Math 135A


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Course: Math 135A, Ordinary Differential Equations

Text: G. Simmons, Differential Equations with Applications and Historical Notes, 2nd Edition, McGraw Hill

Schedule of Lectures:

Section 1-4: General remarks on solutions, families of curves, orthogonal trajectories

Section 5: Motion problems

Section 6: The brachistochrone, treated without calculus of variations

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

Section 17: Homogeneous equations with constant coefficients

Section 18: The method  of undetermined coefficients

Section 19: The method of variation of parameters

Section 20: Vibrations in mechanical and electrical systems

Section 21: Newton's law of gravitation and the motion of the planets

Section 22: Higher order linear equations, coupled harmonic oscillators

Section 23: Operators methods for finding particular solutions

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.