdf, 10 Feb 2012)
Slides: Three possibilities with symbols, rank (129.0 K, pdf, 03 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Maple: lab 5. Linear algebra (170.0 K, pdf, 04 Dec 2012)

#### Week 5, Feb 5 to 9

Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants
• http://www.math.utah.edu/~gustafso/s2013/2250/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 (460.2 K, pdf, 10 Feb 2012)
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 11 to 15

Read sections 4.1,4.2,4.3. Vector space, subspace, independence
• http://www.math.utah.edu/~gustafso/s2013/2250/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 (460.2 K, pdf, 10 Feb 2012)
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 (185.0 K, pdf, 21 Dec 2012)

#### Week 7, Feb 18 to 22

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/s2013/2250/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 (460.2 K, pdf, 10 Feb 2012)
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)

#### Week 8, Feb 25 to Mar 1

• http://www.math.utah.edu/~gustafso/s2013/2250/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 (168.4 K, pdf, 26 Feb 2013)
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)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Text: FAQ for maple lab 6, S2013 (1.9 K, txt, 23 Nov 2010)
Maple: lab 6. Spring mass systems. (33.1 K, pdf, 04 Dec 2012)

#### Week 9, Mar 4 to 8

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/s2013/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (351.3 K, pdf, 15 Apr 2009)
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/s2013/2250/lectureslides2250/references/
Maple: Lab 7. Laplace applications (156.0 K, pdf, 04 Dec 2012)

#### Week 10, Mar 18 to 22

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/s2013/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (351.3 K, pdf, 15 Apr 2009)
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/s2013/2250/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/s2013/2250/lectureslides2250/references/
Text: Laplace theory problem notes S2013 (17.2 K, txt, 03 Dec 2012)
Text: Final exam study guide (8.2 K, txt, 05 Dec 2012)
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 (785.8 K, pdf, 16 Nov 2008)

#### Week 11, Mar 25 to 29

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/s2013/2250/lectureslides2250/linearDEhigherorder/
Slides: Electrical circuits (124.8 K, pdf, 04 Mar 2012)
Slides: Forced damped vibrations (280.7 K, pdf, 04 Mar 2012)
Slides: Forced vibrations and resonance (240.3 K, pdf, 04 Mar 2012)
Slides: Forced undamped vibrations (214.2 K, pdf, 03 Mar 2012)
Slides: Resonance and undetermined coefficients (199.4 K, pdf, 03 Mar 2012)
Slides: Unforced vibrations 2008 (667.9 K, pdf, 03 Mar 2012)
• http://www.math.utah.edu/~gustafso/s2013/2250/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 12, Apr 1 to 5

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/s2013/2250/lectureslides2250/systems/
Slides: Systems and brine tanks (95.3 K, pdf, 04 Mar 2012)
Manuscript: Systems of DE examples and theory (785.8 K, pdf, 16 Nov 2008)
Slides: Systems and home heating (109.8 K, pdf, 04 Mar 2012)
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/s2013/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 05 Dec 2012)
Maple: Lab 8. Optional. Earthquakes (34.4 K, pdf, 04 Dec 2012)
Maple: Lab 9. Optional. Tacoma narrows (33.7 K, pdf, 04 Dec 2012)
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 13, Apr 8 to 12

Read sections 7.5 /w Laplace, 8.1, 8.2. Jordan form, Putzer's formulas, generalized eigenanalysis, Cayley-Hamilton-Zeibur theorem, matrix exponential, spectral methods, variation of parameters for systems.
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/systems/
Manuscript: Dynamical systems (696.4 K, pdf, 03 Nov 2008)
Manuscript: Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 05 Dec 2012)
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)

#### Week 14, Apr 15 to 19

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/s2013/2250/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/s2013/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 05 Dec 2012)

#### Week 15, Apr 22,23,24

Read section 9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs. In-class final exam review begins.
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/systems/
Manuscript: Dynamical systems (696.4 K, pdf, 03 Nov 2008)
Manuscript: Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
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)
• http://www.math.utah.edu/~gustafso/s2013/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 05 Dec 2012)

