## Differential Equations

Syllabus.

The Greek alphabet.

Homework sets distributed in class.

Worked examples distributed in class.

Summary of the course so far.

Summary of the course so far, arranged day-by-day.

Summary of assignments so far.

Sections 1.1, 1.2, and 1.4 of the text.

The "Chart Method" for certain integrals.

A summary of integration using partial fractions.

Justifying the logistic Equation.

Solving the Logistic Equation.

The Chain Rule in higher dimensions..

Proof of Clairaut's Theorem (equality of mixed partials).

Proof of the theorem on p59.

"Almost exact" equations.

The Catenary.

Summary of theory of infinite series (shorter).

Summary of theory of infinite series (longer).

The proof of the Picard theorem.

Taylor's Theorem (Lagrange form).

Solving linear inequalities.

Expanding polynomials in powers of (x-a).

An introduction to complex numbers.

Two-by-two matrices and linear equations.

Why to expect exponential solutions of second-order linear homogeneous equations with constant coefficients.

Some properties of determinants.

A summary of section 2.1.

An expansion of the calculation on p169.

A summary of section 2.5.

A proof of Lemma 2 p228.

Some elementary properties of the Laplace transform.

The Dirac delta "function".

The convolution integral.

Some facts from a linear algebra course.

Summary of secs 3.9 through 3.13.