Mathematics 212
Differential Equations
Chapter 5: Second-Order Linear Equations I
Class Notes
5.1 Introduction: Modeling Vibrations (
pdf
)
5.2 State Variables and Numerical Approximation (
pdf
)
5.3 Operators and Linearity (
pdf
)
5.4 Solutions and Linear Independence (
pdf
)
Biography and
sketch
of
Josef Hoëné de Wronski
(1778-1853)
Wikipedia entry for
Josef Hoëné de Wronski
(1778-1853)
5.5 Variation of Constants and Green's Functions (
pdf
)
Biography of
George Green
(1793-1841) and his
commemorative plaque
on the floor of Westminster Abbey.
Wikipedia entry for
George Green
(1793-1841)
5.6 Power Series Solutions (
pdf
)
5.7 Polynomial Solutions (
pdf
)
Homework Exercises from DE
5.1 -- 1, 3, 5, 7, 11, 13
5.2 -- 1, 3, 7, 11, 12, 13
5.3 -- 3, 5, 7, 11, 15, 19
5.4 -- 1, 5, 11, 15, 19, 23, 24, 25
5.5 -- 3, 5, 9, 14
5.6 -- 3, 5, 7, 13, 19
5.7 -- 1, 2, 3, 4, 5
Homework Exercises from AMC for DE
6.1 -- 1, 2, 3, 4, 5, 6 (Plotting Solutions)
6.2 -- 1, 2, 3, 4, 5 (Simple Pendulum)
6.3 -- 1, 2, 3, 4, 5 (Greens Function)
6.4 -- 3, 6, 8, 9, 10, 11, 12 (Beats, Resonance, Frequency Response)
6.6 -- 1, 3, 5, 7, 9, 11, 13, 15, 16, 17 (Series Solutions)
cparrish@sewanee.edu