Math 224-01: Differential Equations: Reading Homework 3.4

  1. Undriven Constant Coefficient Linear ODEs, II : is it odd that we haven't specified ``second-order ODEs'' here? what equations do we obtain solutions for in this section?
    1. Complex-Valued Functions and Solutions : what questions do we think about here? what are their answers? how is D[y] defined for complex-valued functions?
      1. Point : how is linearity important when considering polynomial operators?
      2. Point : how is the exponential function e(alpha + ibeta)t written using Euler's formula?
      3. Point : what's D[ealpha + ibeta t]? what does this mean about P(D)[ert] for complex values of r?
    2. Finding Solution Formulas : how do we conclude that u(t) and v(t), the real and imaginary parts of a solution e(alpha+i beta)t to P(D)[y] = 0, are themselves solutions to P(D)[y] = 0?
      1. Point : what are the solutions to P(D)[y] = y'' + a y' + b y = 0 for any a and b?

Math 224-01: Differential Equations: Reading Homework 3.4
Last Modified: Thu Mar 2 23:24:40 2000
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