Math 307: what we've covered so far
- Wednesday, 3 January: Introduction, basics about
differential equations.
- Friday, 5 January: Covered separable
equations (Section 2.2) and started discussing
autonomous equations (Section 2.5).
- Monday, 8 January: Covered linear
equations (Section 2.1) and continued with
autonomous equations.
- Wednesday, 10 January: Finished autonomous equations,
briefly discussed Euler's method (Section 2.7).
- Friday, 12 January: Covered second order linear
homogeneous equations with constant coefficients
(Section 3.1).
- Wednesday, 17 January: Covered generalities about
linear homogeneous equations, the Wronskian
(Sections 3.2 and 3.3).
- Friday, 19 January: Started discussing complex
numbers, Euler's formula.
- Monday, 22 January: Applications of Euler's formula.
- Wednesday, 24 January: exam.
- Friday, 26 January: Discussed complex roots of the
characteristic equation (Section 3.4).
- Monday, 29 January: Covered repeated roots of the
characteristic equation and reduction of order
(Section 3.5), and started discussing nonhomogeneous
equations (Section 3.6).
- Wednesday, 31 January: Continued with nonhomogeneous
equations: the method of undetermined
coefficients (Section 3.6).
- Friday, 2 February: Finished discussing undetermined
coefficients, started on variation of
parameters (Section 3.7).
- Monday, 5 February: finished variation of parameters,
started discussing mass-spring systems
(Section 3.8).
- Wednesday, 7 February: Continued with mass-spring systems,
started talking about the effects of external
forces (Sections 3.8 and 3.9).
- Friday, 9 February: continued discussing forced mechanical
vibrations, especially beats and
resonance (Section 3.9).
- Monday, 12 February: Reviewed Chapter 3.
- Wednesday, 14 February: exam.
- Friday, 16 February: started discussing Taylor
polynomials.
- Monday, 19 February: no class (President's Day).
- Wednesday, 21 February: more on Taylor polynomials, as well
as power series and convergence.
- Friday, 23 February: Taylor series in general,
ln(x), geometric series.
- Monday, 26 February: substitution, differentiation,
and integration of power series (notes),
convergence and the ratio test (Section
5.1).
- Wednesday, 28 February: radius of
convergence and reindexing sums
(Section 5.1).
- Friday, 2 March: started discussing how to solve a
differential equation with power series (Section 5.1).
- Monday, 5 March: another example of solving a
differential equation with a power series (Airy's
equation, Section 5.2).
- Wednesday, 7 March: more on power series solutions
(Sections 5.2 and 5.3).
- Friday, 9 March: a lower bound on the radius of
convergence for power series solutions (Section 5.3).
Questions or comments? E-mail me at palmieri@math.washington.edu.
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Last modified: Mon Apr 29 12:11:05 PDT 2002