Spring 2012 Reading Assignments 2250-1 7:30am 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: December 10, 2011, 12:10 MST. Today: November 29, 2024, 11:54 MST.

Chapter 1: First Order DE

Week 1, Jan 9 to 13

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/s2012/2250
Syllabus: 2250 7:30 S2012 (238.8 K, pdf, 26 Dec 2011)
How to improve written work (26.6 K, pdf, 09 Dec 2011)
Gradesheet: 2250 7:30 S2012 (134.1 K, pdf, 26 Dec 2011)

http://www.math.utah.edu/~gustafso/s2012/2250/lectureslides2250/firstorderDE/
Slides: Method of quadrature (247.9 K, pdf, 11 Dec 2011)
Exercise 1.3-8 template (102.2 K, jpg, 29 Aug 2008)
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)

Week 2, Jan 16 to 20

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/s2012/2250/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 (127.3 K, pdf, 03 Mar 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/s2012/2250/lectureslides2250/references/
Maple: lab 1. Quadratics, plots, derivatives, Jacobian (76.7 K, pdf, 09 Dec 2011)
Maple: lab 2. Swamp cooler [option 1] (135.7 K, pdf, 09 Dec 2011)
Maple: lab 2. Freezing pipes [option 2] (87.6 K, pdf, 09 Dec 2011)
Using maple at home (6.8 K, txt, 28 Dec 2011)

Week 3, Jan 23 to 27

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/s2012/2250/lectureslides2250/firstorderDE/
Slides: Earth to the moon (127.3 K, pdf, 03 Mar 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/s2012/2250/lectureslides2250/references/
Maple: lab 3. Numerical DE (60.0 K, pdf, 09 Dec 2011)
Maple: lab 4. Numerical DE (56.4 K, pdf, 09 Dec 2011)
Maple: code for maple labs 3 and 4 (5.1 K, txt, 10 Dec 2011)
Text: How to use maple at home (6.8 K, txt, 28 Dec 2011)
Special problems for Maple lab 3 and 4, statements (109.3 K, pdf, 10 Dec 2011)
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 (35.5 K, pdf, 09 Dec 2011)
Notes on numerical DE report for Ch2 Ex 12 (51.8 K, pdf, 09 Dec 2011)
Notes on numerical DE report for Ch2 Ex 4 (35.0 K, pdf, 09 Dec 2011)
Notes on numerical DE report for Ch2 Ex 6 (47.9 K, pdf, 09 Dec 2011)

Week 4, Jan 30 to Feb 3

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/s2012/2250/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 (233.6 K, pdf, 03 Mar 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 (117.8 K, pdf, 03 Mar 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/s2012/2250/lectureslides2250/references/
Maple: lab 5. Linear algebra (71.4 K, pdf, 09 Dec 2011)

Week 5, Feb 6 to 10

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

http://www.math.utah.edu/~gustafso/s2012/2250/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (4.8 K, txt, 03 Oct 2010)
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 (154.1 K, pdf, 03 Mar 2012)

Week 6, Feb 13 to 17

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

http://www.math.utah.edu/~gustafso/s2012/2250/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 (154.1 K, pdf, 03 Mar 2012)
Slides: Vector models, vector spaces (144.1 K, pdf, 03 Mar 2012)
Slides: Vector space, subspace, independence (182.3 K, pdf, 03 Mar 2012)

Week 7, Feb 20 to 24

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/s2012/2250/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 (154.1 K, pdf, 03 Mar 2012)
Text: History of telecom companies (1.4 K, txt, 30 Dec 2009)

Week 8, Feb 27 to Mar 2

Read sections 5.1,5.2,5.3,5.4. Linear constant DE, superposition, atoms, vibrations, steady-states, observables

http://www.math.utah.edu/~gustafso/s2012/2250/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 (168.3 K, pdf, 03 Mar 2012)
Slides: Atoms, Euler's theorem, examples (130.3 K, pdf, 03 Mar 2012)
Slides: Picard, linear nth order DE, superposition (181.5 K, pdf, 03 Mar 2012)

http://www.math.utah.edu/~gustafso/s2012/2250/lectureslides2250/references/
Text: FAQ for maple lab 6, S2012 (1.9 K, txt, 23 Nov 2010)
Maple: lab 6. Spring mass systems. (16.7 K, pdf, 09 Dec 2011)

Week 9, Mar 5 to 9

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/s2012/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (350.5 K, pdf, 06 Mar 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/s2012/2250/lectureslides2250/references/
Maple: Lab 7. Laplace applications (60.6 K, pdf, 09 Dec 2011)

Week 10, Mar 19 to 23

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/s2012/2250/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (350.5 K, pdf, 06 Mar 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 (108.1 K, pdf, 04 Mar 2012)

http://www.math.utah.edu/~gustafso/s2012/2250/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/s2012/2250/lectureslides2250/references/
Text: Laplace theory problem notes F2008 (8.9 K, txt, 18 Nov 2010)
Text: Final exam study guide (8.2 K, txt, 11 Dec 2011)
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 26 to 30

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/s2012/2250/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/s2012/2250/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 (1.4 K, txt, 30 Dec 2009)
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 2 to 6

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/s2012/2250/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/s2012/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 11 Dec 2011)
Maple: Lab 8. Optional. Earthquakes (18.3 K, pdf, 09 Dec 2011)
Maple: Lab 9. Optional. Tacoma narrows (17.4 K, pdf, 09 Dec 2011)
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 9 to 13

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/s2012/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 11 Dec 2011)
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 16 to 20

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/s2012/2250/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/s2012/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 11 Dec 2011)

Week 15, Apr 23,24,25

Read section 9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs.

http://www.math.utah.edu/~gustafso/s2012/2250/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/s2012/2250/lectureslides2250/references/
Text: Final exam study guide (8.2 K, txt, 11 Dec 2011)

Main References S2012

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