This syllabus is subject to change, depending on what we actually get to cover in any given class
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topic: Modeling
readings: modeling notes
assignments: all (answers)
class 02: Thu Sep 3
topic: Modeling (continued), and Separation of Variables
readings: 1.1, 1.2
assignments: 1.1: all odd 3-21. 1.2: all odd 1-13, 19,21, all odd 25-35.
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class 03: Thu Sep 10
topic: Separation of Variables (continued)
readings: 1.2
assignments: see class 02.
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class 04: Tue Sep 15
topic: Slope Fields (including computer demostration using JOde); Euler's method; quiz on separation of variables and modeling.
readings: 1.3
assignments: all odd 1-13, 14, 15, 17. (For numerical assignments, there is a package available in the CD ROM that comes with the book. A strongly suggested alternative is the Java Applet, JOde, which runs on any Java-enabled browser, including those at the University computer labs.)
class 05: Thu Sep 17
topic: Euler's Method (over- and under-estimation using second derivatives), Existence and Uniqueness, Equilibria and Phase Line
readings: 1.4, 1.5, 1.6
assignments: 1.4: 1, 5, 7, 13, 15. 1.5: 1, 3, 5, 7, 10(optional). 1.6: 1, 3, 5, 7, 9, 11, 13, 15, 23, 25, 27, 31, 33, 37, 39, 43.
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class 06: Tue Sep 22
topic: finish Phase Line; start Bifurcations; quiz on slope fields
readings: short bifurcation notes , 1.7
assignments: 1, 3, 5, 9, 11, 17, 18.
class 07: Thu Sep 24
topic: continue Bifurcations; Linear Differential Equations, Integrating Factors
readings: 1.8, 1.9
assignments: 1.8: all odd 1-13, 21, 23. 1.9: all odd 1-11, 21, 23.
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class 08: Tue Sep 29
topic: Modeling via Systems (most of the time in class spent working with JOde demos on computer; quiz on Euler and phase lines
readings: 2.1
assignments: 1, 2, 7, 8, 9, 17, 19, 21, 23, 25, 26, 27, 29.
class 09: Thu Oct 1
topic: Equlibria; Geometry of Systems
readings: 2.2
assignments: all odd 1-27.
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class 10: Tue Oct 6
topic: Analytic Methods, Phase Plane. (Reading assignment: Euler's Method - for systems, this is entirely analogous to what we did for just one equation). Quiz on bifurcations and integrating factors
readings: 2.3, 2.4, notes on phase planes
assignments: 2.3: all odd 1-11, 19. 2.4: 1, 3, 5, 14, 15.
class 11: Thu Oct 8
topic: Linear Systems, start Matrix Exponentials
readings: 3.1, notes on matrix exponentials |
class 12: Tue Oct 13
topic: continue Matrix Exponentials
readings: see class 11
assignments: 3.1: all odd 1-9, 13, 17, 19, 21, 27, 29, 33, 35. from notes: all (answers)
class 13: Thu Oct 15
 topic: exam 1 Through 2.4 included
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class 14: Tue Oct 20
topic: Work-out of exam problems. Matrix Exponentials (continued)
readings: see class 12
assignments: see class 12
class 15: Thu Oct 22
topic: Matrix Exponentials (continued).
readings: 3.2
assignments: all odd 1-19
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class 16: Tue Oct 27
topic: . Straight-Line Solutions. Phase Plane: Real Eigenvalues
readings: 3.3
assignments: all odd 1-15.
class 17: Thu Oct 29
topic: Quiz on Matrix Exponentials. Phase plane: Complex Eigenvalues. Repeated and Zero Eigenvalues.
readings: 3.4
assignments: all odd 1-15, 19, 21, 23.
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class 18: Tue Nov 3
topic: continue Repeated and Zero Eigenvalues; start Trace-Determinant Plane
readings: 3.5
assignments: all odd 1-17.
ALSO: project due today (phase planes for species competition)
class 19: Thu Nov 5
topic: Quiz on general solutions of linear systems, and phase plane pictures. Continue Trace-Determinant Plane (emphasizing one-parameter families)
readings: 3.7
assignments: parts "c" of: 3, 7, 11, 13.
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class 20: Tue Nov 10
topic: Second-Order Linear
readings: 3.6
assignments: all odd 13-29; 36(a,b).
class 21: Thu Nov 12
topic: Another quiz on general solutions of linear systems, and phase plane pictures. Continue 2nd order Linear. 3-Dim Linear
readings: 3.8
assignments: 4, 5, 6, 7. |
class 22: Tue Nov 17
topic: Forced Harmonic Oscillators, Sinusoidal Forcing
readings: 4.1, 4.2
assignments: 4.1: all odd 1-41. 4.2: odd 1-13, 17, 27.
class 23: Thu Nov 19
topic: Continue Sinusoidal Forcing. Steady State
readings: 4.4
assignments: Write the steady-state solution of the odd problems 1-9 of section 4.2 in the form A cos(wt+f). Answers here done by a student in a previous semester (note added 03Dec09: error in Problem 7; the '2' in the second derivative should be a '4', obviously; see Maple answers), and here done using Maple. (Note: in the Maple script, I did the problems directly, using the method in class: fit an expression such as "Kexp(2it)".)
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class 24: Tue Nov 24
topic: Continue Steady State. Resonance (probably not covering “beats” due to lack of time)
readings: 4.3
assignments: all odd 1-13 (not 15,17 because did not cover “beats”)
ENJOY YOUR THANKSGIVING BREAK!
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class 25: Tue Dec 1
topic: Equilibria, Linearization
readings: 5.1
assignments: all odd 1-17, except 5.
class 26: Thu Dec 3
topic: exam 2, covering chapters 3 and 4
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class 27: Tue Dec 8
topic: Discrete Systems
readings: 8.1
assignments: all odd 1-9, 15, 19, 23, 27, 31. last computer assignment (forced oscillators)
class 28: Thu Dec 10
topic: Fixed/Periodic points. Quiz on linearization.
readings: 8.2
assignments: 1, 7, 9, 13, 15.
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according to:
http://finalexams.rutgers.edu/index.php?level=Undergraduate&campus=1&semester_month=9&subject=640&course=252®id=26163&Search=Search
the exam is:
Wednesday 23-Dec 12:00-3:00 PM
(same room where class takes place)
(SUBJECT TO CHANGE IF UNIVERSITY RE-SCHEDULES)
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