Differential Equations SYLLABUS - updated 19.Sept.2002 
    TESC
    PS Home
    Logistics
    Content
    return to DiffEq
    Communication
    2002-2003
     .
    Differential Equations meets Tuesdays 1 - 6:30 p.m. Room 2242, Lab II. This includes seminar.

    Texts: Differential Equations, SECOND edition by Blanchard, Devaney, Hall - bring to every class; get the correct edition!

    AEM = Advanced Engineering Mathematics by Kreyszig

    animated exercises (ae) available online
    Wk Date Read Before Class Homeworkdue the following week  (AEM)
    Kreyszig    		 Seminar
    1 Oct. 1 1.1 Intro to program, Intro. to DEs, modeling, Web-X 1.1 #1,3,4,8,9,10a,b,(11),13,(15) 
    Start Lab 1.4
    Make plane reservations for break    		 1.1 None
    2 8 1.2 Separation of Variables (Analytic Technique)
    1.3 Slope Fields (Geometrical/Qualitative Tech.)
    1.4 Euler's Method (Numerical Technique)    		 1.2 p. 33 #1, 3, 7, 9, 15, 25, (36)
    1.3 p. 48 #1, 7, 9, 15, 11, 13, 17, (19, 21)
    1.4 p. 63 #1, 3, 13, (15)
     Lab 1.4 #1, team    		 1.3
    1.7
    1.2    		 Aleph

    1-63
    3 15 1.5 Existence and Uniqueness Theorems
    1.6 Equilibria and the Phase Line    		 1.5 p. 73 #1, 3, 5, 7, 13, (18)
    1.6 p. 91 #1, 3, 5, 7, 13, 15, 17, 29,31,35,(46)
    Finish Lab 1.4 #2,3 as homework. Typed!    		 1.9 65-117
    4 22 App. A First-Order Linear Equations Revisited
    1.8 Linear Differential Equations, Integrating Factor
    1.9 Changing variables    		  App.A p. 708 #1, 3, 5, 7, 9 + animated exercise
       (25)
    1.8 p.122 # 1,3,9,13,15,17, 25
    1.9 p.134 # 1, 3, 7, 9, 11, 19
    Start Lab 1.5 (due 5.Nov.)    		   119 - 169
    5 29  1.7 Bifurcations & 1st quiz (ONLY announced quiz)  1.7 p. 107 #1, 3, 9, 15, 21
    Finish Lab 1.5    		   to 231
    6 Nov 5 2.1 Modeling via Systems: mass-on-spring; prey
    2.2 GEOMETRY of Systems; vector fields    		 p. 19 #18, 19. 
    2.1 p. 160 #1-4, 9, 10, 15, (20)
    2.2 p. 178 #1, 3, 9, 11, 13, 15 + a.e.    		 2.5
    8.4    		 Chaos

