Spring 2010 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: January 17, 2010, 14:26 MST. Today: April 18, 2024, 18:30 MDT.

Chapter 1: First Order DE

Week 1, Jan 11 to 15

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/s2010/
7:30 Syllabus S2010 (150.5 K, pdf, 11 Jan 2010)
How to improve written work (41.5 K, pdf, 01 Jan 2010)
7:30 Gradesheet S2010 (80.3 K, pdf, 03 Jan 2010)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/firstorderDE/
Slides: Method of quadrature (125.8 K, pdf, 26 Aug 2008)
Exercise 1.3-8 template (102.2 K, jpg, 29 Aug 2008)
Slides: Partial fraction theory (121.5 K, pdf, 30 Aug 2009)
Slides: Picard, Peano, direction fields (247.3 K, pdf, 26 Jul 2009)
Slides: Separable DE method, equilibrium solutions (110.2 K, pdf, 23 Jan 2010)

Week 2, Jan 19 to 22

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/s2010/lectureslides2250/firstorderDE/
Slides: Autonomous DE (69.9 K, pdf, 03 Sep 2009)
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 (99.4 K, pdf, 20 Jan 2008)
Slides: Earth to the moon (91.9 K, pdf, 27 Jan 2010)
Slides: Applications of linear DE (374.2 K, pdf, 28 Jul 2009)
Slides: Partial fraction theory (121.5 K, pdf, 30 Aug 2009)
Slides: Brine tanks (62.9 K, pdf, 30 Nov 2009)
Slides: Home heating (73.8 K, pdf, 30 Nov 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Maple lab 1. Quadratics, plots, derivatives, Jacobian (112.5 K, pdf, 01 Jan 2010)
Maple lab 2. Swamp cooler [option 1] (159.0 K, pdf, 01 Jan 2010)
Maple lab 2. Freezing pipes [option 2] (112.1 K, pdf, 01 Jan 2010)
Using maple at home (4.0 K, txt, 06 Jan 2010)

Week 3, Jan 25 to 29

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/s2010/lectureslides2250/firstorderDE/
Slides: Earth to the moon (91.9 K, pdf, 27 Jan 2010)
Slides: Newton friction models (109.3 K, pdf, 29 Aug 2009)
Slides: Numerical methods manuscript (112.1 K, pdf, 03 Sep 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Maple lab 3. Numerical DE (82.5 K, pdf, 01 Jan 2010)
Maple lab 4. Numerical DE (78.9 K, pdf, 01 Jan 2010)
Maple code for maple labs 3 and 4 (5.1 K, txt, 03 Jan 2009)
How to use maple at home (4.0 K, txt, 06 Jan 2010)
Maple lab 3, problem 1 solution (184.6 K, jpg, 08 Feb 2008)
Notes on numerical DE report for Ch2 Ex 10 (49.5 K, pdf, 01 Jan 2010)
Notes on numerical DE report for Ch2 Ex 12 (64.4 K, pdf, 01 Jan 2010)
Notes on numerical DE report for Ch2 Ex 4 (49.5 K, pdf, 01 Jan 2010)
Notes on numerical DE report for Ch2 Ex 6 (65.9 K, pdf, 01 Jan 2010)

Week 4, Feb 1 to 5

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/s2010/lectureslides2250/linearalgebra/
Slides: Elementary matrix theorems (114.4 K, pdf, 03 Oct 2009)
Beamer slides: 3 possibilities with symbol k (60.0 K, pdf, 31 Jan 2010)
Slides: Three possibilities with symbol k (72.8 K, pdf, 31 Jan 2010)
Slides: Introduction to linear algebraic equations (155.6 K, pdf, 06 Aug 2009)
Slides: Infinitely many solutions case (93.8 K, pdf, 03 Oct 2009)
Slides: No solution case (58.4 K, pdf, 03 Oct 2009)
Slides: Unique solution case (86.0 K, pdf, 03 Oct 2009)
Manuscript: Linear algebraic equations (292.8 K, pdf, 01 Feb 2010)
Slides: Three possibilities with symbols, rank (100.3 K, pdf, 23 Sep 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Maple lab 5. Linear algebra (94.2 K, pdf, 01 Jan 2010)

