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Algebraic Curves of the Second Order in the Plane and in Space.

Ellipse, hyperbola, parabola. Director property of ellipse and hyperbola.

The equation of an ellipse, hyperbola, and parabola in the polar coordinate system.

General equation of a curve of the second order. Canonical equation of a curve of the second order.

Reducing the quadratic form to canonical form.

Quadratic Forms. Matrix of a Quadratic Form. Positively Definite Quadratic Forms, Sylvester's Criterion.

Tables and Formulas

Derivative Table.

Table of Derivatives of Composite Functions.

Table of Higher Order Derivatives.

Table of Integrals

Taylor Series

Comparison of functions O(f) and o(f).