New PDF release: Boolean algebras

By Sikorski R.

ISBN-10: 3540044698

ISBN-13: 9783540044697

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3 Circle and Sphere following properties: Circle. 3) and a sphere with radius r have the Circle Sphere Diameter 2r Circumference 2pr Area pr 2 Diameter 2r Surface Area 4pr 2 Volume 4pr 3=3 The chord of a circle is a line segment intersecting two points on the circle. 4. 4 Intersecting chords. GEOMETRY, TRIGONOMETRY, AND HYPERBOLIC FUNCTIONS 25 If x ,, 2r, we obtain the approximation x% h2 2r which is useful in optics. 5. 6. 5 Right circular cylinder. 2 Right circular cone. TRIGONOMETRY Trigonometric functions are defined as ratios of the lengths of sides of a right triangle.

5 SERIES REPRESENTATIONS A polynomial may be written in a power series expansion as P(z) ¼ 1 X C m zm m¼0 where {Cm , m ¼ 0, . . ,1} are expansion coefficients of the power series. The power series is a polynomial of degree n if it has the form Pn (z) ¼ n X C m zm , Cn = 0 m¼0 Example: The second-degree polynomial P2 (z) ¼ a þ bz þ cz2 has the expansion coefficients C0 ¼ a, C1 ¼ b, C2 ¼ c, and Cj ¼ 0 for all j . 2. Taylor Series and Maclaurin Series A function f (z) of the complex variable z may be represented by the Taylor series f (z) ¼ 1 X f (m) ðaÞ ðz À aÞm m!

4. 4 Intersecting chords. GEOMETRY, TRIGONOMETRY, AND HYPERBOLIC FUNCTIONS 25 If x ,, 2r, we obtain the approximation x% h2 2r which is useful in optics. 5. 6. 5 Right circular cylinder. 2 Right circular cone. TRIGONOMETRY Trigonometric functions are defined as ratios of the lengths of sides of a right triangle. 1, we make the following definitions for an acute angle a: sine a ¼ sin a ¼ a opposite ¼ c hypotenuse c 1 ¼ a sin a b adjacent cosine a ¼ cos a ¼ ¼ c hypotenuse cosecant a ¼ csc a ¼ c 1 ¼ b cos a a opposite tangent a ¼ tan a ¼ ¼ b adjacent secant a ¼ sec a ¼ cotangent a ¼ cot a ¼ b 1 ¼ a tan a Notice that the sides a, b, c are referred to as the opposite, adjacent, and hypotenuse, respectively.

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Boolean algebras by Sikorski R.


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