    1-31
    7 12 2.2 More on Geometry of Systems & vector fields
    2.3 Analytic Methods for Special Systems    		 2.2 p.178 # 17, 19, 21, 27
    p. 163 #19. 
    2.3 p. 192 #1, 3, 5, 11, 15, 17
    Start Lab 2.3    		   35 - 56
    8 19 2.4 Euler's Method for Systems
    2.5 Lorenz Equations    		 2.4 p. 205 possibly # 1, 3, 5, 7, 9, 11 
    2.5 possibly 1, 3, 4, 5
    Finish Lab 2.3    		   57 - 80
    9 Dec 3 LINEAR SYSTEMS
    3.1 Linear Systems: Properties and Linearity Princip.
    3.2 Straight-Line Solutions
    3.3. Phase Planes for Lin Sys with Real Eiengvalues    		 3.1 p. 244 #5, 9, 17, 25, 27, 29, (35)
    3.2 p. 263 #1-7 odd, 11, 13, (20), 21, 23
    3.3 p.279 #1-11 odd, 15, 19, (21)
    Start Lab 2.4    		 3.0
    3.1
    3.2
    3.3    		 81 - 118
    10 10 EXAM - HW, Lectures thru 3.3; presentations Bring: portfolio; book; notebook; journal None
      20 Evaluation conferences: stay through Dec. 20th ! Bring faculty evaluation to conference. Self-eval. due Dec. 17
    Winter assignments may change before winter qtr. (draft 19.Sept.2002)
    1 Jan 7 Appendix B: Complex Numbers 
    3.4 Complex Eigenvalues 
    3.5 Special Cases: Repeated and Zero Eigenvalues    		 3.4 p. 296 #1-15 odd, 23, 25
    3.5 p. 313 #1-7 odd, 11, 21, 23
    Finish Lab 2.4 (due 14.Jan.)    		 12.1
    12.2    		 119 - 181
    2 14 3.6 Second-Order Linear Equations
    3.7 The Trace-Determinant Plane    		 3.6 p. 328 #1,3, 7, 9, 13, 15, 17, 21, 23, (38)
    3.7 p. 344 #2, 3, 5, 9, 11, 14
    Start Lab 3.2    		   189 - 211
    3 21 4.1 Forced Harmonic Oscillators
    4.2 Sinusoidal Forcing    		  4.1 p. 381 #1-13 odd, 20, 21, 23, (25) 
    4.2 p. 394 #1, 5, 9, 11, 13, 16-19, (23)
    Finish Lab 3.2     		 2.9 213 - 240
    4 28 4.3 Undamped Forcing and Resonance
    4.4 Amplitude and Phase of the Steady State
    4.5 Tacoma Narrows Bridge    		 4.3 p. 406 #1, 3, 9, 20-23 (26)
    4.4 p.418  # 1, 2, 3, 5, 9, 11, (26)
    4.5 p.421 # 1, 3, 5, 7
    Start Lab 4.3    		 2.11
    2.12    		 241 - 270
    5 Feb 4 NONLINEAR SYSTEMS
    5.1 Equilibrium Point Analysis
    5.2 QUALITATIVE ANALYSIS    		 5.1 p. 452 #1, 3, 7, 9, 11, 17, 23, 25
    5.2 p. 467 #1-11 odd
    Finish Lab 4.3    		 3.4 273 - 317 
    6 11 5.3 Hamiltonian Systems
    5.4 Dissipative Systems    		 5.3 p.483 # 1, 5, 7, 9, 11, 15
    5.4 p.504 ! 1, 5, 7, 9, 13, 19, 21
    Start Lab 5.2    		   Math&Humor

    Ch.1-2
    7 18 3.8 Linear Systems in 3-D
    5.5 Nonlinear Systems in 3-D
    5.6 Periodic Forcing of Nonlinear Systems ,Chaos    		 3.8 p.357 # 1, 3, 5, 7
    5.5 p.516 # 1, 3, 5
    5.6 p.531 # 5, 7, 9
    Finish Lab 5.2    		 3.5
    3.6    		 Chap. 3 - 4
    8 25 6.1 - 6.3 Laplace Transforms 6.1 p. 553 #1, 3, 7, 9, 15, 17
    6.2 p. 561 #1-7 odd,  9, 11, 17
    6.3 p. 575 #1, 3, 15, 17, 27, 29, 31     		 5.1 - 5.2 Chap. 5 - 6
    9 Mar 4 6.4 - 6.6 Delta Functions and Qualitative Theory of Laplace Transforms (& Kreyszig 4.1 - 4.2) 6.4 p.584 #1, 3, 5
    6.5 p. 592 # 1, 3, 5, 7, 9
    6.6 p. 600 # 1, 3, 5, 7, 9
    Start Lab 6.1    		 5.3 - 5.9 summative seminar ?
    10 11 EXAM      
    1 Apr 1 Kreyszig 10.1 - 10.5 Fourier Analysis ( ~ review ) Kreyszig is our only text for spring.
    Finish Lab 6.1 (due 8.April)    		    
    2 8 10.6-10.11 Forced Oscillations; Fourier Transforms   B6.1  
    3 15 11.1 - 11.4 PARTIAL DIFFERENTIAL EQUATIONS      
    4 22 11.5 - 11.7 Heat & Wave Equations      
    5 29 1.8, 11.8 - 11.12 Laplace's Equation; Potential      
    6 May 6 19.1 - 19.7 Numerical Methods for PDE's      
    7 13 EXAM      

     

    Images courtesy of http://www.freeimages.co.uk/, www.animation.com, www.scienceclips.com
    Maintained by: E.J. Zita