 |
Section 1-4: General remarks on solutions, families of curves,
orthogonal trajectories |
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Section 5: Motion problems |
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Section 6: The brachistochrone, treated without calculus of
variations |
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Section 7-11: Homogenous and exact equations, integrating
factors, linear first order equations, reduction of order |
|
Section 12: The catenary, assign 13 as reading (review of
RLC circuits) |
|
Section 14-16: Second order linear equations, homogeneous
equations, the use of a known solution to find another |
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Section 17: Homogeneous equations with constant coefficients |
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Section 18: The method of undetermined coefficients |
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Section 19: The method of variation of parameters |
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Section 20: Vibrations in mechanical and electrical systems |
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Section 21: Newton's law of gravitation and the motion of
the planets |
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Section 22: Higher order linear equations, coupled harmonic
oscillators |
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Section 23: Operators methods for finding particular
solutions |
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Section 24-25: Oscillations and the Sturm separation
theorem, Sturm comparison theorem |
|
Section 27-31: Review of power series, series solutions of
first order equations, second order equations, ordinary points, regular
singular points, Gauss's hypergeometric equation. |