#### Main References S2013

This set includes the syllabus, extra credit problems, maple labs, maple tutorials and maple examples.
• http://www.math.utah.edu/~gustafso/s2013/2250/
Syllabus (155.7 K, pdf, 04 Mar 2013)
How to improve your written work (82.8 K, pdf, 03 Dec 2012)
Grade sheet for record keeping (57.3 K, pdf, 04 Mar 2013)
Extra credit ch1 (116.5 K, pdf, 04 Dec 2012)
Extra credit ch2 (32.0 K, pdf, 16 Feb 2013)
Extra credit ch3 (199.6 K, pdf, 04 Dec 2012)
Extra credit ch4 (132.9 K, pdf, 04 Dec 2012)
Extra credit ch5 (177.7 K, pdf, 04 Dec 2012)
Extra credit ch6 (91.4 K, pdf, 04 Dec 2012)
Extra credit ch7 (125.7 K, pdf, 04 Dec 2012)
Extra credit ch8 (146.6 K, pdf, 04 Dec 2012)
Extra credit ch9 (121.5 K, pdf, 04 Dec 2012)
Extra credit ch10 (125.2 K, pdf, 04 Dec 2012)
Extra credit ch10X (127.7 K, pdf, 04 Dec 2012)
Final exam study guide (8.2 K, txt, 05 Dec 2012)
Maple: lab 1 (215.4 K, pdf, 04 Dec 2012)
Maple: lab 1 code (0.8 K, txt, 15 Mar 2012)
Maple: lab 2 Swamp cooler (240.5 K, pdf, 04 Dec 2012)
Maple: lab 2 Swamp cooler code (1.3 K, txt, 15 Mar 2012)
Maple: lab 2a Freezing pipes (198.3 K, pdf, 04 Dec 2012)
Maple: lab 2a Freezing pipes code (1.2 K, txt, 15 Mar 2012)
Maple: lab 3 Numerical DE (152.4 K, pdf, 04 Dec 2012)
Maple: lab 3 Numerical DE code (5.3 K, txt, 10 Dec 2012)
Maple: lab 3 code snips (6.6 K, mws, 15 Mar 2012)
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: lab 4 Numerical DE (138.2 K, pdf, 04 Dec 2012)
Maple: lab 4 text (3.1 K, txt, 15 Mar 2012)
Maple: lab 4 code snips (4.3 K, mws, 15 Mar 2012)
Maple: lab 5 Linear algebra (170.0 K, pdf, 04 Dec 2012)
Maple: lab 5 Linear algebra text (2.1 K, txt, 15 Mar 2012)
Maple: lab 5 maple work sheet (10.8 K, mws, 15 Mar 2012)
Maple: lab 6 Spring mass system (33.1 K, pdf, 04 Dec 2012)
Maple: lab 6 Spring mass system text (4.9 K, txt, 15 Mar 2012)
Maple: lab 6 Spring mass system worksheet (13.1 K, mws, 15 Mar 2012)
Maple lab 6 FAQ (1.9 K, txt, 23 Nov 2010)
Maple: lab 7 Laplace applications (156.0 K, pdf, 04 Dec 2012)
Maple: lab 7 Laplace applications text (3.3 K, txt, 15 Apr 2012)
Maple: lab 7 worksheet (15.4 K, mws, 15 Apr 2012)
Maple: lab 8 Extra Credit earthquakes (34.4 K, pdf, 04 Dec 2012)
Maple: lab 8 earthquakes text (6.8 K, txt, 15 Mar 2012)
Maple: lab 8 earthquakes worksheet (16.5 K, mws, 15 Mar 2012)
Maple: lab 9 Extra Credit: Tacoma narrows (33.7 K, pdf, 04 Dec 2012)
Maple: lab 9 Tacoma narrows text (6.3 K, txt, 15 Mar 2012)
Maple: lab 9 Tacoma narrows worksheet (14.4 K, mws, 15 Mar 2012)
Maple: lab 10 Extra Credit: Brine Tanks. Glucose-Insulin. (291.9 K, pdf, 04 Dec 2012)
Maple: lab 10 Brine Tanks and Glucose-Insulin text. (0.8 K, txt, 15 Mar 2012)
How to use maple 15 (3.2 K, txt, 22 Nov 2012)
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)
Sita Gakkhar's maple lab 2 example worksheet (178.4 K, mw, 21 Aug 2010)
Sita Gakkhar's maple lab 2 example (136.7 K, pdf, 02 Mar 2009)
Special exam review problems for ch1, ER-1, ER-2 (109.6 K, pdf, 04 Dec 2012)
Html: Utah Maple Web Help (2.0 K, html, 03 Dec 2012)