Gustafson's 2250 Reading Assignments S2015

Spring 2015 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.

Last Modified: January 06, 2015, 05:30 MST. Today: April 26, 2024, 07:25 MDT.

Week 1, Jan 12 to 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/s2015/2250
Syllabus: 2250 S2015 (262.3 K, pdf, 18 Mar 2015)
How to improve written work (82.3 K, pdf, 16 Dec 2013)
Homework Book Mark: 2250 S2015 (76.8 K, pdf, 18 Mar 2015)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/firstorderDE/
Slides: Method of quadrature (242.8 K, pdf, 09 Jan 2015)
Exercise 1.3-8 template (102.2 K, jpg, 09 Dec 2012)
Slides: Partial fraction theory (148.6 K, pdf, 14 Dec 2014)
Slides: Picard, Peano, direction fields (293.7 K, pdf, 03 Mar 2012)
Slides: Separable DE method, equilibrium solutions (294.2 K, pdf, 13 Jan 2015)
Html: Utah Maple Web Help (2.1 K, html, 30 Jan 2016)

Week 2, Jan 19 to 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/s2015/2250/lectureslides2250/firstorderDE/
Slides: Autonomous DE (101.8 K, pdf, 14 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 (126.0 K, pdf, 15 Dec 2014)
Slides: Earth to the moon (124.2 K, pdf, 01 Jan 2015)
Slides: Applications of linear DE (484.2 K, pdf, 16 Jan 2014)
Slides: Partial fraction theory (148.6 K, pdf, 14 Dec 2014)
Slides: Brine tanks (95.3 K, pdf, 03 Mar 2012)
Slides: Home heating (99.3 K, pdf, 09 Apr 2014)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Using maple at home (7.3 K, txt, 05 Dec 2012)
Html: Utah Maple Web Help (2.1 K, html, 30 Jan 2016)

Week 3, Jan 26 to 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/s2015/2250/lectureslides2250/firstorderDE/
Slides: Earth to the moon (124.2 K, pdf, 01 Jan 2015)
Slides: Newton friction models (138.9 K, pdf, 11 Jan 2015)
Slides: Numerical methods (149.7 K, pdf, 26 Jan 2014)
Manuscript: Numerical methods (389.2 K, pdf, 13 Sep 2010)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Maple: code for Chapter 2 (0.0 K, txt, 31 Dec 1969)
Text: How to use maple at home (7.3 K, txt, 05 Dec 2012)
Html: Utah Maple Web Help (2.1 K, html, 30 Jan 2016)

Week 4, Feb 2 to 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/s2015/2250/lectureslides2250/linearalgebra/
Slides: Elementary matrix theorems (154.2 K, pdf, 11 Feb 2015)
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, 14 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, 13 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/s2015/2250/lectureslides2250/references/
Maple: XC lab 5. Linear algebra (160.8 K, pdf, 29 Nov 2014)

Week 5, Feb 9 to 13

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

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (0.0 K, txt, 31 Dec 1969)
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 (154.2 K, pdf, 11 Feb 2015)
Slides: Inverse matrix, frame sequence method (97.0 K, pdf, 11 Feb 2015)
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, 20 Dec 2012)

Week 6, Feb 16 to 20

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

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/linearalgebra/
Slides: Elementary matrix theorems (154.2 K, pdf, 11 Feb 2015)
Slides: Geometry of linear transformations (98.6 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: Rank, nullity and elimination (156.3 K, pdf, 20 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 23 to 27

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/s2015/2250/lectureslides2250/linearalgebra/
Slides: Base atom, atom, basis for linear DE (117.6 K, pdf, 03 Mar 2012)
Slides: Elementary matrix theorem (154.2 K, pdf, 11 Feb 2015)
Manuscript: Linear algebraic equations manuscript (429.7 K, pdf, 30 Jan 2014)
Slides: Orthogonality (124.8 K, pdf, 04 Dec 2014)
Text: Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Slides: Partial fraction theory (148.6 K, pdf, 14 Dec 2014)
Slides: The pivot theorem and applications (189.2 K, pdf, 03 Mar 2012)
Slides: Rank, nullity and elimination (156.3 K, pdf, 20 Dec 2012)
Text: History of telecom companies (1.9 K, txt, 03 Apr 2013)

Week 8, Mar 2 to 6

Read sections 5.3,5.4. Linear constant DE, superposition, atoms, vibrations, steady-states, observables Read EPbvp3.7. electric circuits. Read 5.5. Variation constants, undetermined coefficients.