Week 5, Feb 8 to 12

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

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/linearalgebra/
Notes on determinant problems 3.6 (4.3 K, txt, 05 Oct 2008)
Slides: Determinants 2008 (188.3 K, pdf, 26 Apr 2010)
Slides: Digital photos, Maxwell's RGB separations, visualization of matrix add (153.7 K, pdf, 16 Oct 2009)
Slides: Elementary matrix theorems (114.4 K, pdf, 03 Oct 2009)
Slides: Inverse matrix, frame sequence method (71.6 K, pdf, 02 Oct 2009)
Manuscript: Linear algebraic equations (292.8 K, pdf, 01 Feb 2010)
Slides: Matrix operations (122.5 K, pdf, 02 Oct 2009)
Slides: More on digital photos, checkerboard analogy (109.5 K, pdf, 02 Oct 2009)
Slides: Rank, nullity and elimination (111.6 K, pdf, 29 Sep 2009)

Week 6, Feb 16 to 19

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

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/linearalgebra/
Elementary matrix theorems (114.4 K, pdf, 03 Oct 2009)
Geometry of linear transformations (59.5 K, pdf, 03 Feb 2010)
Linear algebraic equations manuscript (292.8 K, pdf, 01 Feb 2010)
Matrix operations (122.5 K, pdf, 02 Oct 2009)
Rank, nullity and elimination (111.6 K, pdf, 29 Sep 2009)
Vector models, vector spaces (110.3 K, pdf, 03 Oct 2009)
Vector space, subspace, independence (132.6 K, pdf, 03 Feb 2010)

Week 7, Feb 22 to 26

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/s2010/lectureslides2250/linearalgebra/
Slides: Base atom, atom, basis for linear DE (85.4 K, pdf, 20 Oct 2009)
Slides: Elementary matrix theorem (114.4 K, pdf, 03 Oct 2009)
Manuscript: Linear algebraic equations manuscript (292.8 K, pdf, 01 Feb 2010)
Slides: Orthogonality (87.2 K, pdf, 10 Mar 2008)
Text: Lawrence Page's pagerank algorithm (0.7 K, txt, 06 Oct 2008)
Slides: Partial fraction theory (121.5 K, pdf, 30 Aug 2009)
Slides: The pivot theorem and applications (131.9 K, pdf, 02 Oct 2009)
Slides: Rank, nullity and elimination (111.6 K, pdf, 29 Sep 2009)
Text: History of telecom companies (1.4 K, txt, 30 Dec 2009)

Week 8, Mar 1 to 5

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/s2010/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 (85.4 K, pdf, 20 Oct 2009)
Slides: First and second order linear DE (72.1 K, pdf, 28 Oct 2007)
Slides: How to solve linear DE or any order (104.1 K, pdf, 18 Oct 2009)
Slides: Atoms, Euler's theorem, examples (96.6 K, pdf, 20 Oct 2009)
Slides: Picard, linear nth order DE, superposition (121.7 K, pdf, 18 Oct 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
FAQ for maple lab 6, S2010 (1.9 K, txt, 19 Jul 2009)
Maple lab 6. Spring mass systems. (22.2 K, pdf, 01 Jan 2010)

Week 9, Mar 8 to 12

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/s2010/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (350.5 K, pdf, 06 Mar 2009)
Slides: Laplace and Newton calculus. Photos of Newton and Laplace. (145.3 K, pdf, 01 Nov 2009)
Slides: Laplace examples (101.2 K, pdf, 07 Nov 2009)
Slides: Intro to Laplace theory. Assumes only calculus (109.5 K, pdf, 01 Nov 2009)
Slides: Laplace rules (112.2 K, pdf, 01 Nov 2009)
Slides: Laplace table proofs (130.3 K, pdf, 01 Nov 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Maple Lab 7. Laplace applications (85.7 K, pdf, 01 Jan 2010)

