Math 307: what we've covered so far
- Monday, 27 March. Went over syllabus, started Section 2.1,
linear first order differential equations.
- Wednesday, 29 March. Covered Sections 2.1 and 2.2.
Also discussed direction fields (page 6 in
the book) and integral curves (page 20).
- Friday, 31 March. Covered most of Section 2.6, qualitative
analysis of differential equations and
population growth.
- Monday, 3 April. Finished Section 2.6, discussed modeling
and differential equations (material from Sections 2.5 and 2.7).
- Wednesday, 5 April. Covered Section 3.1, Second
order linear homogeneous equations with constant
coefficients.
- Friday, 7 April. Covered Sections 3.2 and 3.3,
Superposition, the Wronskian, and general solutions to
linear equations. Started discussing complex
numbers, from the supplementary notes.
- Monday, 10 April. Continued discussing complex numbers,
and in particular polar coordinates and
Euler's formula.
- Wednesday, 12 April. Finished discussing complex numbers,
started Section 3.4, complex roots of the
characteristic equation.
- Friday, 14 April. Continued Section 3.4.
- Monday, 17 April. Finished Section 3.4.
- Wednesday, 19 April. Exam.
- Friday, 21 April: Covered Section 3.5, reduction of
order.
- Monday, 24 April: Started Section 3.6, the method
of undetermined coefficients.
- Wednesday, 26 April: Finished Section 3.6.
- Friday, 28 April: Covered Section 3.7, variation of
parameters
- Monday, 1 May: Started Section 3.8, springs.
- Wednesday, 3 May: Finished Section 3.8, started Section
3.9, driven mass-spring systems.
- Friday, 5 May: Finished Section 3.9.
- Monday, 8 May: Reviewed Chapter 3.
- Wednesday, 10 May: Exam.
- Friday, 12 May: Started discussing polynomial
approximations to functions. (pages 1-8 of notes on
infinite series).
- Monday, 15 May: Discussed Taylor series expansions
of functions, in particular the series for
ex and sin(x).
- Wednesday, 17 May: More on Taylor series: The
geometric series, convergence.
- Friday, 19 May: More on Taylor series:
substitution, log, arctan, binomial series.
- Monday, 22 May: Discussed Section 5.1: radius of
convergence, reindexing sums.
- Wednesday, 24 May: Discussed Section 5.2, solving
differential equations with power series.
- Friday, 26 May: Continued Section 5.2.
- Wednesday, 31 May: Discussed Section 5.3, more on
power series solutions.
Questions or comments? E-mail me at palmieri@math.washington.edu.
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