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/linearDEhigherorder/
Slides: Picard-Lindelof, superposition (67.9 K, pdf, 01 Nov 2007)
Slides: Atoms, Euler's theorem, examples (117.2 K, pdf, 01 Nov 2007)
Slides: Atoms, independence, Euler's theorem (115.5 K, pdf, 01 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, 24 Feb 2014)
Slides: Atoms, Euler's theorem, examples (130.5 K, pdf, 25 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, 27 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/s2015 /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/s2015/2250/lectureslides2250/references/
Text: FAQ for maple lab 6, S2015 (1.9 K, txt, 22 Nov 2010)
Maple: XC lab 6. Spring mass systems. (135.5 K, pdf, 29 Nov 2014)

Week 9, Mar 9 to 13

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/s2015/2250/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, 27 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/s2015/2250/lectureslides2250/references/
Maple: XC Lab 7. Laplace applications (151.5 K, pdf, 29 Nov 2014)

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 16 to 20

This is Spring Break. No classes.

Week 11, Mar 23 to 27

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/s2015/2250/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, 03 Mar 2012)
Slides: Laplace examples (133.2 K, pdf, 27 Mar 2015)
Slides: Intro to Laplace theory. Assumes only calculus (144.8 K, pdf, 25 Mar 2015)
Slides: Laplace rules (160.3 K, pdf, 03 Mar 2012)
Slides: Laplace table proofs (169.6 K, pdf, 03 Mar 2012)
Slides: Laplace second order systems (288.1 K, pdf, 03 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 03 Mar 2012)
Slides: Piecewise functions and Laplace theory (108.5 K, pdf, 03 Mar 2013)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Text: Laplace theory problem notes S2015 (17.7 K, txt, 17 Mar 2014)
Text: Final exam study guide (8.3 K, txt, 06 Jan 2015)
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 30 to Apr 3

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/s2015/2250/lectureslides2250/linearalgebra/
Manuscript: Algebraic eigenanalysis (187.6 K, pdf, 03 Mar 2012)
Text: Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Text: History of telecom companies (1.9 K, txt, 03 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, 03 Mar 2012)

Week 13, Apr 6 to 10

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/s2015/2250/lectureslides2250/systems/
Slides: Systems and brine tanks (95.3 K, pdf, 03 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, 09 Apr 2014)
Slides: Systems eigenanalysis, 4 methods (145.6 K, pdf, 03 Mar 2012)
Slides: Systems Cayley-Hamilton Method (137.7 K, pdf, 28 Mar 2015)
Slides: Second order systems, laplace method (288.1 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Text: Final exam study guide (8.3 K, txt, 06 Jan 2015)
Maple: XC Lab 8. Optional. Earthquakes (32.3 K, pdf, 29 Nov 2014)
Maple: XC Lab 9. Optional. Tacoma narrows (31.8 K, pdf, 29 Nov 2014)
Slides: Triangular systems of DE (113.4 K, pdf, 03 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 03 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 13 to 17

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/s2015/2250/lectureslides2250/systems/
Manuscript: Dynamical systems (1037.6 K, pdf, 05 Apr 2015)
Manuscript: Systems of DE examples and theory manuscript (730.9 K, pdf, 10 Apr 2014)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Text: Final exam study guide (8.3 K, txt, 06 Jan 2015)
Slides: Triangular systems of DE (113.4 K, pdf, 03 Mar 2012)
Slides: Laplace resolvent method (88.1 K, pdf, 03 Mar 2012)
Slides: Systems eigenanalysis, 4 methods (145.6 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/systems/
Dynamical systems manuscript (1037.6 K, pdf, 05 Apr 2015)
Systems of DE examples and theory manuscript (730.9 K, pdf, 10 Apr 2014)
Slides: Introduction to Dynamical systems (145.4 K, pdf, 05 Apr 2015)
Slides: Phase Portraits for Dynamical Systems (221.3 K, pdf, 05 Apr 2015)
Slides: Stability for Dynamical Systems (154.4 K, pdf, 05 Apr 2015)
Slides: Nonlinear classification spiral, node, center, saddle (98.0 K, pdf, 05 Apr 2015)
Slides: Matrix Exponential, Putzer Formula, Variation Parameters (130.1 K, pdf, 03 Mar 2012)

Week 15, Apr 20 to 24

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.

Week 16, Apr 27 to 28

In-class comprehensive final exam review.

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Text: Final exam study guide (8.3 K, txt, 06 Jan 2015)

Final Exam Period, Apr 29 to May 6

Final exam week. Extra credit due dates on Friday May 1. Final exam at 7:15am in WEB 1230 on Wednesday May 6, 2015.

http://www.math.utah.edu/~gustafso/s2015/2250/lectureslides2250/references/
Text: Final exam study guide (8.3 K, txt, 06 Jan 2015)

Main References S2015

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