Differential Equations

Syllabus.
The Greek alphabet.
Homework sets distributed in class.
Worked examples distributed in class.
Summary of the course so far.
Summary of assignments so far.
The "Chart Method" for certain integrals.
A summary of integration using partial fractions.
Solving the Logistic Equation.
The Chain Rule in higher dimensions..
Proof of one direction in the theorem on p59.
The Catenary.
Summary of theory of infinite series (shorter).
Summary of theory of infinite series (longer).
An elementary computation similar to the Picard method.
The proof of the Picard theorem.
Taylor's Theorem (Lagrange form).
Expanding polynomials in powers of (x-a).
Equality of mixed partials.
An introduction to complex numbers.
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.
The Dirac delta "function".
The convolution integral.
Some facts from a linear algebra course.
Summary of secs 3.9 through 3.13.