This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications.

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The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.

Syllabus

WEEK 1: Euler Equations

WEEK 2: Power Series

WEEK 3: Solutions about ordinary points

WEEK 4: Frobenius Theorem

WEEK 5: Finding a Second Solution

WEEK 6: Bessel Functions

WEEK 7: Legendre Polynomials

Differential Equations

Perron-Frobenius Theorem

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