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Readings are sections in Zill //First Course in Differential Equations 
with Modeling Applications//, 9th edition. If you use another text,
look up the lecture topic in the table of contents or index. 

Lectures without a specified topic are buffers for the inevitable lag. 
Homeworks in parentheses will not be collected or graded; however you 
should do them as preparation for the exams.

Please refer to [[gibson:teaching:fall-2011:math527:policies]] for 
specifics on handing in homeworks, exam procedures, etc. 

<code>
lecture topic                              reading   homework    

INTRO
M  8/29 classes cancelled, hurricane irene                    
W  8/31 what is a differential equation?   (1, skim)

FIRST ORDER SYSTEMS
F  9/02 definitions, separable eqns        2.2      HW1 due
W  9/07 1st order linear (var of params)   2.3
F  9/09 exact equations                    2.4      HW2 due
M  9/12 substitutions                      2.5
W  9/14 examples                           3.1-2
F  9/16 EXAM #1                                     (HW3)

HIGHER-ORDER SYSTEMS
M  9/19 motivation, terminology            4.1
W  9/21 y=exp(lambda t), Euler's formula   4.3
F  9/23 under, critical, and overdamping   5.1      HW4 due
M  9/26 
W  9/28 judicious guessing (undet. coeff)  4.4
F  9/30                                             HW5 due
M 10/03 variation of parameters            4.6
W 10/05 
F 10/07 EXAM #2                                     (HW6)

LAPLACE TRANSFORMS
T 10/11 definition, inverse transforms     7.1-2
W 10/12 transform of derivative, IVPs      7.2
F 10/14 s-translation                      7.3.1    HW7 due
M 10/17 t-translation (Heaviside func)     7.3.2
W 10/19 transforms: deriv, convolution     7.4.1-2
F 10/21 transforms: periodic funcs         7.4.3    HW8 due
M 10/24 Dirac delta function               7.5
W 10/26 
F 10/28 EXAM #3                                     (HW9)

SERIES SOLUTIONS
M 10/31 power series review                6.1.1
W 11/02 solutions about ordinary points    6.1.2
F 11/04 regions of convergence                      
M 11/07 solutions about singular points    6.2
W 11/09 bessel functions                   6.3.1    HW10 due (Thu 11/10 in recitation)
F 11/11 legendre polynomials               6.3.2    

SYSTEMS OF EQUATIONS
M 11/14 matrices and vectors               AppII.1
W 11/16 Ax=b, determinants                 
F 11/18 ODEs in matrix form, eigenvalues   8.1      HW11 due
M 11/21 real eigenvalues, distinct         8.2.1
W 11/23 real eigenvalues, repeated         8.2.2    HW12 due
(thanksgiving)
M 11/28 complex eigenvalues                8.2.3    
W 11/30 
F 12/02 EXAM #4                                     (HW13)

NUMERICAL METHODS
M 12/05 Euler method                       9.1
W 12/07 Runge-Kutta                        9.2
F 12/09 Lorenz system                               HW14 due
</code>
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