Week 10, Mar 15 to 19

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/s2010/lectureslides2250/Laplace/
Manuscript: Laplace theory 2008 (350.5 K, pdf, 06 Mar 2009)
Slides: Laplace second order systems (248.9 K, pdf, 01 Nov 2009)
Slides: Laplace resolvent method (56.4 K, pdf, 01 Nov 2009)
Slides: Piecewise functions and Laplace theory (64.7 K, pdf, 01 Nov 2009)

http://www.math.utah.edu/~gustafso/s2010/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 (109.8 K, pdf, 07 Nov 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Laplace theory problem notes F2008 (8.9 K, txt, 31 Dec 2009)
Final exam study guide (8.1 K, txt, 30 Dec 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 29,30,31 and Apr 1,2

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/s2010/lectureslides2250/linearDEhigherorder/
Slides: Electrical circuits (87.1 K, pdf, 11 Oct 2009)
Slides: Forced damped vibrations (235.0 K, pdf, 11 Oct 2009)
Slides: Forced vibrations and resonance (185.3 K, pdf, 11 Oct 2009)
Slides: Forced undamped vibrations (174.7 K, pdf, 11 Oct 2009)
Slides: Resonance and undetermined coefficients (143.3 K, pdf, 07 Nov 2009)
Slides: Unforced vibrations 2008 (620.4 K, pdf, 11 Oct 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/linearalgebra/
Manuscript: Algebraic eigenanalysis (127.8 K, pdf, 23 Nov 2009)
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 (126.8 K, pdf, 11 Apr 2010)

Week 12, Apr 5 to 9

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/s2010/lectureslides2250/systems/
Systems and brine tanks (62.9 K, pdf, 30 Nov 2009)
Systems of DE examples and theory manuscript (785.8 K, pdf, 16 Nov 2008)
Systems and home heating (73.8 K, pdf, 30 Nov 2009)
Systems eigenanalysis, 4 methods (102.8 K, pdf, 30 Nov 2009)
Systems Cayley-Hamilton Method (111.4 K, pdf, 30 Nov 2009)
Second order systems, laplace method (248.9 K, pdf, 01 Nov 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Text: Final exam study guide (8.1 K, txt, 30 Dec 2009)
Maple Lab 8. Optional. Earthquakes (23.6 K, pdf, 01 Jan 2010)
Maple Lab 9. Optional. Tacoma narrows (22.8 K, pdf, 01 Jan 2010)
Slides: Triangular systems of DE (87.4 K, pdf, 08 Apr 2008)
Slides: Laplace resolvent method (56.4 K, pdf, 01 Nov 2009)
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 12 to 16

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/s2010/lectureslides2250/references/
Text: Final exam study guide (8.1 K, txt, 30 Dec 2009)
Slides: Triangular systems of DE (87.4 K, pdf, 08 Apr 2008)
Slides: Laplace resolvent method (56.4 K, pdf, 01 Nov 2009)
Slides: Systems eigenanalysis, 4 methods (102.8 K, pdf, 30 Nov 2009)

Week 14, Apr 19 to 23

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/s2010/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/s2010/lectureslides2250/references/
Text: Final exam study guide (8.1 K, txt, 30 Dec 2009)

Week 15, Apr 26,27,28

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

http://www.math.utah.edu/~gustafso/s2010/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 (126.2 K, pdf, 30 Nov 2009)
Slides: Phase Portraits for Dynamical Systems (205.5 K, pdf, 11 Dec 2009)
Slides: Stability for Dynamical Systems (125.7 K, pdf, 30 Nov 2009)
Slides: Nonlinear classification spiral, node, center, saddle (75.3 K, pdf, 12 Dec 2009)
Slides: Matrix Exponential, Putzer Formula, Variation Parameters (85.3 K, pdf, 14 Dec 2009)

http://www.math.utah.edu/~gustafso/s2010/lectureslides2250/references/
Text: Final exam study guide (8.1 K, txt, 30 Dec 2009)

Main References S2010

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