Math 311 - Q - Intro to Differential Equations

Tues/Thurs 12:30PM - 1:45PM, Dooly Memorial 316

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Office Hours: Wednesdays, 1-3pm

Course Description: We will study the theory and applications of ordinary differential equations (ODE): first-order ODE, linear ODE, obtaining solutions of ODE as series, the Laplace transform.
Text: Differential Equations and Boundary Value Problems, 4th Edition, Edwards and Penney
Content: We will cover sections 1.1-1.5, 2.1-2.3, much of chapters 3 and 7, parts of 4,5,6.

Exams: There will be two exams and a final.
      Exam1. TUES Sept 16    Exam2. TUES Oct 14    Exam 3. THURS Nov 13 (Set by registrar)
You will be responsible for the material covered in the lectures, the readings, and the homework.
* Dates of Exams are subject to change.

Homeworks: Homework will be assigned below. It will be due at the beginning of class on Thursdays. No late homework will be accepted. Your lowest homework grade will be dropped.

Grades: Overall Score = Hwk 25% + Exam1 25% + Exam2 25% + Exam3 25%
Letter grades will approximately follow standard cutoffs A>90, B>80, C>70.

Academic Honesty: Each student will uphold the University of Miami Honor Code.

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Homeworks and Notes

Math Lab Schedule (Free drop-in tutoring)

dfield and pplane - Java applets for direction fields and phase portraits
    Example outputs as pdfs: y'=x^2-y^2 ; y'=x^2-y-2 ; y'=y-sin(x) ; x' = t * sin(x)

Due Date	Readings	Problems
Aug 28	1.1	1.1: # 3, 9, 15, 19, 22, 47 (scans of problems - pdf)
Sept 4	1.2-1.4	1.2: # 9, 13, 19, 25; 1.3: # 3 (y'=y-sin(x), see also this), 9 (y'=x^2-y-2), 21, 27 1.4: # 1, 13, 23, 64; (scans of problems - pdf. These two might be difficult to read. 1.4.13: y^3 dy/dx=(y^4+1)cos x, 1.4.23: dy/dx + 1 = 2y, y(1)=1 )
Sept 11	1.5, 1.6	1.5: # 11, 21 1.6: # 11, 23, 35, 49, 66, 67 More to come...
Sept 18	2.1, 2.2	EXAM1 Tues Sept 16
Sept 25
Oct 2
Oct 9
Oct 16		EXAM2 TUES Oct 14 FALL RECESS Thurs Oct 16
Oct 23
Oct 30
Nov 6
Nov 13		REVIEW Tues Nov 11 EXAM3 THURS Nov 13
Nov 20
Nov 27		THANKSGIVING RECESS
Dec 4
Dec 9		Final?

Slope Fields

• dfield from above works well
• A basic non-Java slope field
• Mathematica Demonstration Slope Field, not as flexible, but plots some solution curves.
• Wind Map of the US (More of a stream plot)

Mathematica Demonstrations for Visualizing Differential Equations

• Mass-Spring, Beats
  • FreeVibrationsOfASpringMassDamperSystem
  • BeatFrequencyOfSoundWaves
  • ComplexAdditionOfHarmonicMotionsAndThePhenomenonOfBeats
  • ForcedOscillatorWithDamping
• Linear Systems
  • TwoDimensionalLinearSystems
  • VisualizingTheSolutionOfTwoLinearDifferentialEquations
  • PhasePortraitAndFieldDirectionsOfTwoDimensionalLinearSystems
  • EquationTrekker
  • FixedPointOfA2x2LinearSystemOfODEs
• Predator-Prey
  • PredatorPreyModel
  • PredatorPreyDynamicsWithTypeTwoFunctionalResponse

Chaotic Systems

• Duffing
  • http://www.math.udel.edu/~hsiao/m302/JavaTools/osduffng.html
• Lorenz
  • http://demonstrations.wolfram.com/LorenzAttractor/

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